Centre for Advanced Computational Chemistry: Centre of Excellence of the SASComenius University, Faculty of Natural Sciences Slovak Academy of Sciences, Institute of Inorganic Chemistry
The 9-th Central European Symposium on Theoretical Chemistry
BOOK OF ABSTRACTS
http://www.qch.fns.uniba.sk/cestcNový Smokovec, Slovakia, September 12-15, 2010
Bratislava 2010
ISBN 978-80-223-2907-1
Editors: Jozef Noga, Miroslav Melicherčík, Ivan Černušák
Centre for Advanced Computational Chemistry: Centre of Excellence of the SASComenius University, Faculty of Natural Sciences Slovak Academy of Sciences, Institute of Inorganic Chemistry
Organizing Committee
Jozef Noga, chairman
Ivan Černušák
Vladimír Kellö
Miroslav Urban
Advisory committee:
Stanislav Biskupič Petr ČárskyIvan Hubač
Bogumił Jeziorski Stanislaw Kucharski
Hans LischkaPeter SurjánPeter Szalay
Miroslav Urban
Centre for Advanced Computational Chemistry: Centre of Excellence of the SASComenius University, Faculty of Natural Sciences Slovak Academy of Sciences, Institute of Inorganic Chemistry
The symposium was supported by
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Contents
PLENARY LECTURES
Roman Čurík: A message to quantum chemists: What we learned about DFT by modelling electron-molecule collisions 10
Christoph Flamm: In silico Evolution of Early Metabolism 11
Thomas S. Hofer, Bernd M. Rode, Bernhard R. Randolf: Characterisation of anisotropic ion hydration via QM/MM models 12
Florent Louis, Romain Vandeputte, Sébastien Canneaux, Marc Ribaucour: Thermochemical data calculation by quantum chemistry methods: application to ten species involved in low-temperature oxidation mechanism of o-xylene 13
Miroslav Medveď, Šimon Budzák, Jozef Noga, Ivan Černušák, Denis Jacquemin, Eric A. Perpète: Study and design of nonlinear optical materials: from molecules, through oligomers to polymers 15
Matthew K. MacLeod, Josef Michl: Trying to Understand the Mysterious Fluorescence of σ Systems: Oligosilanes 16
Monika Musiał: Fock space coupled cluster theory for two-valence sectors 17
Ágnes Nagy: Pair density functional theory 18
Katarzyna Pernal: Treating static and dynamic correlation with range-separated density and density matrix functionals 20
Piotr Piecuch, Wei Li: Local correlation coupled-cluster methods exploiting cluster-inmolecule ansatz and their multi-level generalizations 21
András Stirling: Reaction mechanism from quantum chemistry: unbiased and biased simulations 23
SHORT LECTURES
Prokopis Andrikopoulos, Stepan Sklenak, Zdenek Sobalik: Periodic DFT study of N2O decomposition over Fe-ferrierite 25
Alexei V. Arbuznikov, Hilke Bahmann, Martin Kaupp: Local hybrids: conceptually simple hyper-GGA exchange-correlation functionals for the Kohn-Sham density functional calculation of a wide range of properties 27
Kiran Bhaskaran-Nair, Ondrej Demel, Jir Pittner: Multireference State-Specic Mukherjee’s Coupled Cluster Methods With Triexcitations 29
Petr Čársky: Prospects of using MP2 for electron scattering 31
Kalju Kahn, Bernard Kirtman, Jozef Noga, Seiichiro Ten-no: Anharmonic Vibrational Analysis with Traditional and Explicitly Correlated Coupled Cluster Methods 32
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Dariusz Kędziera, Lukasz Mentel: Wave function in the relativistic two componet methods 34
Tatiana Korona: Local treatment of electron correlation for first-order molecular properties from expectation-value CCSD theory 35
Katarzyna Kulczycka, Joanna Trylska, Joanna Sadlej: Internal flexibility of clindamycin 36
István Mayer: The promotion energy of an atom in a molecule 38
Leszek Meissner: An extension of the coupled-cluster corrected configuration interaction method 39
Mariusz P. Mitoraj, Artur Michalak, Tom Ziegler: A Combined Charge and Energy Decomposition Scheme for Analysis of Chemical Bonds and Reaction Paths 40
Dana Nachtigallová, Mario Barbatti, Jaroslaw J. Szymczak, Hans Lischka: Photodynamics of pyrimidine-based molecules: Effect of substitution and initial energy 41
László Nyulászi, Oldamur Hollóczki: Some predictions on stable molecules: failure and success 42
Ivana Paidarová, Philippe Durand: Kinetic equations and dissipation 43
Łukasz Piękoś, Artur Michalak: Molecular dynamics modeling of half-metallocene titanium(IV) ethylene polymerization catalysts 45
Konrad Piszczatowski, Grzegorz Łach, Michał Przybytek, Jacek Komasa, Krzysztof Pachucki, Robert Moszyński, Bogumił Jeziorski: Relativistic, QED and nonadiabatic effects in the interaction of hydrogen atoms 46
Michał Przybytek, Trygve Helgaker: Gaussian and Finite-Element method for the calculation of Coulomb integrals 48
Dorota Rutkowska-Zbik, Malgorzata Witko: DFT Studies on Catalytic Oxidation of Cyclohexene on Manganese Porphyrins 50
Ján Šimunek, Jozef Noga: Orbital Optimized Second-Order Many-Body Perturbation Theory Via Coupled Cluster Ansatz 52
L. Skala, V. Kapsa: Quantum mechanics and mathematical statistics 54
Ágnes Szabados: The problem of small coefficients in SS-MRPT 55
Péter Szakács, Péter R. Surján: Jahn-Teller distortion and zero-field-splitting in carbon nanotubes 56
Štefan Varga: The Brillouin zone integration problem in density fitting of extended systems 57
Libor Veis, Jiří Pittner: Quantum chemical computations on quantum computers 58
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Aleš Vítek, Lenka Ličmanová, Ivana Paidarová, René Kalus: Structural changes in the water tetramer and hexamer. A combined Monte Carlo and DFT study 60
Zoboki Tamás, Mayer István, Surján R. Péter: Electron Correlation Calculations with Strictly Localized Orbitals 62
POSTERS
Dóra Barna, Gyula Tasi: Energy decomposition of alkyl-substituted furan molecules 64
L. Bucinsky, J. Kozisek, S. Biskupic, D. Jayatilaka, M. Gall: Relativistic effects vs. X-ray constrained Hartree Fock 66
Šimon Budzák, Ivan Černušák, Miroslav Medveď: Weak interactions between air pollutants 67
Sébastien Canneaux, Catherine Hammaecher, Florent Louis, Laurent Cantrel: A Theoretical Study of the H-abstraction Reactions of H2, H2O, HI, and OH by the IO (2Π3/2) Radicals 69
Sébastien Canneaux, Eddy Thiriot, Florent Louis, Laurent Cantrel: SPyDERS: MD Modelling Software for Nuclear Safety 71
Aleksandra Chmielowska, Maria Jaworska, Piotr Lodowski: Structure and electronic properties of A-cluster in Acetyl-CoA synthase: insight from DFT 72
Ondřej Demel, Kiran Bhaskaran Nair, Jan Šmydke, Jiří Pittner: Noniterative triples correction in Mukherjee’s coupled cluster method via uncoupled approach 73
Jozef Federič, Ivan Černušák: MD modelling of tungsten carbide slab 75
R. W. Gora, R. Zalesny, W. Bartkowiak, J. M. Luis, B. Kirtman, H. Reis, M. G. Papadopoulos: Nonlinear optical properties of endohedral fullerene complexes 77
Ireneusz Grabowski, Andrew Teale, Szymon Śmiga, Karol Jankowski: Correlation potentials and electron densities obtained from correlated Optimized Effective Potential method and ab initio Wave Function Theory methods 79
Péter Jeszenszki, Ágnes Szabados, Péter R.Surján: Exact diagonalization of bosonic Hamiltonians 80
Anna Kaczmarek-Kędziera: Properties of encapsulated organic molecules 81
Stanislav Kedžuch, Ondřej Demel, Jiří Pittner, Jozef Noga: Multireference R12 Coupled Cluster Theory 82
Hyungrae Kim, Stepan Sklenak: ONIOM study of the catalytic mechanism of Dihydroneopterin Aldolase 83
Katarzyna Kowalska-Szojda, Monika Musiał, Stanisław A. Kucharski: The factorized quadruple excitations for potential energy surfaces with Λ functional 85
Anežka Křístková, Olga L. Malkina: The use of perturbation-stable localization in calculation and analysis of SO-correction to NMR chemical shifts 86
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Anežka Křístková, Olga L. Malkina, Stanislav Komorovský, Elena Malkin, Vladimir G. Malkin: NMR spin-spin couplings and overlap of densities of localized molecular orbitals 87
Piotr Kubisiak, Andrzej Eilmes: Relative Complexation Energies for Li+ Ion in Solution: Molecular Level Solvation Versus Polarizable Continuum Model Study 88
Mojmír Kývala: Secon-dorder Douglas–Kroll–Heß (DKH2) spin–orbit and parity-violating Hamiltonians 89
Piotr Lodowski, Maria Jaworska, Paweł M. Kozłowski, Tadeusz Andruniów: Quantum chemical calculations of photophysical properties of Methyl- and Adenosylcobalamin 90
Jakub Malohlava, Aleš Vítek, René Kalus: Protonated water clusters – structures and thermodynamics 91
Gergely Matisz, Walter M.F. Fabian, Sándor Kunsági-Máté: Hydrogen bonded clusters around aromatic π-systems 93
Gergely Matisz, Walter M.F. Fabian, Sándor Kunsági-Máté: Liquid structure of primary alcohols (methanol, ethanol, 1-propanol, 1-butanol) within the QCE theory 94
Katarína Mečiarová, Lukáš Demovič, Ivan Černušák: Effect of spin-orbit coupling on potential curves and spectroscopic properties of IO and I2 95
Miroslav Melicherčík, Lukáš Demovič, Michal Pitoňák, Pavel Neogrády: Applicability of Graphical Processing Units to Coupled Clusters Calculations 97
Balázs Nagy, József Csontos, Mihály Kállay, Gyula Tasi: Accurate ab initio heats of formation and standard molar entropies for several atmospherically important formyl derivatives 99
Péter Nagy, Imre Pápai: Catalytic hydrogenation of Quinolines via frustrated Lewis pairs: Mechanistic insight from theory 101
Jana Páleniková, Vladimír Kellö: Electric properties of 2-cyclopenten-1-on 103
Ewa Pastorczak, Katarzyna Pernal, Krzysztof Szalewicz: Long-range corrected dispersionless density functional 104
Lukáš F. Pašteka, Miroslav Urban: Electric properties of low-lying excited states of acetone and their interaction with water 105
Mariusz Pawlak, Mirosław Bylicki, Prasanta K. Mukherjee: Muonic systems with Debye-screened Coulomb interactions 107
Marek Pederzoli, Jiří Pittner: A non-adiabatic molecular dynamics study of azobenzene isomerization after excitation to the S1 state based on overlaps of CASSCF wave functions 108
Robert Ponec, Lukáš Bučinský, Carlo Gatti: Relativistic effects on metal-metal bonding. Comparison of the performance of ECP and scalar DKH description on the picture of metal-metal bonding in Re2Cl8(2-) 109
Mariusz Radoń, Ewa Brocławik, Kristine Pierloot: High Valent Iron-Oxo Complexes with Organic Macrocycles: DFT and Ab Initio Study 110
J. Rimarčík, M. Ilčin, L. Rottmannová, E. Klein, V. Lukeš:
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Quantum Chemical Study of the Energetics of Phenolic Compounds 112
Agnieszka Rogowska, Artur Michalak, Monika Srebro, Mariusz Mitoraj: The Influence of Substituents on the Activity of Half-Titanocene Catalysts for Ethylene Polymerization: Theoretical Study 114
Zoltán Rolik, Mihály Kállay: A local Coupled Cluster algorithm 116
Lenka Rottmannová, Ján Rimarčík, Erik Klein, Vladimír Lukeš: Thermodynamics of homolytic S–H bond dissociation in mono-substituted thiophenols 117
Eva Scholtzová, Pavel Mach: Computational study of weak interactions in the biologically active compounds 119
Jakub Šebera, Stanislav Záliš, Pavel Kubát, Kamil Lang, Tomáš Polívka: TD-DFT investigation of S1 and S2 singlet states of TMPyP(n) and complexes of TMPyP4 with sulfonated calix[m]arenes 121
Lucia Šimová, Pavel Neogrády, Miroslav Urban: Application of OVOS technique in calculations of small semiconductor clusters 123
R. Słupski, J. Komasa, K. Jankowski, J. Wasilewski: Benchmark electron density calculations on Be-like atoms 125
Szymon Śmiga, Ireneusz Grabowski: Comparison of the several correlated OEP methods in KS-DFT with correct asymptotic behavior 127
Jan Šmydke, Petra Ruth Kaprálová: Theoretical Study of Ionization and Excitation of He Gas Exposed to Intense XUV Radiation 129
Lukáš Sobek, Jiří Pittner: Femtosecond non-adiabatic molecular dynamics: a study of photochemical deactivation of indole 131
Roland Šolc, Daniel Tunega, Martin H. Gerzabek, Hans Lischka: Theoretical study of radical sites in gallic and protocatechuic acids 133
Anna Stachowicz, Jacek Korchowiec: Charge Sensitivity Analisys in Force Field Atoms Resolution 135
Miroslav Šulc, Roman Čurík: Cold electron collisions with nonpolar molecules 137
Martin Šulka, Michal Pitoňák, Miroslav Urban, Pavel Neogrády: OVOS technique with controlled accuracy in noniterative triples calculations 139
Nargis Sultana, Walter M. F. Fabian: Substituent effect on OH- addition to substituted benzocyclobutene-1, 2-diones: A DFT study 141
Robert Toboła, Fabien Dumouchel, Jacek Kłos, François Lique: Calculations of fine-structure resolved collisional rates for NH(X3Σ−)-He system 142
Daniel Tunega, Roland Šolc, Hasan Pašalić, Martin H. Gerzabek, Hans Lischka: Wetting of clay mineral surfaces – molecular dynamics simulation 143
Lucie Zárubová, Karel Oleksy: Optimalizations of the molecular clusters by the evolutional algorithms method 145
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PLENARY LECTURES
The 9th Central European Symposium on Theoretical Chemistry
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A message to quantum chemists: What we learned about DFT by modelling electron-molecule collisions
Roman Čurík
J. Heyrovský Institute of Physical Chemistry ASCR Doleškova 3
18223 Prague, Czech Republic [email protected]
We explore an implementation of correlation-polarization interactions for electrons
scattering by polyatomic molecules. The short-range correlation is approximated by local
and non-local DFT models commonly used in quantum chemistry and solid state physics.
We explain a necessity of long-range corrections for needs of collision calculations and
adapt a hybrid model in which short-range correlation is connected to a long-range
polarization potential [1,2]. The long-range polarization is represented by general full
tensor components. Furthermore, we propose a robust and stable technique to calculate
momentum-space matrix elements of such a composite potential. The quality of several
selected DFT functionals is tested by scattering calculations for a class of small
hydrocarbon molecules.
[1] Padial NT and Norcross DW 1984 Phys. Rev. A 29 1742 (1984)
[2] Telega S, Bodo E and Gianturco FA Eur. Phys. J. D 29 357 (2004)
Acknowledgement
It is our pleasure to thank Prof. Baerends (Free University, Amsterdam) for encouraging
discussions and useful suggestions. This work was supported by the Czech Ministry of
Education (grants OC10046 and OC09079) and the Grant Agency of the Czech Republic
(grant 202/08/0631).
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In silico Evolution of Early Metabolism
Christoph Flamm
Institute for Theoretical Chemistry, University of Vienna, Waehringerstrasse 17,
1090 Wien, Austria [email protected]
Metabolic networks of higher organisms share many key pathways such as
glycolysis or biosynthesis of most amino acids. In the literature several competing
hypotheses for the evolutionary mechanisms that shape these pathways and the
architecture of metabolic networks have been discussed, each of which finds support
from comparative analysis of extant genomes. Alternatively, direct simulation studies on
the the principles of metabolic evolution are rare because of the demanding pre-
requisites. A central component of such a computational model is an algebraic chemistry
model which acts as a substrate on which a metabolism can be selected. This component
must be sufficiently involved to mimic the complexity of a modern metabolic network,
without restricting the possible chemistry to the 'known' extant end results. In addition, a
genetic system that expresses catalysts and a non-trivial map from sequence/structure
features of the catalysts to their respective functions within the metabolic network must
be implemented. Finally, a fitness function that can be selected for and which evaluates
metabolic efficiency is crucial. In my presentation I will give a brief overview of the
dominating mechanisms that governing pathway evolution and the architecture of modern
metabolism, followed by an in-depyh discuss of the various components that comprise
our simulation framework. Finally first results from large-scale evolutionary simulations
will be presented.
[1] Flamm C, Ullrich A, Ekker H, Mann M, Hoegerl D, Rohrschneider M, Sauer S,
Scheuermann G, Klemm K, Hofacker IL, Stadler PF: Evolution of Metabolic
Networks: A Computational Framework. J Sys Chem 1:4 (2010).
[2] Benkoe G, Flamm C, Stadler PF: A graph-based toy model of chemistry. J Chem Inf
Comp Sci 43:1085-1093 (2003).
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Characterisation of anisotropic ion hydration via QM/MM models
Thomas S. Hofer, Bernd M. Rode, Bernhard R. Randolf
Theoretical Chemistry Division. University of Innsbruck
Innrain 52a 6020 Innsbruck, Austria
E-mail: [email protected]
While most mono-atomic ions exhibit a uniform potential in each direction of
space, some species do not follow this example leading to ansiotropic solvation
structures. This behaviour is observed in the case of main group as well as for transition
metal ions. While the presence of stereo-chemically active lone pairs is well-studied in
the case of crystals (e.g. of SnO), experimental and theoretical examinations of the
solvation of these compounds is a challenging and complex task. The construction of
classical interaction potentials enabling an accurate description of the ion-solvent
interaction has to be considered a difficult and challenging task and hence, a quantum
chemical treatment appears to be most practical approach. In particular hybrid
approaches, treating the chemical most relevant region at a quantum mechanical level
while the interactions in the remaining part are evaluated via classical potentials, appear
to be the method of choice. The recently formulated quantum mechanical charge field
molecular dynamics (QMCF MD) approach [1,2] proved to be a versatile tool for the
study of solvated species.
Applications of the QMCF MD framework to anisotropically hydrated ions are
presented. The system covered are Pd2+, Pt2+, Ge2+, Sn2+ and Pb2+.
[1] B. M. Rode, T. S. Hofer, B. R. Randolf, C. F. Schwenk, D. Xenides,
V. Vchirawongkwin, Theor. Chem. Acc. 2006, 115(2-3), 77-85
[2] T. S. Hofer, A. B. Pribil, B. R. Randolf, B. M. Rode,
Adv. Quant. Chem. 2010, 59 213-246
Acknowledgement
Financial support for this work provided by the Austrian Science Fund (FWF) is
gratefully acknowledged.
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Thermochemical data calculation by quantum chemistry methods: application to ten species involved in low-temperature oxidation
mechanism of o-xylene
Florent LOUIS, Romain VANDEPUTTE, Sébastien CANNEAUX, Marc RIBAUCOUR
PhysicoChimie des Processus de Combustion et de l’Atmosphère (PC2A) UMR 8522 CNRS/Lille1, Université Lille 1 Sciences et Technologies, Cité scientifique, Bât C11/C5, 59655 Villeneuve d’Ascq Cedex, France
Thermokinetic modeling studies of surrogate fuel combustion are carried out to
understand the mechanisms of formation of pollutants and toxic compounds in automotive
engines. A surrogate fuel is composed of molecules representative of each family of compounds
included in a commercial fuel: alkanes, aromatic compounds, cyclanes, alkenes, oxygenated
compounds. Among aromatic compounds, xylenes are good representative of alkylbenzenes.
Their percentages in mass in an European gasoline are 3.06, 5.70, and 1.96% for o-, m-, and p-
xylene, respectively. A low-temperature oxidation thermokinetic model of o-xylene is currently
elaborated in our laboratory. Thermochemical data of species involved in the mechanism are
usually estimated using the THERM software based on Benson group additivity theory. However,
due to missing groups in THERM group database, thermochemical data of many species cannot
be estimated. The aim of this work was to determine thermochemical data of ten species (see
Table 1) using quantum chemistry methods.
Quantum chemistry calculations were performed using the GAUSSIAN03 program suite.
ΔfH°(298 K) were calculated using four composite methods (G3, G3MP2, G3B3, and CBS-QB3)
and isodesmic reaction technique to cancel the systematic error in the molecular orbital
calculations. Sets of five isodesmic reactions were used for each target species. Total energies
were corrected by ZPVE and vibration frequencies were scaled using appropriate scaling factors.
Final values of ΔfH°(298 K) were obtained by averaging the values obtained from each isodesmic
reaction and then by averaging the averaged values given by each calculation method. They are
reported in Table 1. For species 4-7 owing many conformers, ΔfH°(298 K) was calculated by a
population-weighted average of each conformer ΔfH°(298 K). The mole fraction of each
conformer was determined using a Boltzmann distribution based on the energy difference
between conformers. For species 1, 2, 5-8 ΔfH°(298 K) values are available in the literature.
Except for species 2, the differences between our determination and the literature value are less
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than 5 kJ.mol-1. ΔfH°(298 K) of species 3, 4, 9, and 10 has been determined for the first time to
our knowledge.
Table 1: Values of ΔfH°(298 K) in kJ.mol-1 calculated in this work for the ten species.
species N° ΔfH°(298 K) species N° ΔfH°(298 K)
o-xylene 1 19,4 3-hydroxybenzaldehyde 6 -217,5
2-methylbenzyl radical 2 181,8 2,3-dimethylphenol 7 -160,2
2-methylbenzylperoxy radical 3 86,2 1-ethyl-2-methylbenzene 8 -0,9
2-methylbenzylhydroperoxyde 4 -58,6 2-(hydroperoxymethyl)benzyl radical 9 110,2
2-hydroxybenzaldehyde 5 -243,5 2-(hydroperoxymethyl)benzaldehyde 10 -144,3
S°(298 K) and Cp°(T) (300 ≤ T ≤ 1500 K) were calculated using molecular properties
determined at B3LYP/6-311++G(d,p) level of theory and statistical thermodynamics through
evaluation of translational, vibrational, electronic, and rotational partition functions. The
contribution of internal rotors such as CH3, CH2, CH2CH3, OH, CH2OOH, OOH, CHO was
determined in two different ways depending on the temperature. S°(298 K) and Cp°(300 K) were
calculated using the rigid-rotor-harmonic-oscillator model. Cp°(T) at T ≥ 400 K were calculated
by treating separately translational, vibrational, and external rotational contributions and
contribution from internal rotation. In this case, the torsion frequencies corresponding to internal
rotations were excluded in the calculation of vibrational contribution. The contribution to Cp°(T)
from an internal rotation was determined using direct integration over energy levels of the
internal rotation potential energy. The HR-public program was used for this integration. This
technique employs the expansion of the internal rotation potential in Fourier series, the
calculation of the Hamiltonian matrix on the basis of wave functions of free internal rotation, and
the subsequent calculation of energy levels by direct diagonalization o the Hamiltonian matrix.
S°(298 K) and Cp°(T) of o-xylene determined in this work are in good agreement with literature
values. This makes us trustful in S°(298 K) and Cp°(T) values determined for the other species in
this work.
The 9th Central European Symposium on Theoretical Chemistry
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Study and design of nonlinear optical materials:from molecules, through oligomers to polymers
Miroslav Medveď,1 Šimon Budzák,1 Jozef Noga,2 Ivan Černušák,3 Denis Jacquemin4 and Eric A. Perpète4
1 Department of Chemistry, Faculty of Science, Matej Bel University, Tajovského 40
SK-97401 Banská Bystrica, Slovakia, [email protected] 2 Department of Inorganic Chemistry, Faculty of Natural Sciences, Comenius University,
Mlynská dolina, SK-842 15 Bratislava, Slovakia 3 Department of Physical and Theoretical Chemistry, Faculty of Natural Sciences,
Comenius University, Mlynská dolina, SK-842 15 Bratislava, Slovakia 4 Unité de Chimie Physique Théorique et Structurale, Facultés Universitaires Notre-
Dame de la Paix Rue de Bruxelles, 61 5000 Namur, Belgium
Organic π-conjugated oligomers and polymers represent an excellent alternative to
traditional inorganic NLO crystals because they can be easily synthesized and chemically
modified. Extremely fast switching times, resistance to high intensity radiation,
possibility of thin-layer fabrication and low electric permitivity are important properties
in favor of organic NLO materials.
In the search for the large β, various strategies have been adopted. The most
obvious is the so-called push-pull strategy, in which a conjugated chain (e.g.
oligomethylene or phenylene) is capped at its ends by an electron-donor group on one
side and an electron-acceptor group on the other. In our recent studies we have been
interested in the so-called AB systems, where a suitable combination of delocalizability
and asymmetry can be achieved by designing π-conjugated chains from asymmetric unit
cells (containing two or more different nuclei). We successfully designed various AB
oligomers containing B, N, and C skeleton atoms with interesting NLO properties.
We will discuss various aspects of theoretical investigation of NLO properties
including (i) electron correlation effects, (ii) suitability of hybrid as well as recently
proposed LC-DFT methods, (iii) numerical differentiation problems, (iv) extrapolation
(from oligomeric values to polymeric limit) techniques and others. Possibilities of
investigation of NLO properties of infinite periodic systems will also be outlined.
This work has been supported by the Grant Agency of the Slovak Republic VEGA
(projects No. 1/0356/09 and No. 1/0428/09).
The 9th Central European Symposium on Theoretical Chemistry
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Trying to Understand the Mysterious Fluorescence of ó Systems: Oligosilanes
Matthew K. MacLeod and Josef Michl
University of Colorado, Boulder, CO, USA, and Academy of Sciences of the Czech Republic,Prague, Czech Republic
Saturated hydrocarbons absorb in the vacuum UV part of the spectrum but produce verybroad and weak fluoresce bands at much longer wavelengths. The huge Stokes shifts suggestprofound differences between the equilibrium geometries of the ground and the singlet excited state.That should not be surprising, since electronic excitation in saturated systems involves electrons ofthe bonds that hold the molecule together. The nature of the geometry changes that take place uponexcitation is not known.
We have been examining the silicon analogs of saturated hydrocarbons, the peralkylated
n 2n+2oligosilanes Si R . Like hydrocarbons, they contain saturated and tetravalent tetrahedral atomsin the main chain or cycle (Si instead of C), only single bonds, and no lone pairs. Oligosilaneshowever are easier to study since they absorb throughout the near UV region, and their spectra aremuch simpler, although they, too, contain fairly numerous closely spaced transitions. The differenceoriginates in the lower electronegativity of the backbone Si atoms relative to the lateral alkylsubstituent atoms, and in some ways the oligosilanes resemble fluorocarbons more thanhydrocarbons.
Like hydrocarbons, short-chain peralkylated oligosilanes (n < 8) generally fluoresce atstrikingly long wavelengths, with huge Stokes shifts. A compound with no observable absorptionabove 250 nm can emit in the blue or even in the green part of the visible spectrum. Remarkably,some oligosilanes fluoresce in two different spectral regions. In contrast, longer-chain peralkylatedoligosilanes (n > 6) generally exhibit Franck-Condon allowed fluorescence with a minimal Stokesshift and apparently very little difference between ground state and excited state equilibriumgeometries. The behavior of these more normal emitters can be understood in terms of extensiveó-electron delocalization, and has been dealt with elsewhere (some conformers of the chain with n= 7 show Stokes-shifted fluorescence and others fluoresce with no Stokes shift).
We shall report the results of calculations at several levels of theory (CC2, CASPT2, TD-DFT) that we have performed to answer the following questions: (i) What are the equilibriumgeometries of the highly distorted first excited states of peralkylated oligosilanes? (ii) Can oneunderstand the nature of the geometrical distortion from the ground state in simple intuitive terms?
The 9th Central European Symposium on Theoretical Chemistry
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Fock space coupled cluster theory for two-valence
sectors
Monika Musia�l
University of Silesia, Institute of Chemistry
Szkolna 9
40-006 Katowice, Poland
The Fock space (FS) coupled cluster (CC) theory offers a very convenient tool
for the description of excited, ionized and electron attached states. At the level
of one-valence sectors the FSCC provides ionization potentials (IP) and electron
affinities (EA) for the (0,1) and (1,0) sectors, respectively. For the two-valence
sectors we obtain double ionization potentials (DIP), double electron affinity (DEA)
and excitation energies (EE) which correspond to (0,2), (2,0) and (1,1) sectors,
respectively. The same quantities are obtained with the equation-of-motion (EOM)
CC approach and the IP-EOM as well as EA-EOM are identical to FS values unlike
the two-valence situation. In this talk an efficient computational scheme for the
treatment of the two-valence sectors within the Fock space CC theory is described
as well as a comparative analysis of the DIP, DEA and EE values obtained via EOM
formalism.
The 9th Central European Symposium on Theoretical Chemistry
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Pair density functional theory
Á. Nagy
Department of Theoretical Physics University of Debrecen,
H–4010 Debrecen, HungaryInstitution...
The pair density is a fundamental quantity. It is similar in role to the electron
density of the density functional theory. According to the Hohenberg-Kohn theorems in
the nondegenerate ground state the density determines the external potential and the
ground-state energy takes its minimum at the true electron density. It was shown [1, 2]
that the Hohenberg-Kohn theorems can be extented: in the nondegenerate ground state
the pair density determines the external potential and the groundstate energy takes its
minimum at the true pair density
In the density functional theory the electron density is generally calculated by
solving the Kohn-Sham equations. It was shown [3] that Kohn-Sham-like equations can
be constructed in the pair density functional theory. It turned out that the problem of an
arbitrary ground-state system with even electrons can be reduced to a two-particle
problem. The effective potential in this auxiliary equation contains an unknown term, the
Pauli potential.
In order to perform calculations one has to approximate the Pauli term. Exact
relations for functionals are proved to be important in constructing approximate
functionals in the density functional theory. Therefore virial theorem and hierarchy of
equations were obtained for the potential vp [4]. The electron-electron cusp condition and
asymptotic behaviour of the effective potential of the two-particle equation were also
derived [5]. Recently, exact differential and integral constraints for the pair density have
been presented [6].
A novel method for determining the Pauli potential has recently been proposed [7].
Starting from a reliable description of the pair density an analytical expression has been
obtained for atomic systems. In the derivation a recent method [8] of constructing the
exact Hamiltonian corresponding to the correlated three-parameter variational wave
The 9th Central European Symposium on Theoretical Chemistry
19
function was utilized and test calculations were done for the Be and isoelectronic C2+ and
O4+ ions [7].
[1] A. Gonis, T. C. Schulthess, J. van Ek and P. E. A. Turchi, Phys. Rev. Lett. 77 (1996),
2981.
[2] P. Ziesche, Phys. Lett. A 195 (1994), 213; Int. J. Quantum. Chem. 60 (1996), 149.
[3] Á. Nagy, Phys. Rev. A, 66, 022505 (2002).
[4] Á. Nagy and C. Amovilli, J. Chem. Phys. 121, 6640 (2004).
[5] Á. Nagy and C. Amovilli, J. Chem. Phys. 128, 11411 (2008); J. Chem. Phys. 132,
109902 (2010).
[6] Á. Nagy and C. Amovilli, Chem. Phys. Lett. 469, 353 (2009).
[7] C. Amovilli and Á. Nagy, J. Chem. Phys. 129 204108(2008).
[8] C. Amovilli, N. H. March, I.A. Howard and Á. Nagy, Phys. Lett. A372 4053 (2008).
Grant OTKA No. K67923 is gratefully acknowledged.
The 9th Central European Symposium on Theoretical Chemistry
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Treating static and dynamic correlation with range-separated density and density matrix functionals
Katarzyna Pernal
Institute of Physics, Technical University of Lodzul. Wólczańska 219
93-005 Lodz, [email protected]
It is well known that static and long-range correlation effects are not well treated by local or semilocal density functionals. They are accurate, however, for systems where dynamic correlation dominates. On the other hand, recently proposed functionals of one-electron reduced density matrix (density matrix) proved capable of treating static correlation effects correctly.
We propose a new method, based on range-separation of Coulomb electron-electron interaction. It employs density and density matrix functionals in the short- and long-range regimes, respectively.
The method has been successfully applied to the homogeneous electron gas. The long-range correlation energy of the electron gas is excellently reproduced by a modified Buijse-Baerends density matrix functional [1].
The same functional combined with a short-range PBE (Perdew-Burke-Ernzerhof) density functional reproduces accurately dissociation curves of simple molecules. Therefore, the new approach corrects the deficiency of the density functional in the dissociation limit, where static correlation effects are present.
The new method scales with the 4th power of the number of basis set functions. An efficient projected gradient algorithm is employed in the optimization process [2]. The total computational cost is comparable to that of DFT methods.
[1] K. Pernal, Phys. Rev. A 81, 052511 (2010).[2] E. Canc?s and K. Pernal, J. Chem. Phys. 128, 134108 (2008).
Acknowledgement This work was supported by Polish Ministry of Science and Higher Education grant No. N N204 159036
The 9th Central European Symposium on Theoretical Chemistry
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Local correlation coupled-cluster methods exploiting cluster-in-molecule ansatz and their multi-level generalizations
Piotr Piecuch and Wei Li
Department of Chemistry, Michigan State University
East Lansing, Michigan 48824 USA
Coupled-cluster (CC) methods have greatly impacted modern quantum chemistry,
but, as all electronic structure approaches that aim at the accurate description of many-
electron correlation effects, they face significant challenges when dealing with the in-
creasingly complex molecular problems chemists are interested in. This includes prohibi-
tive costs of CC calculations for larger molecular systems. To help to address this chal-
lenge, we have extended [1,2] a number of CC methods, including CCSD, CCSD(T), and
the completely renormalized extension of CCSD(T), abbreviated CR-CC(2,3) [3], to lar-
ger systems with hundreds of atoms through the use of the local correlation, cluster-in-
molecule (CIM) ansatz [1,2,4]. The resulting CIM-CCSD, CIM-CCSD(T), and CIM-CR-
CC(2,3) methods are characterized by (i) the linear scaling of the CPU time with the
system size when the same level of theory is applied to all CIM subsystems, (ii) the use
of orthonormal orbitals in subsystem calculations, (iii) the natural coarse-grain par-
allelism, which can be further enhanced by the additional fine-grain parallelism of each
subsystem calculation, (iv) the high computational efficiency, enabling calculations for
large molecular systems at high levels of CC theory, (v) the purely non-iterative character
of local triples corrections to CCSD energies, and (vi) the applicability to the covalently
and weakly bound molecular systems. In addition, one can use the flexibility of the CIM
local correlation ansatz to mix different CC or CC and non-CC methods within a single
calculation, enabling the rigorous formulation of multi-level local correlation theories [2]
that combine the high-level CC methods, such as CR-CC(2,3), to treat, for example, the
reactive part of a large molecular system with the lower-order ab initio (e.g., MP2)
scheme(s) to handle the chemically inactive regions without splitting it into ad hoc
fragments and saturating dangling bonds. By comparing the results of the canonical CC
calculations with the single- and multi-level CIM-CC calculations for normal alkanes
The 9th Central European Symposium on Theoretical Chemistry
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[1,2], water clusters [1], the diffusion of atomic oxygen on the silicon surface [5], and the
proton transfer in the aggregates of dithiophosphinic acids with water [2], we de-
monstrate that the CIM-CCSD, CIM-CCSD(T), and CIM-CR-CC(2,3) approaches, and
their multi-level extensions accurately reproduce the corresponding canonical CC corre-
lation and relative energies, including chemical reaction pathways, while offering savings
in the computer effort by orders of magnitude.
[1] (a) W. Li, P. Piecuch, J. R. Gour, and S. Li, J. Chem. Phys. 131, 114109 (2009). (b) W. Li, P. Piecuch, and J. R. Gour, in: Theory and Applications of Computational Chemistry - 2008, AIP Conference Proceedings, Vol. 1102, edited by D.-Q. Wei and X.-J. Wang (AIP, Melville, NY, 2009), p. 68. (c) W. Li, P. Piecuch, and J. R. Gour, in: Progress in Theoretical Chemistry and Physics, Vol. 19, Advances in the Theory of Atomic and Molecular Systems: Conceptual and Computational Advances in Quantum Chemistry, edited by P. Piecuch, J. Maruani, G. Delgado-Barrio, and S. Wilson (Springer, Dordrecht, 2009), p. 131. (d) W. Li and P. Piecuch, J. Phys. Chem. A, in press; Articles ASAP; Publication Date (Web): April 7, 2010. [2] W. Li and P. Piecuch, J. Phys. Chem. A 114, 6721 (2010). [3] (a) P. Piecuch and M. Włoch, J. Chem. Phys. 123, 224105 (2005). (b) P. Piecuch, M. Włoch, J. R. Gour, and A. Kinal, Chem. Phys. Lett. 418, 467 (2006). [4] (a) S. Li, J. Ma, and Y. Jiang, J. Comput. Chem. 23, 237 (2002). (b) S. Li, J. Shen, W. Li, and Y. Jiang, J. Chem. Phys. 125, 074109 (2006). [5] P. Arora, W. Li, P. Piecuch, J. W. Evans, M. Albao, and M. S. Gordon, J. Phys. Chem. C, in press; Articles ASAP; Publication Date (Web): July 6, 2010.
Supported by the Chemical Sciences, Geosciences and Biosciences Division, Office of
Basic Energy Sciences, Office of Science, U.S. Department of Energy (Grant No. DE-
FG02-01ER15228; P.P).
The 9th Central European Symposium on Theoretical Chemistry
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Reaction mechanism from quantum chemistry:
unbiased and biased simulations
Andras Stirling
Chemical Research Center of the Hungarian Academy of Sciences
Budapest, Hungary
The continuously increasing processor capacity allows the use of more realistic
models and more demanding computational technics to study chemical reactions.
Larger models can provide access to really collective atomic motions and in the same
time ensure a chemically more reliable environment for the reactions in silico. The
size and complexity of these models put the free energy surface into focus instead of
the potential energy surface. Indeed, much deeper insight can be obtained into the
reaction mechanisms by exploring free energy surfaces spanned by suitable reaction
coordinates.
Chemical reactions are usually activated events, thus their observations in molec-
ular dynamics simulations is highly unlikely. Therefore the simulations have to be
biased in some way to render these rare events observable and to measure their free
energy barriers. In this talk I will give an overview of the most important meth-
ods and illustrate some of these with actual calculations on different reactions. An
important methodological issue is the selection of appropriate reaction coordinates
(order parameters) and I will also address this problem.
The 9th Central European Symposium on Theoretical Chemistry
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SHORT LECTURES
The 9th Central European Symposium on Theoretical Chemistry
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Periodic DFT study of N2O decomposition over Fe-ferrierite
Prokopis Andrikopoulos, Stepan Sklenak and Zdenek Sobalik J. Heyrovsky Institute of Physical Chemistry of the ASCR, v. v. i.
Dolejškova 2155/3, 182 23 Prague 8, Czech Republic [email protected]
INTRODUCTION
To borrow the title from a recent science paper [1], nitrous oxide is no laughing matter.
Its twofold impact on the environment as ozone depleting agent and a potent greenhouse
gas, places an increased importance on the research of N2O elimination from industrial
streams [2-4]. Iron-exchanged zeolites provide a promising catalytic system for this
process and in particular iron-exchanged Ferrierite (Fe-FER) with a higher catalytic
activity than the more prevalent ZSM-5 and Beta zeolite frameworks [5]. To ascertain
where this superiority lies, we embarked on an in-depth computational analysis of the Fe-
FER system.
Figure 1.Transition State structure of adjacent cooperating active sites of the β1xβ1 type on
Fe-FER. The Fe···NNO-Fe moiety is formed facilitating an easier N-O bond scission.
COMPUTATIONAL DETAILS
Spin polarized periodic DFT calculations were carried out employing the VASP code [6-
9]. The Kohn–Sham equations were solved variationally in a plane-wave basis set using
the projector-augmented wave (PAW) method of Blöchl [10], as adapted by Kresse and
Joubert [11]. The exchange-correlation energy was described by the PW91 generalized
The 9th Central European Symposium on Theoretical Chemistry
26
gradient approximation (GGA) functional [12-13]. Brillouin zone sampling was restricted
to the Γ-point. The plane-wave cutoff of 400 eV was utilized for geometry optimizations
while a smaller cutoff of 300 eV was used for the molecular dynamics simulations (MD).
The MD simulations were run for 5 ps at 300 K and the structures of ten distinct
"snapshots" collected from the last 500 fs of each MD simulation were optimised. The
most stable conformer was then used for subsequent calculations.
RESULTS AND DISCUSSION
Initially, the iron-centered active sites for the reaction, incorporated in the unit cell of
FER, were optimized with Molecular Dynamics. Three distinctive active sites were
investigated namely Alpha, Beta-1 and Beta-2 accommodating Fe(II). Concerning the
latter two types, the possibility of cooperation between sites is illustrated (Figure 1),
contrary to the isolated Alpha sites. The study of the Alpha type site can be used as an
approximate system for other zeolite frameworks where cooperation among sites is less
likely to occur. Having the active site for the reaction optimized as thoroughly as
possible, we commence on studying the mechanism of the decomposition of N2O.
Another uncertainty, the nature of nitric oxide role on the reaction can also be addressed
through this computational effort.
REFERENCES [1] D.J. Wuebbles, Science 326 (2009) 56. [2] 2009 U.S. Greenhouse Gas Inventory Report, Environmental Protection Agency, (http://tinyurl.com/emissionsreport). [3] M. Prather, Science 279 (1998) 1339. [4] A.R. Ravishankara, J.S. Daniel, R.W. Portmann, Science 326 (2009) 123; M. Dameris, Angew. Chem. 122 (2010) 499; Angew. Chem. Int. Ed. 49 (2010) 489. [5] K. Jisa, J. Novakova, M. Schwarze, A. Vondrova, S. Sklenak, Z. Sobalik, J. Catal. 262 (2009) 27; I. Melian-Cabrera, C. Mentruit, J.A.Z. Pieterse, R.W. van den Brink, G. Mul, F. Kapteijn, J.A. Moulijn, Catal. Comm. 6 (2005) 301. [6] G. Kresse, J. Furthmuller, Phys. Rev. B 54 (1996) 11169. [7] G. Kresse, J. Furthmuller, Comput. Mater. Sci. 6 (1996) 15. [8] G. Kresse, J. Hafner, Phys. Rev. B 48 (1993) 13115. [9] G. Kresse, J. Hafner, Phys. Rev. B 49 (1994) 14251. [10] P.E. Blöchl, Phys. Rev. B 50 (1994) 17953. [11] G. Kresse, D. Joubert, Phys. Rev. B 59 (1999) 1758. [12] J.P. Perdew, J.A. Chevary, S.H. Vosko, K.A. Jackson, M.R. Pederson, D.J. Singh, C. Fiolhais, Phys. Rev. B 46 (1992) 6671. [13] J.P. Perdew, Y. Wang, Phys. Rev. B, 45, (1992), 13244.
The 9th Central European Symposium on Theoretical Chemistry
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Local hybrids: conceptually simple hyper-GGA exchange-correlation functionals for the Kohn-Sham density functional calculation of a wide
range of properties
Alexei V. Arbuznikov, Hilke Bahmann, Martin Kaupp
Institute of Physical and Theoretical Chemistry, University of Würzburg Am Hubland
D-97074 Würzburg, Germany E-mail: [email protected]
Among the most popular exchange-correlation functionals, a particular place is
occupied by the well-known “global hybrid functionals” (like B3LYP, PBE0 or TPSSh)
that provide high accuracy in the description of many molecular properties. Due to their
inclusion of a certain percentage of the “exact” (Hartree-Fock-like) exchange energy,
global hybrids are able to balance the elimination of Coulomb self-interaction and
inclusion of nondynamical correlation. However, their performance is restricted by
insufficient flexibility, since the description of different properties may require very
different amounts of exact exchange. The flexibility is fundamentally enhanced by
passing to a position-dependent exact-exchange admixture governed by a so-called local
mixing function (LMF) that leads to the notion of local hybrid functionals. The latter
constitute a new promising generation of hyper-GGA functionals for the simultaneous
accurate description of various properties within Kohn-Sham DFT.
The overall performance of local hybrids is a matter of a very subtle balance
between their basic ingredients: (i) ansatz and parameterization of the LMF; (ii) density-
functional approximation of the exchange mixed with the exact exchange; (iii) nature of
the (dynamic) correlation functional. Up to now, the best performance has been attained
partially in a semi-empirical way with a scaled ratio of von Weizsäcker kinetic energy
density to local kinetic energy density as LMF [1] (the latter may also include spin
polarization [2] and electron density itself), LSDA exchange, and LSDA correlation.
Further progress can be aided by insights from the adiabatic connection (AC) formalism
[3] and careful analysis of exact constraints (Lieb-Oxford bound, density-scaling
properties, etc.) a density functional should obey.
The 9th Central European Symposium on Theoretical Chemistry
28
Our best local hybrids include a minimal number of adjustable parameters (one or
two) and turn out to be superior in the description of atomization energies, reaction
barrier heights [1,2,4], NMR chemical shifts, EPR g tensors [5], and electric response
properties (polarizabilities and hyperpolarizabilities) [6] compared to traditional hybrids
that often suffer from being overparameterized. A brief comparison will be also made for
the analytical structure and performance of our local hybrids to those designed in other
research groups [7], as well as to more complicated hyper-GGA functionals [8].
Currently, local hybrids are more computationally expensive than global hybrids.
However, we show that the situation can be significantly improved by avoiding an
explicit evaluation of the exact-exchange energy density on a grid, and by applying a
more efficient way for the evaluation of the LMF-including two-electron integrals.
Finally, an outlook on the extension of local hybrids to the computation of other
properties (including higher-order response ones) will be given.
[1] H. Bahmann, A. Rodenberg, A. V. Arbuznikov, M. Kaupp J. Chem. Phys. 126 (2007)
011103.
[2] A. V. Arbuznikov, H. Bahmann, M. Kaupp, J. Phys. Chem. A 113 (2009) 11898.
[3] A. V. Arbuznikov, M. Kaupp, J. Chem. Phys. 128 (2008) 214107.
[4] M. Kaupp, H. Bahmann, A. V. Arbuznikov, J. Chem. Phys. 127 (2007) 194102.
[5] A. V. Arbuznikov, M. Kaupp, J. Chem. Theory Comput. 5 (2009) 2985.
[6] A. V. Arbuznikov, M. Kaupp, Int. J. Quantum Chem., in press.
[7] J. P. Perdew, V. N. Staroverov, J. Tao, G. E. Scuseria, Phys. Rev. A 78 (2008)
052513.
[8] M. M. Odashima, K. Capelle, Phys. Rev. A 79 (2009) 062515.
This work has been funded by Deutsche Forschungsgemeinschaft (project KA1187/10-1)
within Priority Program 1145, “Modern and universal first-principles methods for many-
electron systems in chemistry and physics”.
The 9th Central European Symposium on Theoretical Chemistry
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Multireference State-Specific Mukherjee’s
Coupled Cluster Methods With Triexcitations
Kiran Bhaskaran-Nair, Ondrej Demel, and Jirı Pittner
J. Heyrovsky Institute of Physical Chemistry, v.v.i.18223 Prague 8, Czech Republic
The standard coupled cluster (CC) method, like other single reference methods,
exhibits a poor performance when quasidegeneracies are encountered, unless high-
level excitations are included. Such situations are, however, often of great chemical
interest, for example during bond breaking, double bond twisting, for diradicals, and
reaction intermediates; therefore a multireference (MR) generalization of CC theory
is highly desirable. Such a generalization is not unique; one possibility is based on
the Jeziorski-Monkhorst ansatz, where every reference determiant has is own set
of cluster amplitudes. The state-universal method (SUCC) gives energies of several
states in one calculation, but often suffers from severe convergence difficulties due to
the intruder state problem. The state-specific methods, where only one eigenvalue
of the effective Hamiltonian has a physical meaning, are free from the intruder state
problem, and have thus attracted a great attention in the last decade.
The first proposed state-specific MRCC method, Brillouin-Wigner coupled cluster
(BWCC), is insensitive to intruder states, has only linear scaling with the number
of references, and exhibits a very simple structure of amplitude equations coupled
only through the exact energy. However, it lacks the important property of the
standard CC theory, size-extensivity. The state-specific MRCC method formulated
by Mukherjee et. al. (MkCC) [1], and later developed by Evangelista et. al. [2],
Kallay et. al. [3], and Pittner et. al. [4] seems presently to be the most promising.
The 9th Central European Symposium on Theoretical Chemistry
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We have developed a linked formulation of the MkCC method and implemented
it at the truncation level with non iterative triples (MR MkCCSD(T)) and with
iterative triexcitations (MR MkCCSDT) in the ACES II package. Recently the
uncoupled MkCC formalism [5] has also been investigated, in order to determine
how its performance changes with the size of the basis set, size of the model space,
various multireference character of different molecules, and inclusion of connected
triple excitations. The assessment of these methods has been performed on the
spectroscopic constants of the first three electronic states of the oxygen molecule,
on the singlet-triplet gap in methylene and twisted ethylene, and on several other
systems, where a comparison with other multireference coupled cluster treatments
and with experimental data is possible.
Considering the computational cost, the MR MkCCSDT method aim to provide
a benchmark treatment of small systems, while the MR MkCCSD(T) variants can
be used for application calculations of medium-sized molecules.
References
[1] U. S. Mahapatra, B. Datta, and D. Mukherjee, J. Chem. Phys. 110, 6171 (1999).
[2] F. A. Evangelista, A. C. Simmonett, W. D. Allen, H. F. Schaefer III, and J.
Gauss, J. Chem. Phys. 128, 124104 (2008).
[3] S. Das, D. Mukherjee, and M. Kallay, J. Chem. Phys. 132, 074103 (2010).
[4] K. Bhaskaran-Nair, O. Demel, and J. Pittner, J. Chem. Phys. 129, 184105
(2008).
[5] O. Demel, K. Bhaskaran-Nair, and J. Pittner, J. Chem. Phys. in Press .
The 9th Central European Symposium on Theoretical Chemistry
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Prospects of using MP2 for electron scattering
Petr Čársky ...
J. Heyrovský Institute of Physical Chemistry. Academy of Sciences of the Czech RepublicDolejškova 3
18223, Prague 8, Czech Republic [email protected]
The idea of using diagrammatic approach similar to the Brueckner-Goldstone
linked cluster perturbation expansion goes already to the dark age of the theory of
electron scattering. Its first application to atomic targets at the second-order theory was
reported already in 1960’s [1]. The first application of the full second-order optical
potential to molecular targets was reported by a decade later [2]. It was the calculation on
the hydrogen molecule. Since then no application was attempted because of technical
difficulties of such calculations. The purpose of this contribution is to show that the
calculations of this type are now feasible even on commonly used computers of the
Opteron type. Merits and limitations of second-order calculations will be mentioned.
[1] H. P. Kelly, Phys. Rev. 131, 684 (1963), 136, 896 (1964), 160, 44 (1967)
[2] A. Klonover and U. Kaldor, Chem. Phys. Lett. 51, 321 (1977)
The 9th Central European Symposium on Theoretical Chemistry
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Anharmonic Vibrational Analysis with Traditional and Explicitly Correlated Coupled Cluster Methods
Kalju Kahn, Bernard Kirtman, Jozef Noga, Seiichiro Ten-no
Department of Chemistry and Biochemistry, University of California, Santa Barbar
CA 93106,[email protected]
Achieving the spectroscopic accuracy in ab initio calculation of vibrational spectra
is challenging due to two well-understood limitations. First, accurate energy derivatives
require a good description of electron correlation. Second, meaningful correlated
calculations require large one-electron basis sets. Furthermore, dipole moment and
hyperpolariability derivatives, which determine the infared and Raman intensities,
respectively, also strongy depend on the level of theory. We have now explored the
convergence of quadratic, cubic and quartic force constants with traditional and explicitly
correlated coupled cluster methods [1]. The convergence of harmonic frequencies with
Dunning’s cc-pVXZ family of basis sets in traditional CCSD(T) calculations is slow
(Figures 1 and 2).
Figure 1. Convergence of the harmonic
frequency of HF in traditional and
explicitly correlated CCSD(T)
calculations.
Figure 2. Convergence of the harmonic
stretching frequency of H2O in
traditional and explicitly correlated
CCSD(T) calculations.
The 9th Central European Symposium on Theoretical Chemistry
33
We find a similar frustratingly slow convergence for many cubic and quartic
constants in traditional calculations (Figures 3 and 4). The addition of diffuse functions
often markedly improves convergence. An excellent convergence of harmonic
frequencies and cubic force constants is provided by explicitly correlated R12/B, R12/C
and F12/C methods with R12-suited basis sets. The Slater type geminal, however,
outperforms the linear r12 for quartic force constants and vibrational anharmonicity
constants in water.
Figure 3. Convergence of the cubic
force constant in HF in traditional and
explicitly correlated calculations.
Figure 4. Convergence of the mixed
cubic force constant in H2O in traditional
and explicitly correlated calculations.
We have carried out a systematic analysis of core correlation and quadruple
excitation contributions to quadratic, cubic and quartic force constants. Core correlation
and quadruple contributions significantly affect harmonic frequencies but their effect to
vibrational anharmonicity constants is small. The converged force constants from
explicitly correlated CCSD(T) calculations succeed in reproducing the fundamental
frequencies of water molecule with spectroscopic accuracy after corrections for post-
CCSD(T) effects are made.
[1] K. Kahn, B. Kirtman, J. Noga, and S. Ten-no, Anharmonic Vibrational Analysis of
Water with Traditional and Explicitly Correlated Coupled Cluster Methods, J. Chem.
Phys. 133 (2010).
The 9th Central European Symposium on Theoretical Chemistry
34
Wave function in the relativistic two componet
methods
Dariusz Kedziera, �Lukasz Mentel
Department of Chemistry and Photochemistry of PolymersGagarina
87-100 Torun, Poland
Rapid growth of interest in the field of the chemistry of heavy elements was
followed by the development of the two–component methods of relativistic quantum
chemistry. The ongoing progress in this kind of methods was monitored only by the
accuracy of the obtained energies for one–electron systems. Finally, the solutions
for energy became available and soon a wide variety of two–component methods
have earned to be called accurate or even exact [1–5]. Nowadays, the scientific
effort can be directed to generalizations and seeking similarities between methods
different on first sight. Moreover, the present understanding allows to look at the
problems that were hidden behind the energy issue, for instance the properties of
the two–component wave functions.
References
[1] B.A.Hess, Phys. Rev. A 33, 3742 (1986).
[2] M. Barysz, A.J. Sadlej, J. Chem. Phys. 116, 2696 (2002)
[3] W. Kutzelnigg, W. Liu, J. Chem. Phys. 123, 241102 (2005)
[4] M. Ilias, T. Saue, J. Chem. Phys. 126, 064102 (2007).
[5] D. Kedziera, M. Barysz, Chem. Phys. Lett. 446, 176-181 (2007)
The 9th Central European Symposium on Theoretical Chemistry
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Local treatment of electron correlation for
first-order molecular properties from
expectation-value CCSD theory
Tatiana Korona
University of Warsaw, Faculty of Chemistry
ul. Pasteura 1
02-093 Warsaw, Poland
Expectation-value coupled cluster (CC) theory of first-order molecular properties
[1, 2] is an attractive alternative to response CC theory, as it allows to calculate
these properties without a need to solve an additional expensive set of equations for
the zeroth-order Lagrangian multipliers. On the other hand, the sizes of molecules
treatable by CC theory can be significantly extended if local methods are applied for
electron correlation. In this contribution the accuracy of local approximations has
been studied for expectation-value coupled cluster theory restricted to single and
double excitations (XCCSD), applied to first-order one-electron molecular proper-
ties, such as dipole and quadrupole moments. It has been found that the standard
local settings suitable for the local CCSD energy often lead to significant errors for
the multipole moments. However, the analysis of the Møller-Plesset expansion of the
XCCSD formula allows to formulate a modified set of local approximations, which
is better adapted for a description of first-order properties. The existence of local
options appropriate for the local XCCSD method opens a possibility to perform
low-cost calculations of first-order properties on the local CCSD level [3].
References
[1] Jeziorski, B., Moszynski, R., Int. J. Quantum Chem. 48, 161 (1993).
[2] Korona, T., Jeziorski, B., J. Chem. Phys. 125, 184109 (2006)
[3] Korona, T., submitted to Theor. Chem. Acc.
The 9th Central European Symposium on Theoretical Chemistry
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Internal flexibility of clindamycin
Katarzyna Kulczycka 1,2,* , Joanna Trylska2, Joanna Sadlej3
1Interdisciplinary Centre for Mathematical and Computational Modelling, University of Warsaw
Żwirki i Wigury 9302-089 Warsaw, Poland
2College of Inter-Faculty Individual Studies in Mathematics and Natural Sciences, University of Warsaw
Żwirki i Wigury 9302-089 Warsaw, Poland
3Faculty of Chemistry, University of WarsawPasteura 1
02-093 Warsaw, Poland*[email protected]
Clindamycin is one of the antibiotics (lincosamides) which are used to treat many
diseases caused mostly by Gram-positive bacteria but also to boost immunity.
Lincosamides interact with the large subunit (50S) of the bacterial ribosome and inhibit
the process of bacterial protein synthesis. The increase of resistance in many strains of
bacteria against known antibiotics is caused by their expanded usage in medical practice.
This is a very important reason for continuous work to find new, better, more effective
drugs.
Currently, there are two available structures of clindamycin in the complex with the
50S1,2 ribosomal subunit (Protein Data Bank). The conformations of both antibiotics in
these complexes are significantly different. In this work we investigate internal dynamics
of clindamycin using the Car-Parrinello molecular dynamics. We performed molecular
dynamics simulations starting from both crystal conformers. The CP2K package was
used in our calculations.
[1] Schluenzen, F.; Zarivach, R.; Harms, J.; Bashan, A.; Tocilj, A.; Albrecht, R.; Yonath, A.; Franceschi, F. Nature, 2001, 413, 814-821.[2] Tu D.; Blaha G.; Moore P.B. Steitz TA, Cell, 2005,121, 257-270.
Acknowledgement
The 9th Central European Symposium on Theoretical Chemistry
37
The authors acknowledge support from ICM University of Warsaw (BST1450/2009,
G31-4 and G18-4), Polish Ministry of Science and Higher Education (N N301 245236)
and Foundation for Polish Science (Focus program). The research for this talk was
partially supported by the EU through the European Social Fund, contract number UDA-
POKL.04.01.01-00-072/09-00.
The 9th Central European Symposium on Theoretical Chemistry
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The promotion energy of an atom in a molecule
Istvan Mayer
Chemical Research Center, Hungarian Academy of Sciences
H-1525 Budapest, P.O. Box 17
Hungary
Using the concept of the effective minimal basis set introduced some time ago,
a proper definition is proposed for the atomic promotion energy in the molecule,
which the atom can be assigned after the orbital deformations are introduced but
before any bonding, delocalization and charge transfer effects are taken into account.
The first pivoting calculations indicate that these promotion energies can be quite
substantial and are characteristic for the chemical nature of the atom.
Acknowledgement: Support of the Hungarian Scientific Research Fund—grant OTKA
No. 71816—is acknowledged.
The 9th Central European Symposium on Theoretical Chemistry
39
An extension of the coupled-cluster corrected
configuration interaction method
Leszek Meissner
Institute of Physics, Nicolaus Copernicus University
87-100 Torun, Poland
e-mail: [email protected]
The standard coupled-cluster (CC) approach for correlation energy calculations provides a
set of nonlinear equations for cluster amplitudes and the energy expression. The set of CC
equations is usually solved using Jacobi-type iterative schemes combined with additional pro-
cedures for speeding up the convergence. An alternative route leading to the coupled-cluster
method can be obtained by introducing a modification of the configuration interaction (CI)
matrix. While the first approaches of this type have been called Coupled-Cluster Corrected
CI methods or, more frequently, Coupled Electron Pair Approximations (CEPAs), their
quite recent reformulation using intermediate Hamiltonian formalism is known as the size-
consistent self-consistent CI method ((SC)2 CI). Within the scheme the CC wave function
is partitioned into the linear and nonlinear components and contributions from the latter
one are incorporated through modification of the CI matrix. The solution is obtained by
diagonalization of the dressed CI matrix that must be done in a self-consistent manner since
the dressing depends on the matrix eigenvector. A possible generalization of this approach
can be obtained by treating the problem in a more formal way. The standard set of CC
amplitude equations does not depend on the CC energy that is calculated after determin-
ing the cluster amplitudes, however, simple manipulations can make the equations energy
dependent. A further rearrangement of the equations shows that diagonalization techniques
can be used to solve them. The scheme is quite flexible so even Newton-Raphson algorithm
can be used within this framework. Some numerical examples showing the convergence of
different iterative methods are presented.
The 9th Central European Symposium on Theoretical Chemistry
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A Combined Charge and Energy Decomposition Scheme for Analysis of Chemical Bonds and Reaction Paths
Mariusz P. Mitoraja,b, Artur Michalaka, Tom Zieglerb
a Jagiellonian University, R.Ingardena 3, 30-060 Cracow, Poland. b Department of Chemistry, University of Calgary, 2500 University Dr NW, Calgary, Alberta Canada.
In the present work we have introduced a new scheme for the electronic structure analysis
by combining the Extended Transition State (ETS) method1 with the Natural Orbitals for
Chemical Valence (NOCV)2. The ETS-NOCV3 charge and energy decomposition scheme makes
it not only possible to decompose the deformation density, Δρ, into the different components
(such as σ, π, δ, etc.) of the chemical bond, but it also provides the corresponding energy
contributions to the total bond energy. Thus, the ETS-NOCV scheme offers a compact,
qualitative and quantitative, picture of the chemical bond formation within one common
theoretical framework. The applicability of the ETS-NOCV scheme is demonstrated for various
types of covalent and donor-acceptor bonds. We also included the applications involving inter-
and intra-molecular (agostic) hydrogen bonding (see Figure below). Finally, we will show that
ETS-NOCV can be used not only to analyze the stationary points on PES, but its is also able to
describe the changes in electronic structure along the reaction paths. Decomposition of energetic
reaction barrier into the stabilizing (electronic and electrostatic) and destabilizing (Pauli repulsion
and geometry reorganization) components will be discussed in a detailed way for the examples
of reactions of industrial importance (activation of B-H bond of ammonia borane, β-hydride
eliminations, Diels-Alder cycloadditions).
Figure. The contours of relevant deformation density contributions describing the bonding between the cationic nickel based fragment and the n-propyl group together with the corresponding energies obtained from ETS-NOCV scheme3.
agosticorborb ρρσ ΔΔ ,1
[1] Ziegler, T., Rauk, A. Theor. Chim. Acta 46, 1, (1977). [2] Nalewajski, R.F.; Mrozek, J.; Michalak, A. International Journal of Quantum Chemistry 61,589,(1997); Michalak, A.; Mitoraj, M.; Ziegler, T. J. Phys. Chem. A. 112(9), 1933, (2008). [3] Mariusz P. Mitoraj, Artur Michalak and Tom Ziegler J. Chem. Theory Comput. 5 (4), 962.
The 9th Central European Symposium on Theoretical Chemistry
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Photodynamics of pyrimidine-based molecules: Effect of substitution and initial energy
Dana Nachtigallová1, Mario Barbatti2, Jaroslaw J. Szymczak2 and Hans Lischka1,2
1Institute of Organic Chemistry and Biochemistry, Academy of Sciences of the Czech
Republic, Flemingovo nam. 2, CZ-16610 Prague 6, Czech Republic 2Institute for Theoretical Chemistry – University of Vienna,
Waehrinegrstrasse 17, A 1090 Vienna, Austria
Substitution on the hetero-aromatic ring of the nucleic acid bases and their analogues can
significantly influence their excited state lifetime by changing the location of conical
intersections and/or due to the increasing of barriers on the trajectory towards them.
Consequently a relaxation mechanism responsible for a very rapid internal conversion to the
electronic ground state becomes inefficient.
In this study we present the results of an ab initio on-the-fly surface-hopping dynamics
simulation study of 2,4-diamino-pyrimidine for which the lifetime of the order of picoseconds
was measured.[1] Effect of substitution is discussed by comparison with the excited state
behavior of 4-amino-pyrimidine. Dynamics simulations are performed with different initial
energies to discuss the effect of pump energy used in the experiment.
The substitution on the pyrimidine ring of uracil changes its excited state lifetime
dramatically. Exploring the PES helps to explain this effect caused by changes of reaction
paths towards conical intersections.[2]
[1] Z. Gengeliczki, M. P. Callahan, C. I. Pongor, B. Sztára, D. Nachtigallová, P. Hobza, M.Barbatti, H. Lischka, M. S. de Vries; Phys. Chem. Chem. Phys. 12 (2010), 5375.
[2] D. Nachtigallová, H. Lischka, J.J. Szymczak, M. Barbatti, P. Hobza, Z. Gengeliczki, G. Pino, M. P. Callahan, M. S. de Vries; Phys. Chem. Chem. Phys. 12 (2010), 4924.
The 9th Central European Symposium on Theoretical Chemistry
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Some predictions on stable molecules: failure and success.
László Nyulászi, Oldamur Hollóczki, ...
Budapest University of Technology and Economics Department of Inorganic and Analytical Chemistry
Szt Gellért tér 4 H-1111 Budapest, Hungary
The stability of N-heterocyclic carbenes (NHC) together with their successful
catalytic applications [1] induced a search for other stable compounds with divalent
carbon (CR2 type compounds). We have suggested a simple computational tool for these
predictions: stable carbenes exhibit more than 90 kcal/mol stabilization energy in the
isodesmic reaction below [2].
CR2 + CH4 => CH2 (singlet) + CH2R2
In the meantime all the synthesized new stable carbenes fulfilled this criterium,
while we were not always successful in the use of this simple predicting tool. Further
predictions using more detailed stability checks [3] will also be presented.
The stability of carbene complexes is also an important issue, and the complexes
with main group elements are of particular importance in this respect. Our recent results
on the stability of carbene complexes resulting in hexacoordinate silicon compounds will
be presented showing the “interplay” between computational prediction and experiments.
[1] Arduengo III, A. J.; Bertrand, G. L. Chem. Rev. 2009, 109, 3209-3210.
[2] Forró, A.; Veszprémi, T.; Nyulászi, L. Phys. Chem. Chem. Phys. 2000, 3127.
[3] Hoffmann, R.; Schleyer, P. v. R.; Schaefer, H. F. Angew. Chem. Int. Ed. Engl. 2008,
47, 7164.
The 9th Central European Symposium on Theoretical Chemistry
43
Kinetic equations and dissipation.
Ivana Paidarova 1, Philippe Durand 2
1 J. Heyrovsky Institute of Physical Chemistry, ASCR, v.v.i., Dolejskova 3,
CZ-182 23 Praha 8, Czech Republic2 LCPQ, IRSAMC, Universite de Toulouse et CNRS,
31062 Toulouse cedex 4, France
[email protected], [email protected]
The communication stems from our recent work ”Unstable states: from quantum
mechanics to statistical physics” [1], which represents a synthesis of our contribu-
tions towards a unified formulation of dynamics and thermodynamics of irreversible
processes in the spirit of the ideas of Jaynes [2] and Prigogine [3]. It is achieved
by a formalism borrowed from the quantum theory of resonances. The irreversible
dynamics is described by means of projected resolvents, effective Hamiltonians and
effective Liouvillians. The long macroscopic lifetimes are derived from short micro-
scopic lifetimes by perturbation in the complex plane.
In this talk, we focus on kinetic equations of irreversible processes. We present
an approach which extends the linear response theory to non-linear responses far
from equilibrium. It is shown how the empirical kinetic equations can be justified
by first principles. The approach has a general validity and can be applied to many
domains of physics. The origins and manifestations of the energy dissipation and a
brief discussion of entropy production are revealed by means of three simple dissipa-
tive models in distinct fields of physics and chemistry: chemical kinetics, magnetism
and ferroelasticity.
1. Chemical kinetics. The rate constants of the reaction A ⇀↽ B are determined
from first principles. The model implies an unstable transition state assimi-
lated to a short-lived resonance [4, 5].
2. A non-linear dissipative model of magnetism [6]. The model assumes an ”adia-
batic hypothesis” and links the non-linear response with a kinetic equation that
is analogous to the phenomenological laws of transport appearing in the ex-
tended thermodynamics. The approach is illustrated on an elementary model
The 9th Central European Symposium on Theoretical Chemistry
44
of molecular magnet. We discuss the shapes of the hysteresis loops and give
an energetic and entropic analysis along the lines initiated by Jaynes and Pri-
gogine.
3. Dissipative processes in ferroelastics [7]. A simple model of dissipative pro-
cesses is extended to shape memory alloys displaying a pseudoelastic be-
haviour. The characteristic feature of this model is a three-level response to
the acting stress field describing the transition between two opposite states of
saturation through the intermediate parent structural state. The dissipation
is fully associated with the symmetric part of the response function.
References
[1] I. Paidarova and Ph. Durand in: E. J. Brandas and C. Nicolaides (Eds.) Unsta-
ble States in the Continuous Spectra. Analysis, Concepts, Methods and Results,
Advances in Quantum Chemistry, 60, (2010) (in press)
[2] E. Jaynes, Phys. Rev., 106, 620 (1957)
[3] I. Prigogine, Nature, 246, 67 (1973)
[4] Ph. Durand and I. Paidarova, Int. J. Quantum Chem. (2010), (DOI:
10.1002/qua.22584)
[5] I. Paidarova and Ph. Durand, Int. J. Quantum Chem. (2010), (DOI:
10.1002/qua.22630)
[6] Ph. Durand and I. Paidarova, Europhysics Letters, 89, 67004 (2010)
[7] I. Paidarova, V. Paidar, and Ph. Durand, Solid State Phenomena, Proceedings
of PMT 2010: Solid-Solid Phase Transformation in Inorganic Materials, Avignon
(submitted)
This work was supported by the Grant Agency of the Academy of Sciences of the
CR grant no. IAA401870702.
The 9th Central European Symposium on Theoretical Chemistry
45
Molecular dynamics modeling of half-metallocene titanium(IV) ethylene polymerization catalysts
Łukasz Piękoś, Artur Michalak
K. Gumiński Department of Theoretical Chemistry, Faculty of Chemistry, Jagiellonian University,
R. Ingardena 3, 30-060 Kraków, Poland [email protected]
In the present work results of molecular dynamics simulations of half-metallocene titanium(IV) catalysts are presented. Molecular systems under consideration include non-bridged half-metallocene titanium(IV) complexes with aryloxo ligand acting as catalysts in ethylene polymerization process. Catalysts with various ligands and at various catalytic process stages are considered.
Methodology includes Car-Parinello molecular dynamics on the ab initio DFT level (CPMD software package) and Born-Oppenheimer molecular dynamics on the semiempirical level (MSINDO software package). Despite lower accuracy semiempirical approach is still useful due to ca. 3.5 orders of magnitude difference in performance comparing to DFT approach. Such performance allows for simulations on the timescale far beyond ab initio methods. Free molecular dynamics is used to study spontaneous transitions (including conformational changes and ethylene insertion reactions). Constrained molecular dynamics in slow-growth approach is used to obtain free energy profiles of ethylene insertion reaction.
Presented results include spontaneous conformational transitions affecting catalyst reactivity. Example where six stable conformations (including several transitions between them) can be observed on one simulation is also presented. Spontaneous insertion of ethylene is observed, followed by conformational changes which make catalytic cycle in one simulation.
Projections of presented trajectories (i.e. plots of selected coordinates) as well as animated visualizations are presented.
The 9th Central European Symposium on Theoretical Chemistry
46
Relativistic, QED and nonadiabatic effects in the
interaction of hydrogen atoms
Konrad Piszczatowski†, Grzegorz �Lach†, Micha�l Przybytek†, Jacek Komasa§,
Krzysztof Pachucki‡, Robert Moszynski†, Bogumi�l Jeziorski†
†Faculty of Chemistry, University of Warsaw
Pasteura 1
02-093 Warszawa, Poland
§ Faculty of Chemistry, A. Mickiewicz University
Grunwaldzka 6
60-780 Poznan, Poland
‡ Institute of Theoretical Physics, University of Warsaw
Hoza 69
00-681 Warszawa, Poland
The dissociation energy of molecular hydrogen was determined theoretically with
a careful estimation of error bars by including nonadiabatic, relativistic, and quan-
tum electrodynamics (QED) corrections. The relativistic and QED corrections were
obtained at the adiabatic level of theory by including all contributions of the order
α2 and α
3 as well as the major (one-loop) α4 term, where α is the fine structure
constant. The computed α0, α
2, α3, and α
4 components of the dissociation energy
of the H2 isotopomer are 36118.7978(2), −0.5319(3), −0.1948(2), and −0.0016(8)
cm−1, respectively, while their sum amounts to 36118.0695(10) cm−1 [1], where
the total uncertainty includes the estimated size (±0.0003 cm−1) of the neglected
relativistic nonadiabatic/recoil corrections. The obtained theoretical value of the
dissociation energy is in excellent agreement with the most recent experimental de-
termination 36118.0696(4) cm−1 [2]. This agreement would have been impossible
without inclusion of several subtle QED contributions which have not been consid-
ered thus far for molecules. A similarly good agreement is observed for the leading
vibrational and rotational energy differences.
For the D2 molecule our theoretical value of the dissociation energy 36748.3633(9)
cm−1 [1] was significantly different from the experimental value 36748.343(10) cm−1
The 9th Central European Symposium on Theoretical Chemistry
47
[3]. However, the most recent measurements [4] gave the value 36748.3629(7) cm−1,
which is in complete agreement with our result.
Using perturbative theory of nonadiabatic effects proposed by Pachucki and Ko-
masa [5] as well as our relativistic and QED corrections to the interaction potential
we have also calculated the s-wave scattering length for H – H collisions in the elec-
tronic singlet state [6]. The nonadiabatic value (0.2732 bohr) differs by about 40%
from the adiabatic one (0.4316 bohr). However, we have found that using atomic
reduced mass instead of nuclear one in the adiabatic calcualtions, we are able to
reproduce the nonadiabatic result with an error of less than 3%.
References
[1] K. Piszczatowski, G. �Lach, M. Przybytek, J. Komasa, K. Pachucki, and B.
Jeziorski, J. Chem. Theory Comput. 5, 3039 (2009).
[2] J. Liu, E. J. Salumbides, U. Hollenstein, J. C. J. Koelemeji, K. S. E. Eikema,
W. Ubachs, and F. Merkt, J. Chem. Phys. 130, 174306 (2009).
[3] Y. P. Zhang, C. H. Cheng, J. T. Kim, J. Stanojevic, E. E. Eyler, Phys. Rev.
Lett 92, 203003 (2004).
[4] J. Liu, D. Sprecher, C. Jungen, W. Ubachs, and F. Merkt, J. Chem. Phys 132,
154301 (2010).
[5] K. Pachucki and J. Komasa, J. Chem. Phys. 129, 034102 (2008).
[6] K. Piszczatowski, J. Komasa, K. Pachucki, A. van der Avoird,
G. C. Groenemboom, R. Moszynski, B. Jeziorski – to be published.
The 9th Central European Symposium on Theoretical Chemistry
48
Gaussian and Finite-Element method
for the calculation of Coulomb integrals
Micha�l Przybytek, Trygve Helgaker
Center for Theoretical and Computational Chemistry
University of Oslo
Postbox 1033, Blindern
0315 Oslo, Norway
One of the most important challenges in the present time computational chemistry
is an efficient treatment of large biomolecular systems and nanomaterials comprising
as many as several thousands atoms. Both the most popular quantum chemical
methods which can be used for such systems, Hartree-Fock and Density Functional
Theory, need calculation of the Coulomb integrals. In the orbital approach, when
the Gaussian basis set is employed, the number of the Coulomb integrals (and thus
the computational cost) scales as O(N4), where N is the number of atoms. For that
reason, the calculations for truly large systems become prohibitively expensive, and
therefore much effort has been made to reduce the scaling of the computational cost,
possibly down to the most desirable linear O(N) regime.
One of the techniques aimed to achieve the linear scaling in the problem of comput-
ing the matrix elements of the Coulomb operator is the Gaussian and Final-Element
Coulomb method proposed originally in 2007 in the group of Kimihiko Hirao [1]. The
method consists of two main stages. First, the Poisson equation ∇2V (r) = −4πρ(r)
is solved to obtain the potential V (r) related to the electronic density given by ρ(r).
The potential is expanded in a mixed basis set consisting of two types of functions.
The Finite-Element shape functions describe the smooth part of the potential, while
the Gaussian functions with preoptimized exponents and centered on atoms are re-
sponsible for expressing the large variations of the potential close to the nuclei. The
expansion coefficients are obtained by means of solving large and sparse system of
linear equations. In the second stage, the matrix elements of the Coulomb operator
The 9th Central European Symposium on Theoretical Chemistry
49
are actually calculated as an overlap integral Jab = �φaφb|V � =∫
φa(r)φb(r)V (r) dr.
As a result, in the Gaussian and Finite-Element method the problem of calculat-
ing four-center two-electron integrals with the integral kernel 1/r12 is reduced to
the problem of evaluating two- and three-center one-electron overlap integrals (with
functions of different kind) and solving the system of linear equations. Therefore
the computational cost and scaling property for large systems can be significantly
reduced.
References
[1] Y. Kurashige, T. Nakajima, and K. Hirao, J. Chem. Phys. 126, 144106 (2007).
The 9th Central European Symposium on Theoretical Chemistry
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DFT Studies on Catalytic Oxidation of Cyclohexene on Manganese Porphyrins
Dorota Rutkowska-Zbik, Malgorzata Witko
Institute of Catalysis and Surface Chemistry, PAS ul. Niezapominajek 8
30-239 Krakow, Poland [email protected]
Among popular homogeneous catalysts for hydrocarbon oxidation,
metalloporphyrins play a crucial role. This is due to their biological function as cofactors
in P450 class of enzymes responsible for bio-oxidation of both endogenous and
exogenous compounds. On the one hand, metalloporphyrins are able to insert oxygen
atom into C-H bonds, on the other, they may deliver oxygen atom to the double C=C
bonds, yielding epoxide. This dual reactivity is clearly manifested in the case of alkenes,
whose C=C bond and potentially reactive single C-H bonds in α (allylic) position with
respect to the double bond, are both prone to oxygenation. In particular, experiments with
cyclohexene oxidation catalyzed by metalloporphyrins showed that, beside the
cyclohexane oxide, unsaturated products of allylic oxidation (cyclohexen-3-ol and
cyclohexen-3-on) are formed, and the final selectivity pattern is determined by a
competition between the allylic C-H bond and the C=C double bond for the catalyst.
Therefore, the aim of the present work is the theoretical investigation of manganese
porphyrin reactivity towards cyclohexene by using DFT to study the epoxidation and
hydroxylation pathways. For geometric structure evaluation the LDA-VWN and GGA-
BP86 functionals are used. Electronic parameters of the systems are obtained at the
GGA-BP86 and GGA-RPBE levels. Extended all-electron basis sets of contracted
Gaussians are applied. For singlet state systems calculations are performed in a spin-
polarized manner. The charge transfers accompanying complex formations are accounted
for by changes of Mulliken charges for selected atoms or fragments of investigated
systems. The covalent strength of the bonds is measured by Mayer bond indices.
Additionally, spin densities are computed.
The calculations show that a physisorbed prereaction complex is formed in the first
stage of interaction between cyclohexene and manganese porphyrin. Although allylic
The 9th Central European Symposium on Theoretical Chemistry
51
hydroxylation and epoxidation are initiated by different physisorbed prereaction
complexes, they may transform into each other. Once beyond the stage of physisorption,
the substrate is not able to switch easily between the reactivity funnels.
Formation of cyclohexen-2-ol proceeds via oxygen rebound mechanism. The
hydrogen atom is abstracted by the catalyst oxo group. The analysis of the energy profile
for the reaction indicates that the alcohol is formed after the hydrogen migration step
without prior dissociation of the hydrocarbon radical from the catalyst active site. The
reaction involves spin crossing since the catalyst is initially in its singlet state, while
during catalytic process it is promoted to its triplet state.
The key intermediate on the reaction pathway leading to epoxide lies lower on the
potential energy surface than the intermediate leading to alcohol, which explains high
reactivity of manganese porphyrins toward olefin epoxidation.
The intermediate structures, found for both pathways, clearly indicate that each may
lead to only one reaction product.
The 9th Central European Symposium on Theoretical Chemistry
52
Orbital Optimized Second-Order Many-Body Perturbation Theory Via Coupled Cluster Ansatz
Ján Šimuneka, Jozef Nogaa,b
a Department of Inorganic Chemistry, Faculty of Natural Sciences, Comenius University Mlynská dolina CH2
SK-84215 Bratislava, Slovakia [email protected]
b Institute of Inorganic Chemistry, Slovak Academy of Sciences SK-84215 Bratislava, Slovakia
Recently, we have published a study on the one-particle basis set relaxation effect in the
explicitly correlated coupled cluster theory.[1] Our primary goal was to show the error
introduced by the assumption of the generalized Brillouin theorem when one uses the
explicitly correlated R12 based methods with relatively small main computational
(atomic orbital) basis sets. Among others, we have investigated the performance of the
traditional coupled cluster singles (CCS) model if one starts from the reference
determinant corresponding to a Hartree-Fock (HF) solution with very small (or minimal)
basis set, while in the subsequent CCS calculation the virtual space is created using a
much larger basis set. Due to the Thouless theorem [2] the result should be close to the
HF solution with this large basis, nevertheless, it deviates from the correct solution due to
the non-variational nature of the traditional CCS solution. Our observation was that the
energies were generally overestimated. Obviously, variational treatment of coupled
cluster singles (VCCS) leads to the Hartree-Fock solution but such an approach gives rise
to an infinite expansion of connected terms of the effective Hamiltonian. We have
proposed an alternative new approach to obtain the Slater determinant ground state
solution within an independent-particle approximation using the exponential ansatz for
the wave function (Thouless theorem) and exact treatment in terms of variational coupled
cluster singles [3,4].
The 9th Central European Symposium on Theoretical Chemistry
53
Based on our previous work, we propose orbital optimized second-order many-
body perturbation theory via coupled cluster Ansatz. Comparison with conventional CC2
approach will be presented for small set of reactions.
[1] Noga, J.; Šimunek, J. Chem. Phys. 2009, 356, 1-6.
[2] Thouless, D. J. Nucl. Phys. 1960, 21, 225-232.
[3] Šimunek, J.; Noga, J. AIP Conf. Proc. 2010, in press.
[4] Noga, J.; Šimunek, J. Chem. Theory Comput. 2010, in press.
Acknowledgement
This work has been supported by the Alexander von Humboldt Foundation.
Support from the Grant Agency of the Ministry of Education of the Slovak Republic and
Slovak Academy of Sciences VEGA project No. 2/0079/09 as well as by the Slovak
Research and Development Agency (LPP-0031-07) are also acknowledged. This work
has benefitted from the Centers of Excellence program of the Slovak Academy of
Sciences (COMCHEM, Contract no. II/1/2007).
The 9th Central European Symposium on Theoretical Chemistry
54
Quantum mechanics and mathematical statistics
L. Skala, V. Kapsa,
Charles University, Faculty of Mathematics and Physics, Ke Karlovu 3, 121 16 Prague 2, Czech Republic
University of Waterloo, Department of Applied Mathematics, Waterloo, Ontario N2L 3G1, Canada
Basic mathematical apparatus of quantum mechanics like the wave function, coordinate
and momentum operator, corresponding commutation relation, kinetic energy, uncertainty
relations, continuity equation and equations of motion is discussed from the point of view of
probability theory and mathematical statistics. It is shown that the mathematical structure of
quantum mechanics can be understood as generalization of classical mechanics in which the
statistical charakter of results of measurement is taken into account and general properties of
statistical theories are correctly respected.
The 9th Central European Symposium on Theoretical Chemistry
55
The problem of small coefficients in SS-MRPT
Agnes Szabados
Laboratory of Theoretical Chemistry, Lorand Eotvos University
Pazmany Peter setany 1/A
1117 Budapest, Hungary
Among various multireference perturbation approaches (MRPT) the state-specific
(SS) MRPT developed by Mukherjee et al.[1] is one that possesses many desirable
features. Derived from the parent coupled-cluster (CC) theory, SS-MRPT operates
with the Jeziorski-Monkhorst parametrization of the wavefunction. When com-
puting the PT approximation, amplitude equations are linearized, and the energy
correction is computed as the eigenvalue of the second order effective Hamiltonian.
In spite of the manifest intruder free character of the theory, we have found
unexpected divergences in our recent SS-MRPT studies[2]. The effect can be con-
sidered as a PT counterpart of convergence difficulties experienced in related CC
methods[3, 4]. The source of the problem has been attributed to small coefficients
figuring in the expansion of the reference function.
In the present study we give a perturbative analysis of the eigenvalue equation
of the effective Hamiltonian and look for appropriate workarounds of the divergence
problem.
References
[1] P. Ghosh, S. Chattopadhyay, D. Jana, D. Mukherjee, Int. J. Mol. Sci. 3, 733
(2002).
[2] M. R. Hoffmann, D. Datta, S. Das, D. Mukherjee, A. Szabados, Z. Rolik, P. R.
Surjn, J. Chem. Phys. 131 204104 (2009).
[3] A. Engels-Putzka, M. Hanrath, Mol. Phys. 107, 143 (2009).
[4] M. Kallay, S. Das, J. Chem. Phys. 132, 074103 (2010).
The 9th Central European Symposium on Theoretical Chemistry
56
Jahn-Teller distortion and zero-field-splitting in
carbon nanotubes
Peter Szakacs and Peter R. Surjan
Eotvos Lorand University, Laboratory of Theoretical ChemistryPazmany Peter setany 1/A
H-1117 Budapest
The splitting of the spatial and the spin degeneracy in triplett carbon nanotubes
was studied.
Ionized or excited carbon nanotubes corresponding to Cnv pointgroup undergo
Jahn-Teller distortion, if at least one open shell degenerate molecular orbital exsists
in the system [1]. The Jahn-Teller distortion energy was calculated to describe the
degree of the distortion. The magnitude of the phenomenon was found to decrease
with increasing tube length or tube diameter. Calculations were carried out using
the semiempirical modell of Longuett-Higgins and Salem. This method is able to
optimize bond lengths.
Relativistic effects like spin-spin coupling may resolve the degeneracy of MS = 0
states, e.g. triplets (zero-field-splitting, ZFS). The amount of energy splitting is
usually very small. Dependence of ZFS on tube length, Jahn-Teller distortion, tube
diameter and chirality of the tube was investigated using the XHUGE (extended
Hubbard method with geometry optimization) semiempirical method [2].
References
[1] P. Szakacs, D. Kocsis, P. R. Surjan, J. Chem. Phys 132, 034309, 2010.
[2] P. Szakacs, A. Szabados, P. R. Surjan submitted.
The 9th Central European Symposium on Theoretical Chemistry
57
The Brillouin zone integration problem in density
fitting of extended systems
Stefan Varga
Institute of Inorganic Chemistry, Slovak Academy of SciencesDubravska cesta 9
SK-845 36 Bratislava, Slovak Republic
Except for the special case of the Coulomb repulsion contribution [1–3], reciprocal
space integration cannot be avoided when applying the density fitting formalism to
infinite systems with translational periodicity [4, 5]. Careless application of usual
quadrature schemes can be an insidious source of additional numerical error in this
case. The situation is especially unpleasant when working with slow decay Coulomb
fitting metric. We analyse this case and show that it indeed leads to difficult-to-
integrate functions. A simple way how to reformulate the problem in the form
of smooth, easily integrable terms is suggested. Implementation and illustrative
calculations on one-dimensional infinite chain systems are presented as well.
References
[1] S. Varga, M. Milko, J. Noga, J. Chem. Phys. 124, 034106 (2006)
[2] S. Varga, Int. J. Quantum Chem. 108, 1518 (2008)
[3] A. M. Burow, M. Sierka, F. Mohamed, J. Chem. Phys. 131, 214101 (2009)
[4] S. Varga, Phys. Rev. B 71, 073103 (2005)
[5] L. Maschio, D. Usvyat, F. R. Manby, S. Casassa, C. Pisani, M. Schutz,
Phys. Rev. B 76, 075101 (2007)
Acknowledgement. Financial support from COMCHEM, a virtual Center for
Advanced Computational Chemistry sponsored by the Slovak Academy of Sciences
and from Slovak grant agency VEGA (Grant No. 2/0079/09) is acknowledged.
The 9th Central European Symposium on Theoretical Chemistry
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Quantum chemical computations on quantum
computers
Libor Veis and Jirı Pittner
J. Heyrovsky Institute of Physical Chemistry, Academy of Sciences of the Czech
Republic, v.v.i.
Dolejskova 3
18223 Prague 8, Czech Republic
[email protected], [email protected]
Quantum computers are appealing for their ability to solve some tasks much
faster than their classical counterparts, e.g. efficiently factore integers. Also quan-
tum physics (chemistry) could in principle benefit from them. One possibility is an
efficient solution of many-body Hamiltonian eigenvalue problem [1]. As was shown
in the seminal work by Aspuru-Guzik et. al. [2], quantum computers, if available,
would be able to perform the full configuration interaction (FCI) energy calcula-
tions with only a polynomial scaling. This is of course in contrast to conventional
computers where FCI scales exponentially.
We have developed a code for simulation of quantum computers and implemented
our version of the quantum full configuration interaction (QFCI) method which
uses the iterative phase estimation algorithm [3]. This approach reduces demands
on the total number of quantum bits (qubits) as only one is needed in the read-
out part of the quantum register and the whole algorithm proceeds in an iterative
manner. We have tested its performance on the four lowest lying electronic states of
methylene molecule (CH2). This molecule was chosen as a benchmark, because both
of the lowest lying 1A1 states exhibit a multireference character at the equilibrium
geometry.
It has been shown that with a suitably chosen initial state of the quantum register,
one is able to achieve the probability amplification regime of the iterative phase
estimation even in this case.
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References
[1] D. S. Abrams and S. Lloyd, Phys. Rev. Lett. 83, 5162 (1999).
[2] A. Aspuru-Guzik, A. D. Dutoi, P. J. Love, and M. Head-Gordon, Science 309,
1704 (2005).
[3] M. Dobsıcek, G. Johansson, V. Shumeiko, and G. Wendin, Phys. Rev. A 76,
030306 (2007).
The authors gratefully acknowledge the financial support of the Grant Agency of
the Czech Republic (grant no. 203/08/0626) and the Grant Agency of the Charles
University in Prague (grant no. 114310).
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Structural changes in the water tetramer and hexamer. A combined Monte Carlo and DFT study.
Aleš Víteka), Lenka Ličmanováa), Ivana Paidarováb), René Kalusa)
a)University of Ostrava, Department of Physics,
30. dubna 22, 701 03 Ostrava, Czech Republic.
b)J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic,
Dolejškova 3,182 23 Praha 8, Czech Republic
From the point of view of theoreticians, molecular clusters are generally considered
the most challenging objects of molecular physics, mainly due to many degrees of
freedom and the configuration space extremely complicated. The primary importance of
water clusters among molecular clusters is presently beyond any doubt. Their relevance
for atmospheric chemistry as well as for biological applications has been mentioned
many times in the literature.
In the past, many thermodynamical simulations have been performed for water
clusters, using simple empirical (e. g. TIPnP, n = 3, 4, 5, 6) [1 – 3] or semiempirical (e. g.
TTM3F) [4] interaction models. It has been shown, that theoretically calculated
thermodynamical properties (e. g. heat capacity curve) depends very sensitively on used
interaction model and small change of description of potential energy surface leads to
completely different theoretical results.
On the other hand, a time demandingness of accurate high level quantum chemistry
methods is the reason, why haven’t been used for thermodynamic simulations that require
large amounts of repeated calculations of energy in different configurations (of the order
of thousands to millions).
Our work is focused on simulation of water tetramer and hexamer using parallel
tempering Monte Carlo. Heat capacity curves have been calculated for temperature
interval 25 – 225 K. Simulated annealing method has been used to obtain frequency of
occurrence of isomers for different temperatures. Our empirical interaction models used
The 9th Central European Symposium on Theoretical Chemistry
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in Monte Carlo simulations are based on modified TIP6P potential improved by inclusion
of polarizable energy via induced dipoles. Parameters are adjusted on DFT energies of
representative sets of configurations directly of water tetramer or hexamer.
The B97-1 exchange-correlation functional has been used in the present work
together with augmented correlation-consistent basis sets of atomic orbitals up to triple-
zeta quality. The DFT data have been corrected using an empirical correction scheme.
Such a correction doesn’t raise the computational costs, however, with the combination of
the DFT enable to achieve energies close to those obtained by high-level quantum
chemistry methods.
We have also developed a new combination of Boltzmann-reweighting [5] and
multiple histograms [6] methods together with parallel tempering Monte Carlo in order to
obtain the thermodynamic data of clusters in the quantum chemical accuracy. This
approach reduce significantly the number of required repeated quantum chemistry
calculations to acceptable amount, thus only thousands of quantum chemistry energies
are sufficient for well converged thermodynamical data.
[1] W. L. Jorgensen and J. J. Tirado-Rivers, J. Am. Chem. Soc. 110, 1657 (1988).
[2] M. W. Mahoney and W. L. Jorgensen, J. Chem. Phys. 112, 8910 (2000).
[3] H. Nada and J. P. J. M. Eerden, J. Chem. Phys. 118, 7401 (2003).
[4] G. S. Fanourgakis and S. S. Xanteas, J. Chem. Phys. 128, Art. No. 074506 (2008).
[5] J. P. Hansen and I. R. MacDonald, Theory of simple liquids (Academic Press, London, 1986).
[6] A. M. Ferrenberg and R. H. Swendsen, Phys. Rev. Lett. 63, 1195 (1989).
Acknowledgement The work has been financially supported by the Grant Agency of the Academy of Sciences of the Czech Republic (grant no. IAA401870702).
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Electron Correlation Calculations with Strictly LocalizedOrbitals
Zoboki Tamás(a), Mayer István (b) , Surján R. Péter(a)
(a) Eötvös Loránd University, Institute of Chemistry, Laboratory of TheoreticalChemistry
Pázmány Péter sétány 1/A1117 Budapest, Hungary
(b) Chemical Research Center, Hungarian Academy of SciencesH-1525 Budapest, P.O. Box 17, Hungary
In this work, different types of computational methods are presented in order to app-
roximate the correlation energy for a given molecular fragment chosen on the basis of our
chemical intuition. For this purpose we use strictly localized molecular orbitals (SLMOs)
which have the maximal projection in the occupied subspace. It can be shown that if
we project these SLMOs in the occupied space we get their counterparts which are exact
occupied orbitals and also extremely localized[1]. The SLMOs and their projections are
paired in the sense of Löwdin’s pairing theorem.
For approximating the correlation energy, we introduce three different types of appro-
aches all based on the usage of the active block of the Fockian[2].
[1] T. Zoboki, I. Mayer, J. Comp. Chem. (2010) accepted
[2] P. R. Surján, I. Mayer, T. Zoboki in preparation
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POSTERS
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Energy decomposition of alkyl-substituted furan molecules
Dóra Barna, Gyula Tasi
Department of Applied and Environmental Chemistry, University of Szeged
Rerrich B. tér 1. H-6720, Szeged, Hungary
The total energy is perhaps the most significant outcome of a quantum chemical
computation. But despite all of its importance the total energy is only a single number saying
nothing about the interactions present in the system from a chemical point of view. In order to
obtain a detailed and more useful description of the occurring interactions, one should
decompose the total energy into atomic and diatomic contributions which are chemically
meaningful. To do this, one can choose from several, more or less arbitrary decomposition
techniques. One of them [1] is based on the extended virial theorem [2], which, within the
Born-Oppenheimer framework, applies for general (not necessarily variational) wave
functions built up by using finite local one-electron basis sets. In addition to the energy
decomposition, the extended virial theorem makes the evaluation of the quantum chemical
basis sets possible. The extended formula contains three virials because of the fixed nuclei as
well as the fixed centers and exponents of the basis functions, and after its rearrangement, one
can express the total energy with the help of the kinetic energy and the virials.
2 2 0q jq j jqHF
E E ET V R P T V R P ZR Pα
α α
ςς
∂ ∂ ∂+ + + − = + + ∆ + ∆ + ∆ =∂∂ ∂∑ ∑ ∑
eq. (1)
( )E T V T R P Z= + = − − ∆ + ∆ + ∆ eq. (2)
In the stationary points of the potential energy surface together with the basis functions
centered on the nuclei, i.e., using atomic orbitals and assuming “orbital following”, eqs. (1)
and (2) reduce to eqs. (3) and (4).
2 0T V Z+ + ∆ = eq. (3)
E T Z= − − ∆ eq. (4)
This last equation obtained for the total energy can be applied to its exact decomposition into
atomic ( ( )E A ) and diatomic ( ( )E AB ) components.
( ) ( ) ( ) ( )12A A B A A B
E E A E AB E A E AB> ≠
= + = +∑ ∑ ∑ ∑ eq. (5)
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But on formation of a molecule, the states of the atoms involved undergo changes. It is also
obvious that, for a particular element, the atomic energy component depends on the chemical
environment. To get diatomic energies, which are characteristic of the interatomic interactions
present in the system, one might set the atomic energies ( ( )E A ) to the value of the free atoms
( ( )0E A ), via partial redistribution of the original diatomic energy components [3].
( ) ( ) ( ) ( )~
0 AB A
E A E A E A E ABλ≠
= = + ∑ eq. (6)
( ) ( )( ) ( )~
1 A BE AB E ABλ λ= − + eq. (7)
The new diatomic energy components ( ( )~E AB ) now contain all the energy changes due to
the formation of the molecule.
This decomposition method, when performed on an adequate theoretical level, results
in diatomic energy contributions which, after the partial redistribution, are “on the chemical
scale”. The second order Møller–Plesset perturbation (MP2) level is accurate enough to
characterize the strength of the chemical bonds present in the system. The results of these
calculations reflect the experimental bond dissociation energies quite accurately, especially in
the case of the diatomic molecules. The best example is the new diatomic energy component
obtained at the MP2 level for the carbon monoxide, which is equal to the bond dissociation
energy within the experimental error reported. The order of the experimental bond
dissociation energies of various carbon-oxygen and carbon-carbon bonds can also be
reproduced with the transformed diatomic energy contributions.
The energy decomposition based on the extended virial theorem was used on some
alkyl-substituted furan molecules. With the help of the resulted transformed diatomic
contributions the strength of the various carbon-carbon and carbon-hydrogen bonds as well as
the order of the bonding energies were evaluated. This order might be interpreted on the basis
of the number and position of the alkyl groups in the molecule. But in absence of
experimental bond dissociation energies to support the outcome of the energy decomposition
one would need results of high-level theoretical model chemistries, which computations
would be very time-consuming.
[1] G. Tasi, D. Barna, Int. J. Quant. Chem. 109. (2009) 2599.
[2] G. Tasi, I. Mayer, Chem. Phys. Lett. 449 (2007) 221.
[3] S. F. Vyboishchikov, Int. J. Quant. Chem. 108. (2008) 708.
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Relativistic effects vs. X-ray constrained Hartree Fock
L. Bucinsky, J. Kozisek, S. Biskupic, D. Jayatilaka and M. Gall
Institute of Physical Chemistry and Chemical Physics, STU-Bratislava
Radlinského 9
SK-812 37 Bratislava, Slovaka
This study is presenting the relativistic effects and the effects of the X-ray constrained
Hartree-Fock/DFT (XC-HF) approach [1] for the mer,trans-[Ru(Cl)3(Hind)2(NO)]
complex. The quasirelativistic infinite order two component (IOTC) [2,3] and Douglas-
Kroll-Hess 2nd order (DKH2) [4,5] calculations were carried out at both 1-component
(scalar relativistic effects) and 2-component (scalar relativistic effects + SO coupling)
level of theory. The experimentally determined (X-ray refinement) charge density is
compared with XC-HF and XC-BLYP electron density. The X-ray constraint and
relativistic effects in electron densities as well as the difference of the DKH2 and IOTC
electron densities are presented. Picture change effects [6,7] in the DKH2 and IOTC
electron density and structure factors of the studied compound are investigated by
analytical means. The relativistic effects and PCE is considered also for radial
distribution of (NR, DKH2, IOTC, DCH)electron densities of the radon atom. The PCE
correction of DKH2 and IOTC electron densities and structure factors was performed
using the Tonto software package [8].
[1] Jayatilaka, D. & Grimwood, D. J. (2001). Acta Cryst. A57, 76-86.
[2] Barysz, M. & Sadlej, A. J. (2002) J. Chem. Phys. 116, 2696.
[3] Kędziera, D., Barysz, M. (2007) Chem. Phys. Lett. 446, 176.
[4] Wolf, A., Reiher, M. & Hess, B. A. (2002). J. Chem. Phys. 117, 9215-9226.
[5] Reiher, M. & Wolf, A. (2004a). J. Chem. Phys. 121, 2037-2047.
[6] Wolf, A. & Reiher, M. (2006a). J. Chem. Phys. 124, 064102.
[7] Mastarlez, R., Lindth, R. & Reiher, M. (2008). Chem. Phys. Lett. 465, 157-164.
[8] Jayatilaka, D. & Grimwood, D. J. (2000). TONTO. A Research Tool for Quantum
Chemistry. The University of Western Australia, Nedlands, Western Australia, Australia.
see at: http://www.theochem.uwa.edu.au/tonto
Acknowledgement
The support from the grants: APVV (contract No. APVV-0093-07) and VEGA (contracts
No. 1/0817/08 and 1/0127/09) is gratefully acknowledged.
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Weak interactions between air pollutants
Šimon Budzák1, Ivan Černušák2, Miroslav Medveď1
1 Department of Chemistry, Faculty of Natural Sciences, Matej Bel University, Tajovského 40, SK-97400 Banská Bystrica, Slovakia, [email protected],
2 Department of Physical and Theoretical Chemistry, Faculty of Natural Sciences, Comenius University, Mlynská dolina, SK-842 15 Bratislava, Slovakia,
Carbon monoxide belongs to important air pollutants. It constitutes substantial part of the fuel emissions, represents non-negligible part of the cigarette-smoke and is also present in volcanic gases [1]. In this contribution we investigate the intermolecular interactions of neutral H2O, SO2 species and important atmospheric ion NO+ with CO.
Weak interactions in this dimers were studied with standard ab initio methods including MP2 and CCSD(T) method, using augmented correlation corrected polarized series of basis sets. Due to large computational demands the OVOS (Optimized virtual orbital space) approach was used. Interaction energy and its components, vibrational spectra and dipole moments for local minima are reported. In order to find in which layer of atmosphere is formation of such complexes possible, the dependence of Gibbs energy of their formation on temperature was studied.
In the most stable conformations the carbon atom of CO is oriented towards the partner molecule (see Figure 1). The interaction energies are: -32.3 kJ/mol for NO+...CO, -8.2 kJ/mol for CO...H2O and -7.0 kJ/mol for CO...SO2, while the Gibbs energies are -10.5 kJ/mol for NO+...CO, 14.3 kJ/mol for CO...H2O and 6.4 kJ/mol for CO...SO2 at 200 K during the night in the troposphere.
Figure 1 Most stable conformations of studied dimmers
The 9th Central European Symposium on Theoretical Chemistry
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[1] Barbara J, Pitts F, Pitts JN. Chemistry of the Upper and Lower Atmosphere, Amsterdam: Elsevier, 2000.
AcknowledgementWe appreciate the financial support from Slovak Grant Agency VEGA (grant 1/0428/09) and Matej Bel University Grant Agency (grant 02/02/2010)
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A Theoretical Study of the H-abstraction Reactions of H2, H2O, HI,and OH by the IO (2Π3/2) Radicals
Sébastien CANNEAUX,a,d Catherine HAMMAECHER,bFlorent LOUIS, a,d Laurent CANTRELc,d
a PhysicoChimie des Processus de Combustion et de l’Atmosphère (PC2A) UMR 8522 CNRS/Lille1, Université Lille 1 Sciences et Technologies, Cité scientifique, Bât C11/C5, 59655 Villeneuve d’Ascq Cedex, France b Université Catholique de Louvain, Bâtiment Lavoisier, Place L. Pasteur 1, B-1348 Louvain-la-Neuve, Belgiumc Institut de Radioprotection et de Sûreté Nucléaire, DPAM, Centre de Cadarache, BP3, 13115 Saint Paul Lez Durance, Cedex, Franced Laboratoire de Recherche Commun IRSN-CNRS-Lille1 "Cinétique Chimique, Combustion, Réactivité" (C3R), Centre de Cadarache, BP3, 13115 Saint Paul Lez Durance, Cedex, France
During a loss-of-coolant accident due to a break in the Reactor Coolant System
(RCS) of a nuclear Pressurized Water Reactors (PWR), part of the nuclear fuel could
melt and release fission products which will be transported through the RCS and its break
to the reactor containment building, and then possibly to the environment. Radioiodine is
one of the most radiotoxic fission products released from the damaged fuel due to its
ability to form volatile species, and the potential accidental release of volatile iodine to
the environment is a key safety issue for emergency response planning. The gaseous part
of iodine at the RCS break has a great impact on the potential iodine outside releases, and
kinetic limitations occuring in gaseous phase are suspected to promote gaseous iodine
species. To better predict the iodine speciation reaching the containment building,
depending on accident scenarios, the thermokinetic parameters of the main gaseous
reactions which govern the overall iodine behavior in the RCS have to be determined.
Such kinetic reactions could be later implemented in the ASTEC severe accident
simulation software.
In a first step, the reactions of iodine atoms I (2P3/2) with H2, H2O, HI, and OH have
been studied theoretically [1]. The aim of this methodological work was to demonstrate
that standard theoretical methods are adequate to obtain quantitative rate constants for the
reactions involving iodine-containing species.
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In a second step, the computational procedure has been extended to some relevant
reactions involving the iodine oxide radical IO in its ground state (2Π3/2) and the same
species (H2, H2O, HI, and OH). Quantum chemistry calculations and TST kinetic models
are used in this work to compute the temperature dependence of the rate constants for the
abstraction reactions by iodine oxide radicals. Results will be presented and discussed in
this poster.
[1] Canneaux, S.; Xerri, B.; Louis, F. ; Cantrel, L. J. Phys. Chem. A, 2010, in press.
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SPyDERS: MD Modelling Software for Nuclear Safety
Sébastien CANNEAUX,a,c Eddy THIRIOT,b,c Florent LOUIS, a,c Laurent CANTRELb,c
a PhysicoChimie des Processus de Combustion et de l’Atmosphère (PC2A) UMR 8522 CNRS/Lille1 , Université Lille 1 Sciences et Technologies, Cité scientifique, Bât C11/C5, 59655 Villeneuve d’Ascq Cedex, France b Institut de Radioprotection et de Sûreté Nucléaire, DPAM, Centre de Cadarache, BP3, 13115 Saint Paul Lez Durance, Cedex, Francec Laboratoire de Recherche Commun IRSN-CNRS-Lille1 "Cinétique Chimique, Combustion, Réactivité" (C3R), Centre de Cadarache, BP3, 13115 Saint Paul Lez Durance, Cedex, France
The French Institut de Radioprotection et de Sûreté Nucléaire (IRSN) and the
German Gesellschaft für Anlagen und Reaktorsicherheit mbH (GRS) are jointly
developing the ASTEC (Accident Source Term Evaluation Code) software to simulate
severe accidents, which can arise in a pressured-water nuclear reactor (PWR), from
initiating event up to the possible radiological release of fission products (FP) outside.
IODE module of ASTEC is devoted to model the FP behavior inside the nuclear
containment building and more especially the iodine radiochemistry. The FP modeling, in
terms of physical chemistry processing, need the knowledge of numerous properties
which some cannot be experimentally determined. Thus, cooperation began with the
laboratory PC2A from University of Lille 1 to determine some data with a theoretical
chemistry approach.
At the instigation of IRSN, a new molecular dynamics program, named SPyDERS,
is in the making. The initial objective of this code is to calculate energetic values related
to the solvation, such as Henry's law constants (HLC), for compounds of nuclear interest
such as iodine oxides and iodine nitroxides whose volatilities are still questionable.
In this poster, the approach will be detailed and the first operating tests of
SPyDERS will be discussed.
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Structure and electronic properties of A-cluster in Acetyl-CoA synthase: insight from DFT
Aleksandra Chmielowska, Maria Jaworska, Piotr Lodowski
Institute of Chemistry, University of Silesia Szkolna 9
40-006 Katowice, Poland
Acetyl-CoA synthase (ACS) is a bacterial enzyme which catalyses the synthesis of
Acetyl-CoA from coenzyme-A (CoASH), CO and methyl group coming from corrinoid-
iron-sulfur protein (CoFeSP):
CH3-Co(III)FeSP + CO + CoASH ↔ CH3CO-SCoA + Co(I)FeSP + H+ The active centre of ACS consists of A-cluster, dinuclear nickel complex bounded
to the sulfur-iron cubane: Fe4S4 – NipNid. Nip and Nid denote nickel atoms proximal and
distal to the cubane, respectively.
The geometry of A-cluster was optimized with use of DFT/OLYP method and two
main structural conformations were found, closed (I) and open (II) ones. Similar
calculations were performed for A-cluster with ligands (CH3, H, CO, H2O) linked to Nip.
The influence of polar solvent on the structures was taken into account by PCM model.
Atomic charges and spin densities for all structures of A-cluster were analyzed.
Acknowledgement: Calculations were performed at the Wrocław Centre for Networking
and Supercomputing, WCSS, Wrocław, Poland, under calculational Grant No. 51/96.
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Noniterative triples correction in Mukherjee’s
coupled cluster method via uncoupled approach
Ondrej Demel, Kiran Bhaskaran Nair, Jan Smydke, Jirı Pittner
J. Heyrovsky Institute of Physical Chemistry, v.v.i., Academy of Sciences of the
Czech Republic
Dolejskova 3, 18223 Prague 8, Czech Republic
Multireference coupled cluster methods are accurate quantum chemical ab ini-
tio methods designed for treatment of quasidegenerate systems(e.g. biradicals) and
larger sections of potential energy surfaces (e.g. torsion of double bond, dissocia-
tion). However, the multireference generalization of coupled cluster approach is not
unique.
Proposed by Mukherjee et al. [1, 2], the MR MkCC is a Hilbert space state-specific
method which is rigorously size-extensive and resistant to intruder states.
Recently, an uncoupled variant of MR MkCC has been developed by Mukherjee
et. al. [3]. Unlike the original method, the couplings between the cluster equa-
tions corresponding to different references include cluster amplitudes of only one
reference configuration, as well as matrix elements of effective Hamiltonian and its
eigenvector. The reported results showed an excellent agreement between the un-
coupled and standard versions of MkCC method at the singles and doubles level.
This performance was later found to be preserved even when connected triples are
included[4].
In this poster, we report an aplication of the uncoupled MkCC method for nonit-
erative triples correction. The advantage of this scheme lies in the fact that approx-
imate treatment of the coupling terms in the triples equation is sufficient to avoid
the intruders; and, since the coupling terms include only amplitudes of one reference
configuration, iterating of triples equations is no longer required.
The 9th Central European Symposium on Theoretical Chemistry
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References
[1] U. S. Mahapatra, B. Datta, and D. Mukherjee, J. Chem. Phys 110, 6171 (1999).
[2] U. S. Mahapatra, B. Datta, and D. Mukherjee, Chem. Phys. Lett. 299, 42 (1999).
[3] S. Das, D. Datta, R. Maitra, and D. Mukherjee, Chem. Phys. 349, 115 (2008).
[4] O. Demel, K. Bhaskaran Nair, J. Pittner, submitted.
The 9th Central European Symposium on Theoretical Chemistry
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MD modelling of tungsten carbide slab
Jozef Federič, Ivan Černušák
Department of Physical and Theoretical Chemistry, Faculty of Natural Sciences, Comenius University Mlynská dolina CH1
84215 Bratislava, Slovakia [email protected]
We present structural data for tungsten carbide slab from ab initio molecular
dynamics simulations. The motivation is our participation in the EURATOM materials
research, covering simulations of various composites that contain tungsten, carbon or
beryllium atoms. The inner wall of the fusion reactor is made from tungsten, some parts
contains carbon. Tungsten carbide can be formed in the divertor which exhausts impurity
particles and removes heat load from the plasma in the fusion reactor. This is
accompanied by the erosion and deposition of the material, among others tungsten
carbide is formed. We simulated various models of WC slab with the goal to study the
effects of impinging particles on the WC surface in the future. The simulations are
performed using CP2K program, which uses mixed Gaussian and plane waves approach
[1,2].
Three model systems were simulated using NVT ensemble at 300 K temperature,
with 0.5fs step. Model I consists of three layers of atoms: two layers of tungsten and one
layer of carbon in between. Model II contains one extra layer of carbon atoms and model
III contains another layer of tungsten atoms. All systems were in hexagonal closed pack
structure as can be seen in Figure. The periodic boundary conditions were applied along
X and Y axis.
I II III
Figure 1: Three models of tungsten carbide slabs.
The 9th Central European Symposium on Theoretical Chemistry
76
There are two lattice constants in hexagonal closed pack structure. The lattice
constant a is a horizontal distance between two neighbouring atoms of same type and c is
a vertical distance between two neighbour atoms of same type.
Figure 2: Tungsten carbide hexagonal closed pack structure
The experimental values for lattice constants are a=2.906 Å and c=2.837 Å. We
obtained the following values for a: 2.9084 Å ± 0.005 (model I), 2.9052 Å ± 0.004
(model II) and 2.9074 Å ± 0.005 (model III) and for c 2.8046 ± 0.005 (model I), 2.9356
Å ± 0.005 (model II) and 2.8459Å ± 0.054 (model III). The results for models I and III
are in good agreement with the experimental data.
[1] Quickstep: fast and accurate density functional calculations using a mixed Gaussian
and plane waves approach, J. VandeVondele, M. Krack, F. Mohamed, M. Parrinello, T.
Chassaing and J. Hutter, Comp. Phys. Comm. 167, 103 (2005).
[2] Quickstep: Make the atoms dance, M. Krack and M. Parrinello, Forschungszentrum
Jülich, NIC Series, Vol. 25, 29 (2004).
Support from grants APVV-LPP-0150-09, EURATOM-CU contract No. N° FU07-
CT-2006-00441, VEGA 1/0428/09 is acknowledged. We appreciate the computational
support under the HPC-FF project in Jülich Supercomputing Centre.
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77
Nonlinear optical properties of endohedral
fullerene complexes
R. W. Gora,1 R. Zalesny,1 W. Bartkowiak,1 J. M. Luis,2 B. Kirtman,3 H. Reis4 and
M. G. Papadopoulos4
1 Theoretical Chemistry Group, Institute of Physical and Theoretical Chemistry,Wroclaw University of Technology
Wybrzeze Wyspianskiego 27, 50-370 Wroc�law, [email protected]
2 Institute of Computational Chemistry and Department of Chemistry,University of Girona
Campus de Montilivi 17071 Girona, Catalonia, Spain
3 Department of Chemistry and Biochemistry, University of CaliforniaSanta Barbara, California 93106, USA
4 Institute of Organic and Pharmaceutical Chemistry,The National Hellenic Research Foundation
48 Vas. Constantinou Avenue, 11635 Athens, Greece
Growing demand for new photonic materials is a strong impulse for synthesis and
physico–chemical characterization of new molecular systems that show a large non–
linear response to an external electric field. Among this broad group of compounds
are also the endohedrally doped fullerenes. Although such complexes captured inter-
est of scientists, still there is a lack of fundamental studies that would complement
collected experimental data. Previous theoretical studies focused on the structure,
stability and interactions in the host–guest systems. Due to the size of these systems,
as well as the formal and numerical complexity of the problem, relatively little is
known about the role of vibrations of “trapped” atoms or molecules in the nonlinear
optical response of endohedral complexes. Whitehouse and Buckingham proposed
a model, which predicts that in such systems vibrational contributions (in electric
dipole approximation) to the polarizability should be significantly larger than the
corresponding electronic counterparts [1]. Unfortunately, in the literature there are
no reliable calculations to confirm such predictions.
The 9th Central European Symposium on Theoretical Chemistry
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One of the main objectives of this project is verification of the Whitehouse and
Buckingham model. The following two complexes were selected as the model sys-
tems: Li@C60 and Ti@C28. The existence and stability of these complexes has been
confirmed experimentally. The studies, whose results will be presented, were based
on ab initio methods taking into account the electron correlation as well as the
density functional theory.
References
[1] D. B. Whitehouse, A. D. Buckingham, Chem. Phys. Lett. 207, 332 (1993).
This work was partially supported by Wroclaw University of Technology and
computational grant from Wroclaw Center for Networking and Supercomputing
(WCSS).
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Correlation potentials and electron densities obtained from correlated Optimized Effective Potential method and ab initio Wave Function
Theory methods
Ireneusz Grabowski, Andrew Teale, Szymon Śmiga, Karol Jankowski
Institute of Physics, Nicolaus Copernicus University,87-100 Toruń, Poland
[email protected] www.fizyka.umk.pl/~ig
Direct comparison of the correlation potentials, electron densities and correlation energies, generated from few variants of correlated Optimized Effective Potential Method (OEP), standard Density Functional Theory (DFT) and from ab intio Wave Function Theory Methods (WFT), has been employed for analyzing the impact of the correlation effects on those quantities. These methods have been applied to a few atomic and molecular systems. The correlation potentials, energies and densities generated from orbital-dependent OEP (OEP2-sc [1], OEP-ccpt2 [2]) and from WFT methods - Coupled Cluster (CCSD, CCSD(T) ) and second-order Many Body Perturbation Theory (MP2) show very similar and systematic behaviour, reconfirming the correctness of the ab initio DFT (OEP2) methods [3]. In a contrast it has been demonstrated that the VWN5 and LYP correlation functionals do not represent any substantial dynamical correlation effects on the KS-correlation potentials [3] and electron density [4].
[1] R. J. Bartlett, I. Grabowski, S. Hirata, S. Ivanov J. Chem. Phys. 122, 034104 (2005) [2] I. Grabowski, V. Lotrich, R.J. Bartlett J. Chem. Phys. 127, 154111 (2007) [3] I. Grabowski, A. Teale, Sz. Śmiga, K. Jankowski, R.J. Bartlett, In preparation 2010 [4] K. Jankowski, K. Nowakowski, I. Grabowski, J. Wasilewski J. Chem. Phys. 130, 164102 (2009)
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Exact diagonalization of bosonic Hamiltonians
Peter Jeszenszki, Agnes Szabados, Peter R.Surjan
Eotvos Lorand University, Institute of Chemistry, Laboratory of Theoretical
Chemistry
Pazmany Peter setany 1/A.
1117 Budapest, Hungary
Bosonic systems have been extensively studied over the last decade [1-3] due to
the interest generated by quantum gas experiments. A sample of quantum gas can
be produced by trapping atoms at low temperature in an optical lattice generated
by the application of lasers and static magnetic fields. The size of the traps is large
on the quantum chemical scale (1000 nm), for this reason the atoms interact only via
scattering processes. The total spin of an atom results by coupling the nuclear and
electron spins. If this value is an integer, the atoms are to be treated as quasi-bosons
and follow the Bose-Einstein statistics.
In the present work the wave functions of bosonic quantum systems are obtained
by exact diagonalization of the Hamiltonian. In this area exact solutions have been
mainly obtained by iterative methods combined with sparse matrix techniques. We
present a direct-CI code supplemented with the Davidson algorithm applying the
Bose-Hubbard model Hamiltonian.
References
[1] F.Dalfovo, S.Giorgini, L.P.Pitaevskii, S.Stringari, Rev. Mod. Phys., 71, No. 3
(1999).
[2] R.M.Noack, S.R.Manmana, AIP Conf. Proc., 789, 93-163 (2005).
[3] M.Lewenstein, A.Sanpera, V.Ahufinger, B.Damski, A.Sen(De), U.Sen, Advances
in Physics, 56, 243-379 (2007).
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Properties of encapsulated organic molecules
Anna Kaczmarek-Kedziera
Faculty of Chemistry, Nicolaus Copernicus University
Gagarina 7, 87-100 Torun, Poland
E-mail: [email protected]
Encapsulation of organic molecules in nanomaterials can be applied for tuning the
properties of carbon nanotubes, fullerenes or zeolites. It is particularly interesting
in the case of the nanotubes, since unlike the modification of the outer surface of
the tubule, does not cause the loss of the one–dimensionality and may not involve
the surface defects [1–3].
The introductory investigation was performed for the small organic molecules
enclosed in the various type of cages: single-walled carbon nanotube, boron-nitride
tube and C92 fullerene buckyball. The analysis involved the host–guest interaction
and the electric and optical properties of the complexes.
References
[1] K. Yanagi, K. Iakoubovskii, H. Matsui, H. Matsuzaki, H. Okamoto, Y. Miyata,
Y. Maniwa, S. Kazaoui, N. Minami and H. Kataura, J. Am. Chem. Soc. 129,
4992 (2007).
[2] K. Yanagi, Y. Miyata, Z. Liu, K. Suenaga, S. Okada and H. Kataura, J. Phys.
Chem. C 114, 2524 (2010).
[3] W. He, Z. Li, J. Yang and J. G. Hou, J. Chem. Phys. 128, 164701 (2008).
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Multireference R12 Coupled Cluster Theory
Stanislav Kedžuch1, Ondřej Demel2, Jiří Pittner2 and Jozef Noga1,3
1Institute of Inorganic Chemistry, Slovak Academy of Sciences, SK-84536 Bratislava, Slovak Republic
2J. Heyrovsky Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, CZ-18223 Prague 8, Czech Republic
3Department of Inorganic Chemistry, Faculty of Natural Sciences, Comenius University, SK-84215, Bratislava, Slovak Republic
In order to account for static correlation, the explicitly correlated coupled cluster
theory based on the R12 Ansatz is formulated with respect to a multideterminantal
reference using the Brillouin-Wigner approach. Though the latter avoids appearance of
the intruder states, one pays for this desired feature by the loss of size extensivity.
However, to some extent this can be remedied by an a posteriori correction. Since the
BWCC method offers simplest form of amplitude equations among Hilbert space MRCC
ones, we have chosen it as the first step when developing MRCC-R12 approaches. It is
shown that introducing of the basis set incompleteness correction via an explicit inclusion
of the correlation factor into the wave function, separately for each reference, is easily
realizable. Test calculations for the H4 model using an R12 optimized 9s6p4d3 f basis
and its subsets with increasing highest angular momentum show the potential of the MR-
CC-R12 approach. R12 results with mere s functions are very close to values obtained by
using a conventional approach and the full 9s6p4d3 f basis set.
Acknowledgement: This work has been supported by the Grant Agency of the Ministry
of Education of the Slovak Republic and Slovak Academy of Sciences (VEGA project
No. 2/0079/09) and by the Slovak Research and Development Agency (APVV, LPP-
0343-09), as well as by the Grant Agency of the Czech Republic (GACR Project No.
203/07/0070). Also, this work has benefitted from the Centers of Excellence program of
the Slovak Academy of Sciences
(COMCHEM, Contract no. II/1/2007).
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ONIOM study of the catalytic mechanism of Dihydroneopterin Aldolase
Hyungrae Kim, Stepan Sklenak
J. Heyrovsky Institute of Physical ChemistryAcademy of Sciences of the Czech Republic
Dolejskova 3 Prague 8 CZ-18223, Czech Republic
Dihydroneopterin Aldolase (DHNA) catalyzes the conversion of 7,8-
dihydroneopterin (DHNP) to 6-hydromethyl-7,8-dihydropterin (HP) in the folate
biosynthetic pathway, one of principal targets for developing antimicrobial agents [1].
The complete path for the catalytic reaction by E. coli DHNA (EcDHNA) was
investigated using ONIOM method [2]. The aldol reaction proceeds via a sequential
mechanism involving the consecutive proton transfer from C2’ of DHNP via ε-amino
group of Lysine 98, catalytic water to N5 of DHNP and the cleavage of the C1’-C2’
bond. The last step triggers the liberation of Glycoaldehyde (GA) from the active site.
GA release set off the transformation of intermediate structure to final product
(HP), that involves the reorganization of DHNA+intermediate structure complex, reverse
proton transfer from N5 via catalytic water, ε-amino group of Lysine 98 to Tyrosine 53’
hydroxyl group and protonation of C1’ and resulting chirality change of C1’.
We used the 1.07 Å resolution X-ray structure of EcDHNA [3] for our calculations
because of its higher reliability. To incorporate the possible long-range effect of real
enzyme, 81 residues were selected as model system based on the distance (16.2 Å) from
the active site center (C2’). A two-layered ONIOM method as implemented in the
Gaussian 09 program was used in this work. We chose the density functional method
B3LYP employing the 6-31G** basis set as the high level. The semi-empirical PM3
method was selected as low level.
[1] Structural basis for the aldolase and epimerase activities of Staphylococcus aureus
Dihydroneopterin Aldolase. J. Blaszczyk, Y. Li, J. Gan, H. Yan and X. Ji. J. Mol. Biol.
368, 161–169 (2007)
[2] S. Humbel, S. Sieber, K. Morokuma, J. Chem. Phys. 105, 1959 (1996)
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[3] H. Yan. Unpublished results.
Acknowledgement
We thank Prof. Dr. Honggao Yan (Michigan State University) for providing us the
unpublished ecDHNA structure and significantly valuable discussions.
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The factorized quadruple excitations for potential
energy surfaces with Λ functional
Katarzyna Kowalska-Szojda, Monika Musia�l, Stanis�law A. Kucharski
University of Silesia, Institute of Chemistry
Szkolna 9
40-006 Katowice, Poland
[email protected], [email protected], [email protected]
In this work we discuss a possibility of incorporating the fifth-order factorized
connected quadruples [1] into the Λ based coupled cluster functional. The scheme,
scaling as n7, is denoted as ΛCCSD(TQf ), i.e. coupled cluster singles and doubles
with noniterative triples and noniterative factorized quadruples. The factorized
quadruples work well for the near equilibrium geometry but when combined with Λ
based functional provide also reliable description for the distorted geometries. We
discuss the performance of the method by studying the potential energy curves for
F2 and H2O molecules and relating them to the standard CC approaches such as
CCSD, CCSDT, CCSDTQ, CCSD(T) and also ΛCCSD(T) and CCSD(TQf ). The
Λ based corrections improve noticeably the curves bringing them closer to the FCI
or CCSDTQ reference.
References
[1] S. A. Kucharski, R. J. Bartlett, J. Chem. Phys., 108, 9221 (1998).
[2] M. Musia�l, R. J. Bartlett, J. Chem. Phys., 133, xxx (2010).
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The use of perturbation-stable localization in
calculation and analysis of SO-correction to NMR
chemical shifts
Anezka Krıstkova, Olga L. Malkina
Institute of Inorganic Chemistry, Slovak Academy of Sciences
Dubravska cesta 9
845 36 Bratislava, Slovakia
The perturbation-stable (PS) localization procedure, initially developed for analy-
sis of NMR indirect nuclear spin-spin coupling constants [1], has been implemented
for the calculation of the spin-orbit (SO) correction to the NMR chemical shift.
In this poster we present the first benchmark calculations testing the numerical
stability of the results obtained with the new localization scheme. Also, the new
localization procedure has been applied for the analysis of the solvent effect of the
Lewis bases on the 13C SO-shift in iodoalkynes in order to check its usefulness for
interpretation purposes.
References
[1] Anezka Krıstkova, diploma thesis, 2009
We gratefully acknowledge the financial support from COMCHEM, a virtual Cen-
ter for Advanced Computational Chemistry sponsored by the Slovak Academy of
Sciences, and Slovak grant agencies VEGA (grant no. 2/0079/09) and APVV (grant
LPP-0326-09).
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NMR spin-spin couplings and overlap of densities
of localized molecular orbitals
Anezka Krıstkova, Olga L. Malkina, Stanislav Komorovsky, Elena Malkin,
Vladimir G. Malkin
Institute of Inorganic Chemistry, Slovak Academy of Sciences
Dubravska cesta 9
845 36 Bratislava, Slovakia
One of the most important magnetic resonance parameters are indirect nuclear
spin-spin couplings, which are used in various fields of (bio)chemistry for establishing
the molecular structure from NMR spectroscopy data. Their detailed understanding
in terms of molecular and electronic structure, which has been pursued since the
beginning of NMR spectroscopy, is still of central importance in many fields of
research.
In this poster we present a new method of interpretation of spin-spin coupling,
based on its decomposition into contributions from individual localized molecular
orbitals (LMOs) [1], and on the visualization of spin-spin coupling pathways by
real-space functions [2]. In particular, the correlation between the overlap of LMO
densities and the Fermi-contact contribution to spin-spin coupling constants will be
demonstrated.
References
[1] R. Marek, A. Krıstkova, K. Malinakova, J. Tousek, J. Marek, M. Hocek, O. L.
Malkina, V. G. Malkin, J. Phys. chem., 114, 6689 – 6700 (2010)
[2] O. L. Malkina, V. G. Malkin, Angew. Chem. Int. Edition, 42, 4335-4338 (2003)
We gratefully acknowledge financial support from the Slovak grant agency APVV
(grants No. LPP-0326-09 and VVCE-0004-07).
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Relative Complexation Energies for Li+ Ion in Solution: Molecular Level Solvation Versus Polarizable Continuum Model Study
Piotr Kubisiak, Andrzej Eilmes
K. Gumiński Department of Theoretical Chemistry, Jagiellonian University Ingardena 3
30-060, Kraków, Poland
Solvation of inorganic ions in organic solvents plays a great role in chemistry and
biochemistry since many chemical reactions occur in solution. Modeling of the ion–
solvent interactions is therefore of great importance. Typical quantum-chemical
calculations providing information about the structure of complexes and their binding
energies represent the situation in the vacuum and neglect the effect of the environment.
In solution the properties of the complex are affected by the solvent molecules and this
should be reflected in the relative complex stabilities. Effects of this kind are also highly
relevant for ion–polymer interactions in polymer-based solid electrolytes where the
polymer matrix surrounding the ion acts as the solvent, influencing the interactions in the
complex.
In the present work[1] we have studied relative complexation energies of Li+ ion in
two commonly used solvents, acetonitrile and diethyl ether. We have used molecular-
level representation of solvation, embodied in explicit solvent molecules surrounding the
complex to determine the trends in relative binding energies. Our results indicate that
with increasing number of included explicit solvent molecules the differences in
complexation energy between the complexes of different coordination numbers decrease.
Simultaneously we have conducted PCM calculations using various combinations of
atomic radii and molecular surface modeling the molecular cavity in the solvent. We have
shown that the best reproduction of energies for different coordination numbers has been
found for van der Waals molecular surface and Pauling or UFF atomic radii and that
PCM calculations can provide a low-cost alternative for the time-consuming explicit
solvation approach with comparable level of accuracy.
[1] Eilmes, A.; Kubisiak, P. J. Phys. Chem. A 2010, 114, 973
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Second-order Douglas–Kroll–Heß (DKH2)spin–orbit and parity-violating Hamiltonians
Mojmır Kyvala
Institute of Organic Chemistry and BiochemistryAcademy of Sciences of the Czech Republic
Flemingovo namestı 2, 166 10 Praha 6, Czech [email protected]
Analytical expressions have been derived for the one-electron DKH2 spin–orbitHamiltonian and for the one-electron DKH2 parity-violating Hamiltonian through the free-particle Foldy–Wouthuysen (fpFW) transformation followed by the Douglas–Kroll–Heßtransformation of the one-electron Dirac Hamiltonian and of the nuclear spin-independentpart of the one-electron 4-component parity-violating Hamiltonian respectively.
Matrix elements of the one-electron Breit–Pauli (approximate Foldy–Wouthuysen,aFW), fpFW (DKH1) and DKH2 spin–orbit Hamiltonians have been evaluated betweenthe components of the ground scalar pseudo-relativistic (DKH2 CASSCF) state 3Pg ofatoms C, Si, Ge, Sn and Pb to estimate the error introduced by using lower-order spin–orbit Hamiltonians in ab initio all-electron quasi-relativistic calculations of, e.g., zero-field splittings or spin-forbidden transition probabilities in molecules containing heavyelements.
Similarly, matrix elements of the one-electron aFW, fpFW and DKH2 parity-violatingHamiltonians have been evaluated between the components of the two lowest scalarpseudo-relativistic (DKH2 CASSCF) states 2Pu and 4Pg of atoms B, Al, Ga, In andTl to estimate the error introduced by using lower-order parity-violating Hamiltoniansin ab initio all-electron quasi-relativistic calculations of, e.g., electronic energy shifts orelectronic excitation frequency shifts due to parity violation in molecules containing heavyelements.
The active spaces contained 4 (3) electrons in the 4 valence atomic orbitals sp3 or14 (13) electrons in the 14 atomic orbitals (n − 1)d5sp3d5. Different orbitals wereoptimized for different states. Instead of the true atomic (spherical) symmetry, a bit lowersymmetry of the largest binary subgroup of SO(3), the point group D2h, was exploited forconvenience.
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Quantum chemical calculations of photophysical propertiesof Methyl- and Adenosylcobalamin
Piotr Lodowski1
, Maria Jaworska1, Paweł M. Kozłowski2, Tadeusz Andruniów3
1University of Silesia, Institute of Chemistry, Szkolna 9, 40-006 Katowice, Poland, 2Department of Chemistry, University of Louisville, Louisville, Kentucky 40292, USA, 3Department of Molecular Modelling and Quantum Chemistry, Institute of Physical and Theoretical Chemistry, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
Two B12 dependent human enzymes, methylmalonyl-CoA mutase and methionine synthase, incorporate active alkylcobalamins derived from cyanocobalamin (vitamin B12, CNCbl). Methylcobalamin (MeCbl) functions as methyl donor in methionine synthase, with heterolytic cleavage of the cobalt – carbon bond to form cob(I)alamin. Adenosylcobalamin (AdoCbl or coenzyme B12) is the cofactor of enzymes, which catalyze the rearrangement reactions that proceed via mechanisms involving organic radicals generated by homolysis of the coenzyme cobalt – carbon bond to produce an adenosyl radical and cob(II)alamin.
Over the past few years transient absorption spectroscopy has been applied by Sension and co-workers [1] to investigate nature of electronically excited states and photochemistry of alkylcobalamins. While these recent spectroscopic studies provided a new insight into the electronic structure of cob(III)alamins, the nature of their excited states remains largely unexplained.
The analysis of the electronic structure of methyl- and adenosylcobalamin has been performed by means of time-dependent density functional theory (TDDFT). Calculations were carried out using the gradient corrected Becke–Perdew (BP86) functional together with the TZVPP basis set and COSMO solvent model. In the calculations a simplified cobalamin model was used, in which all the corrin side chains were replaced by hydrogen atoms and the 5,6-dimethylbenzimidazole trans axial base was replaced by an imidazole. The calculations were carried out with the use of TURBOMOLE program.
Full geometry optimization was performed for the ground state (S0) and the first singlet excited state (S1). The S1 excited state for both investigated cobalamins is characterized as a MLCT(SBLCT) type and is derived from the d/π → π* excitation, where π and π* orbitals are localized on the corrin ring. For the ground and excited S1 state, potential energy curves were determined as a function of Co-CMe and Co-CAdo bond lengths. The bond length was repeatedly stretched with the step size of 0.05 Ǻ, and the geometries of S0 and S1 states were reoptimized at every point. At each optimized point the manifold of singlet and triplet states were calculated at the TDDFT/BP86/TZVPP level of theory.
[1] D.A. Harris, A.B. Stickrath, E.C. Carroll and R.J. Sension, J. Am. Chem. Soc, 129, 24 (2007) 7583 Acknowledgement: This work was supported by Ministry of Science and Higher Education (Poland) under grant No. N204 028336. The TURBOMOLE calculations were carried out in the Wrocław Centre for Networking and Supercomputing, WCSS, Wrocław, Poland, under calculational Grant No. 51/96. and in the Academic Computer Centre CYFRONET of the University of Science and Technology in Cracow, ACC CYFRONET AGH, Kraków, Poland,under grant No. MNiSW/SGI3700/UŚląski/111/2007.
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Protonated water clusters – structures and thermodynamics
Jakub Malohlava, Aleš Vítek, René Kalus
Department of Physics, Faculty of Science, University of Ostrava 30. dubna 22
70103 Ostrava, Czech Republic [email protected]
This work focuses on protonated water cluster because of their importance in
charge transport and related biological and physical processes. Thermodynamical
parameters of H+(H2O)n clusters with n = 2 – 8 were obtained by Monte Carlo
simulations using the parallel tempering approach [1] combined with the multiple
histogram algorithm [2]. Structures of H+(H2O)n were obtained at T = 0 K by Monte
Carlo simulations using the simulated annealing algorithm [3]. Two empirical models
proposed by Kozack and Jordan [4] were used – the hydronium model where the
hydronium ion, H3O+, interacts with n – 1 water molecules, and the proton model where
the proton, H+, interacts with n water molecules.
Figure: Equilibrium structure at T = 0 K and temperature dependence of the heat
capacity of H+(H2O)5 calculated for the hydronium model.
[1] Swendsen R.H.and Wang J.-S.: Phys. Rev. Lett. 57, 2607 (1986).
[2] Ferrenberg A.M. and Swendsen R.H.: Phys. Rev. Lett. 61, 2635 (1988).
[3] Kirkpatrick S., Gelatt C. D., and Vecchi M. P.: Science 220, 671 (1983).
[4] Kozack R. E., Jordan P. C.: J. Chem. Phys. 96 , 3131 (1992).
The 9th Central European Symposium on Theoretical Chemistry
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Acknowledgement
Grant Agency of the Academy of Sciences of the Czech Republic, grant No.
IAA401870702; University of Ostrava, Students Grant Competition, grant No.
SGS7/PřF/2010.
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Hydrogen bonded clusters around aromatic π-systems
Gergely Matisza,b, Walter M.F. Fabianb, Sándor Kunsági-Mátéa,*
aUniversity of Pécs, Department of General and Physical Chemistry Ifjúság 6., 7624 Pécs, Hungary
bKarl-Franzens University of Graz, Institute of Chemistry Heinrichstr. 28, 8010 Graz, Austria *email: [email protected]
The hydrogen bonded liquids were investigated widely nowadays, both with
Molecular Dynamics (Monte Carlo) simulations beyond the pairwise additive
approximations [1] and the static approach quantum cluster equilibrium QCE model [2]
of F. Weinhold. However, it is obvious to assume that the structure of hydrogen bonded
liquids is modified by the presence of the solute molecules. This effect can be
pronounced in the case of aromatic molecules where the C-H…π and O-H…π bonds are
in competition with the hydrogen bonds which stabilize the clusters in the liquid phase
[3]. Although few experimental results are available in the literature for the benzene –
methanol clusters [e.g. 3,4] the influence of the aromatic ring (i.e. benzene, anthracene)
on the hydrogen bonded clusters is not discussed yet at higher theoretical levels [5]. Here
we present a study of methanol – benzene (anthracene) at the MP2(fc) level of theory to
show the possible structural patterns in the liquid relative to pure methanol calculated at
the same level of theory [6]. The structures determined will be applied in the QCE model
to investigate the structure of the corresponding binary liquid mixtures.
[1] Valdéz-González et al., J. Chem. Phys. 127 (2007) 224507.
[2] F. Weinhold, J. Chem. Phys. 109 (1998) 367.; J. Chem. Phys. 109 (1998) 373.
[3] S. Kunsági-Máté et al., Chem. Phys. Lett. 473 (2009) 284.
[4] R.N. Pribble et al., J. Chem. Phys. 106 (1997) 2145.
[5] B. Brutschy, Chem. Rev. 100 (2000) 3891.
[6] G. Matisz et al., THEOCHEM, in press, doi: 10.1016/j.theochem.2010.07.003
Acknowledgement: This project was supported by the Intergovernmental projects NKTH
(HU 4/2009, RO-14/07). Computations with the Gaussian 09 Rev.A.02. were done on
IBM HPC supercomputer located at the Babes-Bolyai University in Cluj Napoca.
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Liquid structure of primary alcohols (methanol, ethanol, 1-propanol, 1-butanol) within the QCE theory
Gergely Matisza,b, Walter M.F. Fabianb, Sándor Kunsági-Mátéa,*
aUniversity of Pécs, Department of General and Physical Chemistry Ifjúság 6., 7624 Pécs, Hungary
bKarl-Franzens University of Graz, Institute of Chemistry Heinrichstr. 28, 8010 Graz, Austria *email: [email protected]
The hydrogen bonded liquids, like water [1] and various alcohols [2,3] was
investigated previously in several publications via the Quantum Cluster Equilibrium
(QCE) model of F. Weinhold [4]. The advantage of this model (QCE) that we can obtain
the cluster distribution in the liquid phase relatively easily based on ab initio cluster
geometries and cluster properties. For the homolog series of unbranched aliphatic primer
alcohols none a complete investigation was presented until now regarding their structure
within the QCE model. Although force field based MD calculations are possible, they are
not reliable enough to predict the liquid structure adequately.
In our recent publication [5] we have investigated the pure liquid methanol at the
MP2(fc) level of theory in the framework of the QCE model. Here were extend those
studies to the higher homologes of the unbranched aliphatic primary alcohols using the
B3LYP density functional which proved to be adequate in the case of pure methanol.
[1] S.B.C. Lehmann, B. Kirchner et al., J. Chem. Theory Comput. 5 (2009) 1640.; 1650.
[2] P. Borowski et al., Mol. Phys. 101 (2003) 1413.
[3] R. Ludwig, Chemphyschem 6 (2005) 1369.; 1376.
[4] F. Weinhold, J. Chem. Phys. 109 (1998) 367.; J. Chem. Phys. 109 (1998) 373.
[5] G. Matisz et al., THEOCHEM, in press, doi: 10.1016/j.theochem.2010.07.003
Acknowledgement: This project was supported by the Intergovernmental projects NKTH
(HU 4/2009, RO-14/07). Computations with the Gaussian 09 Rev.A.02. were done on
IBM HPC supercomputer located at the Babes-Bolyai University in Cluj Napoca.
The 9th Central European Symposium on Theoretical Chemistry
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Effect of spin-orbit coupling on potential curves and spectroscopic properties of IO and I2
Katarína Mečiarová, Lukáš Demovič and ivan černušák
Department of Physical and Theoretical Chemistry, Faculty of Natural Sciences, Comenius University, Mlynská dolina 84215 Bratislava, Slovakia
Potential energy curves (PEC‘s), spectroscopic constants, equilibrium geometries and dissociation energies were calculated for the ground and excited states of iodine oxide and iodine molecule using the complete active space second-order perturbation theory (CASSCF/CASPT2) and coupled cluster theory through quasiperturbative triple excitations (CCSD(T)), implemented in the moLcas 7.3 program package [2]. The ground state of IO(X2Π) and I2 (X 1Σ+) were computed at the CCSD(T) level. Potential energy curves for excited states of IO (a4Σ-, A2Π) and I2 (A
3Π), which have multi-configuration nature, were computed at the CASSCF/CASPT2 level. The second order spin-free Douglas-Kroll-Hess Hamiltonian was applied to calculate relativistic effects within the spin-adapted CCSD(T) and the CASPT2 method. To include spin-orbit effects, which are important for both ground and excited state of IO and I2 due to the presence of the heavy I, we employed the Restricted Active Space State Interaction method (CASPT2/RASSI-SO), introduced by Roos and Malmqvist [1].
For energy predictions, relativistic basis set ANO-RCC with large contraction (for iodine (22s19p13d5f3g)/[10s9p8d5f3g] and for oxygen (14s9p4d3f2g)/[8s7p4d3f2g]) has been used in all the calculations. C2 symmetry with averaging the degenerate pairs of electronic states was used. Two active spaces were used in the CASPT2 spin-free calculations for IO: the first consisted of 9 valence electron in 6 orbitals (16a/10b inactive and 2a/4b active), followed by CASPT2 calculations with 17 correlated electrons; the second included 9 valence electron in 12 orbitals (16a/10b inactive and 6a/6b active). Two active space were used for I2 molecule: 10 valence electron in 6 orbitals (28a/20b inactive and 2a/4b active) and 10 valence electron in 16 orbitals (28a/20b inactive and 8a/8b active).
Spectroscopic constants (equilibrium bond lengths Re, harmonic frequencies ωe, anharmonicity constants ωexe and ro-vibrational constants αe) and equilibrium geometries were determined by fourth-fifth-order polynomial fit and VIBROT program. Calculated spectroscopic constants, geometries and dissociation energies were compared with existing experimental and theoretical data from the literature.
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[1] B. Roos and P.-A. Malmqvist, Phys. Chem. Chem. Phys., 6, 2919 (2004) [2] Aquilante, F; De Vico, L; Ferre, N, et al., Journal of computational chemistry, 31, 224-247 (2010)
Acknowledgment This work was supported by Slovak Research and Development Agency under the contract No. LPP-0110-07, grant APVV-20-018405, VEGA (1/0428/09) and EUROATOM, contract No. N° FU07-CT-2007-00051. Computational support from the Centre of Excellence program of the Slovak Academy of Sciences (COMCHEM, Contract no. II/1/2007) is gratefully acknowledged.
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Applicability of Graphical Processing Units to Coupled Clusters Calculations
Miroslav Melicherčík, Lukáš Demovič, Michal Pitoňák, Pavel Neogrády
Comenius University, Faculty of Natural Sciences Department of Physical and Theoretical Chemistry
Mlynská dolina CH-1 842 15 Bratislava, Slovakia
Graphical processing unit (GPU) appears to be an excellent tool for the acceleration
of quantum chemistry calculations. We propose some levels of the GPU based software
integration into the coupled clusters singles, doubles [1, 2] and perturbative triples [3, 4]
method CCSD(T).
The GPU is especially efficient for massively parallelized problems, such as
matrix-matrix multiplication [5], as shown on figure 1. Implementation of such routines
in BLAS (basic linear algebra subroutines) library for GPU, named CUBLAS, is included
in the CUDA software development toolkit [6].
Figure 1 Time dependence of matrix-matrix multiplication on size of square matrices N
(blas – single-threaded blas, thrblas – two-threaded blas, cublas – blas on GPU)
First, we simply accelerated CCSD(T) method by replacing the BLAS routines with
corresponding CUBLAS routines and got average speedup 1.24 for CCSD part and 1.80
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for (T) part of calculation. Second, we wrote program that simulates the most time
consuming part of CCSD(T) procedure – part for calculation of noniterative triples.
Within this program, all calculations were performed on GPU and data transfer was done
only at the beginning and at the end of procedure. We achieved average overall speedup
of 3.96 times. Results are summarized in Table 1.
Table 1 Results for (T) simulation
Number of occupied orbitals 20 30 Number of virtual orbitals 200 350
8 cores on CPU 10m 28.147 s 231m 15.709s NVIDIA Tesla S1070 (960 cores) 2m 18.662 s 68m 10.819 s
Speedup 4.53 3.39
[1] J. Čížek, J. Chem. Phys. 45, 4256 (1966)
[2] G. D. Purvis, R. J. Bartlett, J. Chem. Phys. 76, 1910(1982)
[3] M. Urban, J. Noga, S. J. Cole, R. J. Bartlett, J. Chem. Phys. 83, 4041 (1985)
[4] K. Raghavachari, G. W. Trucks, J. A. Pople, M. Head-Gordon, Chem. Phys. Lett.
157, 479 (1989)
[5] NVIDIA CUDA Programming Guide 2.3
<http://developer.download.nvidia.com/compute/cuda/2_3/toolkit/docs/NVIDIA_
CUDA_Programming_Guide_2.3.pdf>
[6] CUBLAS Library documentation 2.3
<http://developer.download.nvidia.com/compute/cuda/2_3/toolkit/docs/CUBLAS
_Library_2.3.pdf>
This work was supported by the Slovak Grant Agency VEGA (contract No. 1/0428/09),
Grant Agency of Comenius Univeristy (No. UK/501/2010)
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Accurate ab initio heats of formation and
standard molar entropies for several
atmospherically important formyl derivatives
Balazs Nagy†, Jozsef Csontos‡, Mihaly Kallay‡, and Gyula Tasi†
† University of Szeged, Department of Applied and Environmental Chemistry
Rerrich B. ter 1.
H-6720 Szeged, Hungary
and‡ Budapest University of Technology and Economics, Department of Physical
Chemistry and Materials Science
P.O. Box 91
H-1521 Budapest, Hungary
Several, so-called chemistry-climate models [1] have been developed to incorporate
the effects of chemical processes in climate modeling. To provide reliable information
these models require accurate kinetic and thermochemical data for the reactions
which play significant role in atmospheric chemistry. Nevertheless, the chemistry of
the troposphere and stratosphere is dominated by free radicals, and experimental
work with radicals is challenging and usually the accuracy of the measurements is
not satisfactory. Therefore, high-accuracy model chemistries can play a crucial role
in providing reliable data for climate modeling.
In the present study, a slightly modified HEAT-345(Q) model chemistry [2] was
applied in order to calculate accurate thermodynamic functions for several open- and
closed-shell formyl derivatives relevant to atmospheric chemistry. Heats of formation
along with standard molar entropies of the radicals FCO, cis- and trans-HOCO, and
NH2CO, as well as the molecules CF2O, HFCO, HClCO, and FClCO were calculated.
The molecular structures of the species, the zero-point vibrational energies as well
as the harmonic frequencies along with the anharmonicity constants were studied
at the CCSD(T)/cc-pVQZ level of theory with all electrons correlated. Single-point
energy calculations were performed invoking coupled-cluster theory up to the pertur-
bative quadruple excitation level [CCSDT(Q)] with the correlation consistent basis
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sets up to aug-cc-pCV5Z. Extrapolation techniques were used to obtain the com-
plete basis set limit in the HF-SCF, CCSD(T), and CCSDT calculations. Additional
contributions including the diagonal Born-Oppenheimer, and relativistic, scalar and
spin-orbit, corrections were also taken into consideration. The total molecular en-
ergies were obtained assuming the additivity of the various contributions.
Heats of formation were calculated using the formation reaction of the species
from the elemental reference compounds. For carbon atom the gaseous state was
used as reference and its 0 K heat of formation was set to the ab initio value,
∆fH◦0 (Cgas) = 711.65±0.32 kJ/mol [3]. To calculate the heat of formation at 298.15
K the thermal correction (∆fH◦298 − ∆fH
◦0 ) was obtained from the NIST-JANAF
tables resulting in ∆fH◦298(Cgas) = 717.13 ± 0.32 kJ/mol.
Standard molar entropies were calculated at 298.15 K at pressure of 1 bar via
the standard formulae of statistical mechanics, i.e., within the rigid-rotor harmonic-
oscillator approximation using the calculated harmonic frequencies and rotational
constants.
The estimated uncertainties of the calculated properties were taken from a re-
cent study [4], where the errors introduced by the present protocol were analyzed
thoroughly.
The accuracy of all the calculated heats of formation and most of the molar
entropies surpasses that of previous experimental and theoretical investigations, and
in these cases our values are recommended as new references.
References
[1] J. Austin, D. Shindell, et al., Atmos. Chem. Phys. 3, 1 (2003).
[2] Y. J. Bomble, J. Vazquez, et al., J. Chem. Phys. 125, 064108 (2006).
[3] G. Tasi, R. Izsak, et al., ChemPhysChem, 7, 1664 (2006).
[4] J. Csontos, Z. Rolik, et al., J. Phys. Chem. A, submitted for publication (2010).
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Catalytic hydrogenation of Quinolines via frustrated Lewis pairs: Mechanistic insight from theory
Péter Nagy, Imre Pápai
Chemical Research Center of HAS P.O. Box 17
H-1525 Budapest, Hungary [email protected]
In the past few years, there has been considerable interest in exploring the reactivity of bulky Lewis acid/base pairs towards small molecule activation. Following the concept of frustrated Lewis pairs (FLPs) introduced by Stephan and coworkers, a number of intermolecular and intramolecularly linked donor/acceptor pairs have been identified that cleave molecular H2 heterolytically under mild conditions.1
Based on a theoretical investigation, a mechanistic model have been proposed that provides a rationale for the unique reactivity of FLPs.2 The model has been built upon density functional theory based identification of the stationary points and single point vibrational analysis or polarisable continuum model calculations. From the calculated gas-phase and solution-phase Gibbs free energies one may conclude that the reactivity is associated with transient intermediates formed between the FLP components, which offer cooperative acid-base interactions with a hydrogen molecule.
However, the scope of synthetic applications of FLPs as hydrogenation catalyst is fairly limited, because these pairs add readily to olefins and acetylenes hampering the hydrogenation process. To bypass that undesirable reactivity, a novel intermolecular FLP has been designed that involves a sterically more demanding mesityl borane combined with small-size bases.3 These pairs show enhanced selectivity in catalytic hydrogenation of a variety of organic compounds.
Quinoline and mesityl borane can also act as an FLP towards hydrogen cleavage, however, the reaction yields tetrahydro products. Consequently, the recently developed borane can be used as an efficient catalyst in the hydrogenation of heteroaromatic rings. Our DFT calculations focusing on the mechanism of these reactions reveal the details of possible reaction pathways. The species depicted in the figure was identified as a key intermediate.
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B(C6F5)2Mes / Quinoline / H2 system
[1] D. W. Stephan and G. Erker, Angew. Chem. Int. Ed. 2010, 49, 46.
[2] T. A. Rokob, A. Hamza, A. Stirling, T. Soós and I. Pápai, Angew. Chem., Int. Ed., 2008, 47, 2435.
[3] G. Erős, H. Mehdi, I. Pápai, T. A. Rokob, P. Király, G. Tárkányi and T. Soós, Angew. Chem. Int. Ed 2010, 49, 1.
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Electric properties of 2-cyclopenten-1-on
Jana Páleniková, Vladimír Kellö
Department of Physical and Theoretical Chemistry, Faculty of Natural SciencesComenius UniversityMlynska Dolina CH-1
842 15 Bratislava, Slovakia [email protected]
The aim of this study is to compare behavior of dipole moments and dipole polarisabilities of organic molecule 2-cyclopenten-1-one (2CP) in the ground state S0 and three electronic excited states S1 (n→π*), T1 (n→π*) and T2 (π→π*). The geometry of 2-cyclopenten-1-one in its ground state S0 was optimized using the CASPT2 method, including ALASKA for analytical gradients, with the 6-311+G(d,p) basis set. Calculations of the electric properties were carried out using coupled cluster methods CCSD and CCSD(T), in conjunction with the Pol [1] basis set and the Z2Pol [2] basis set. The two-determinant CCSD method [3] was used for open-shell singlet. All calculations were performed using the system of quantum chemical programs MOLCAS.
The order of vertical excitation energies 2CP computed using CCSD method with Pol basis set is T1 (3,62 eV), S1 (3,96 eV) and T2 (3,98 eV). There is a large change in dipole moment of the 2CP molecule due to excitation to the T1 and S1 states. Total dipole moment decreased by about 60%. This change is due to excitation in n (nonbonding) orbital located on oxygen atom to π* (π-antibonding) orbital located mainly along the C-C bond. Polarisabilities of the T1 and S1 excited states are much less affected by the excitation from the ground state. The largest change occurs by excitation in the z axis.
[1] A.J. Sadlej, Coll. Czech. Chem. Commun. 53, 1995 (1988).[2] Z. Benková, A.J. Sadlej, R.E. Oakes, S.E. Bell: J. Comput. Chem. 26, 145 (2005).[3] P. Neogrady, P. G. Szalay, W. P. Kraemer, et al.: Collect. Czech. Chem. Commun.
70, 951 (2005).
This work was supported by the Slovak Grant Agency VEGA under the contract No. 1/0520/10. The support is gratefully acknowledged.
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Long-range corrected dispersionless density
functional
Ewa Pastorczak1, Katarzyna Pernal2, Krzysztof Szalewicz3
1 Technical University of Lodz, Institute of Applied Radiation Chemistry
Wrblewskiego 15
93-590 Lodz, Poland
[email protected] Technical University of Lodz, Institute of Physics
Wolczanska 219
90-924 Lodz, Poland3 Department of Physics and Astronomy, University of Delaware
Newark, Delaware 19716, USA
A new density functional, based on dispersionless density functional (DL09) [1]
and Hirao’s long-range correction scheme [2], is proposed.
The DL09 functional is known to predict very accurately the dispersionless parts
of intermolecular interactions, whereas the dispersion part can be computed ab initio
or by a function fitted to computed ab initio values. However, its long-range sepa-
ration performance for a number of systems (e.g. C6H6) dimer could be improved.
Also, DL09 is not suitable for the problems involving forming or breaking chemical
bonds.
The new, long-range corrected DL09, where the exchange part consists of short-
range density functional part and long- and short-range parts of Hartree-Fock ex-
change (given with different coefficients), with reoptimized parameters is expected
to perform as well as, or better, than DL09 for all the systems with intermolecular
interactions and additionally calculate accurately the reaction barrier energies.
References
[1] Pernal K., Podeszwa R.,Patkowski K., Szalewicz K., Phys. Rev. Lett. 103,
263201 (2009).
[2] Iikura H., Tsuneda T., Yanai T., Hirao K., J. Chem. Phys. 115, 3540 (2001).
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Electric properties of low-lying excited states of acetone and their interaction with water
L. F. Pašteka1, M. Urban1,2
1Department of physical and theoretical chemistry, Faculty of natural Sciences,Comenius University, Mlynská dolina, 842 15 Bratislava, Slovakia
2Slovak University of Technology in Bratislava, Faculty of Materials Science and Technology, Institute of Materials Science, J. Bottu 25, 917 24 Trnava, Slovakia
Dipole moments, polarizabilities and hyperpolarizabilities are important molecular properties, for example in connection with optical shifts resulting from the rearrangement of the solvent upon the excitation of the solute molecule. Acetone, investigated in this paper, serves as a prototype of a variety of carbonyl compounds. Their electric properties affect the intermolecular interactions of molecules with the environment in organic and biochemical systems, in which chemiexcitation can occur easily.
The present work focuses on computing the electric properties of low lying singlet and triplet valence states as well as the ground state of acetone. Structures of these states were optimized at the aug-cc-pVTZ/CASPT2 level of the theory. Geometry of the ground state is in the C2v symmetry and geometry of the excited states is in Cs symmetry, since the oxygen leans out of the carbon plane during the excitation, except for 1,3σ-π* state, which is in C2v symmetry with the methyl groups twisted by 180°.
Subsequently, the same method was used in numerical derivatives of energy with respect to the strength of an external electric field (the FFPT approach). In this scheme the 3, 5, 7, 9, 11 and 13-point central differentiation formulae with equidistant step of size of 0.001 a.u., 0.002 a.u., 0.004 a.u., and 0.008 a.u. were used. We also differenciated the polynomial fit through all of the points with various degrees of the polynomes. This approach gave us enough results to be able to enumerate the accuracy of the resulting value in terms of an interval to which all the results belong. For each state the first four energy derivatives are calculated, which allows obtaining the dipole moment, dipole polarizability and first two hyperpolarizabilities.
Dipole moment expectation values obtained from CASSCF computations were also used to calculate higher derivatives and some of the off-diagonal terms of the tensor of polarizability and hyperpolarizability.
Vertical and adiabatic excitation energies are also presented. They primarily serve as a toll for justification of methods used in our computations, since these are the only available experimental data for excited states of acetone.
Significant changes of the geometry and electronic structure upon excitation substantially affect all these molecular properties of acetone.
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We were also interested how interaction with water may affect properties and geometries of the studied states. Monosolvated geometries of each of the studied states were optimized at CASPT2/aug-cc-pVDZ level of theory. Water binds through the H-bond to the oxygen atom in the acetone molecule. There are four such CS configurations for the excited states (see figure below), of which one is by ~2 kcal/mol lower in energy than the other three. This is due to the antiparallel orientation of the acetone and water dipole moments (d), thus total dipole is almost zero and there is small charge separation.
Monosolvatation energies were also computed. BBSE for water-acetone interaction energies is quite large (1-3 kcal/mol) so all energies were counterpoise corrected with inclusion of geometry relaxation effect.
c)
a) b) d)
Acknowledgements: This research was supported by the Slovak Grant Agency, grant VEGA-1/0520/10 and by the Slovak Research and Development Agency APVV, contract No. LPP-0155-09. and by Comenius University, grant UK/294/2010.
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Muonic systems with Debye-screened Coulomb
interactions
Mariusz Pawlakab, Miros�law Bylickia and Prasanta K. Mukherjeec
aInstitute of Physics, Nicolaus Copernicus University
Grudziadzka 5, 87-100 Torun, Poland
[email protected] of Chemistry, Nicolaus Copernicus University
Gagarina 7, 87-100 Torun, PolandcIndian Association for the Cultivation of Science
Jadavpur, Kolkata-700 032, India
We investigate ground states of exotic systems (ppµ, ddµ and ttµ) with Coulomb
interactions weakened by the Debye screening. We noticed that for strong screen-
ing the binding energy per particle becomes in three-particle systems larger than
in bound two-particle subsystems. Despite the repelling interaction of the nuclei,
this leads to so-called Borromean states: bound three-body states for the screen-
ing beyond the critical value for the two-body binding of nucleus-muon pair. The
method of computation involves a basis set of functions dependent explicitly on all
interparticle distances.
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A non-adiabatic molecular dynamics study of
azobenzene isomerization after excitation to the
S1 state based on overlaps of CASSCF wave
functions
Marek Pederzoli and Jirı Pittner
J. Heyrovsky Institute of Physical Chemistry, Academy of Sciences of the CzechRepublic, v.v.i., Dolejskova 3 , 18223 Prague 8, Czech Republic
[email protected], [email protected]
Mario BarbattiMax-Planck-Institut fur Kohlenforschung, Kaiser-Wilhelm-Platz 1, D-45470
Mulheim an der Ruhr, Germany.
Hans LischkaInstitute for Theoretical Chemistry, University of Vienna, Waehrinegrstrasse 17, A
1090 Vienna, Austria.
The mechanism of azobenzene photoisomerization has been debated for decades
and various mechanisms have been proposed for photoisomerization after excitation
to S1 and S2 excited states. We carried out ab initio non-adiabatic dynamical
simulations of cis-to-trans isomerization upon S1 excitation employing the Tully’s
surface hopping method with potential-energy surfaces and couplings determined
”on the fly”. The non-adiabatic couplings have been computed based on overlap of
CASCSF wavefunction.
We confirmed that the azobenzene photoisomerization after n-π excitation occurs
purely as an torsional motion via a S0/S1 conical intersection located near the
midpoint of this rotational pathway.
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Relativistic effects on metal-metal bonding. Comparison of the performance of ECP and scalar DKH description on the picture of
metal-metal bonding in Re2Cl8(2-)
Robert Ponec,a Lukáš Bučinský,b Carlo Gattic aInstitute of Chemical Process Fundamentals, Academy of Sciences of the Czech Republic v.v.i., Prague 6, Suchdol 2, 165 02 Czech Republic bInstitute of Physical Chemistry and Chemical Physics, Slovak University of Technology in Bratislava, Bratislava, Slovakia cIstituto di Scienze e Tecnologie Molecolari del CNR (CNR-ISTM) e Dipartimento di Chimica Fisica ed Elettrochimica, Università di Milano, Via Golgi 19, I-20133, Milano, Italy
The picture of the metal-metal bonding in the Re2Cl8(2-) anion is analyzed using the
so-called domain averaged Fermi holes (DAFH) []. Besides the comparison of scalar
DKH2/B3LYP and ECP/B3LYP DAFH bonding analysis, the systematic comparison of
the “exact” atoms in molecules (AIM) [] generalized form of DAFH analysis with the
approximate Mulliken-like approach is presented. Furthermore the geometry of the
Re2Cl8(2-) anion has been reoptimized at the all-electron (AE) non-relativistic and 1-
component (scalar) and 2-component DKH2 level of theory.
The DAFH bonding analysis based on the AE-DKH2/B3LYP calculations yields
quantitatively the same conclusions as the ECP/B3LYP calculation using the AIM
population analysis. The DAFH analysis at the AE-DKH2/B3LYP level but using the
Mulliken population analysis on the other hand fails. The scalar and spin-orbit relativistic
effects at the AE-DKH2/B3LYP are not significant for the Re-Re, Re-Cl bond distances
and the angle ReReCl.
[1] Ponec R., Yuzhakov G.: Theor. Chem. Acc. 2007, 118, 791-797.
[2] Bader R.F.W.: Atoms in Molecules. A Quantum Theory, Clarendon Press, 1994.
Acknowledgement
The author (R.P.) thanks for the support of this study by the grant of the Grant Agency of
the Czech Republic, grant No: 203/118/09. The support from the grants: APVV (contract
No. APVV-0093-07) and VEGA (contracts No. 1/0817/08 and 1/0127/09) is also
gratefully acknowledged by L.B.
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High Valent Iron-Oxo Complexes with Organic
Macrocycles: DFT and Ab Initio Study
Mariusz Radona, Ewa Broc�lawikb, Kristine Pierlootc
aDepartment of Theoretical Chemistry, Jagiellonian University Ingardena 3, 30-060
Krakow, Poland. bInstitute of Catalysis and Surface Chemistry Niezapominajek 8,
30-239 Krakow, Poland. cDepartment of Chemistry, Catholic University of Leuven
Celestijnenlaan 200F, B-3001 Heverlee (Leuven), Belgium
High valent iron-oxo complexes with organic macrocycles (porphyrin, corrole, etc.)
are usually described as Fe(IV)-oxo coupled to organic radical, so called Cpd I-type
species [1]. Nonetheless, some experiments suggest that these complexes might
have a metastable and highly reactive form, tentatively assigned as an Fe(V)-oxo
electromer [2]. The putative Fe(V)-oxo electromer might be important for catalytic
activity of cytrochrome P450 and syntethic iron-porphyrins [2]. In contrast, the
theory was sceptical as to existence of true Fe(V)-oxo species in heme environment
until very recently [1, 3, 4].
In this study [4] we investigate the relative energies of various electromeric states
for model complexes with porphyrin [FeO(P)+, FeO(P)(Cl)] and with a smaller
mimick of porphyrin [FeO(η2-N2C3H5)+
2 ] using ab initio CASPT2, RASPT2, and
CCSD(T) calculations, as well as standard DFT methods (B3LYP, B3LYP*, OLYP,
BP86). Our results suggest that all the studied complexes have a low lying Fe(V)-
oxo electromer, sometimes appearing even as the ground state. We note, however,
that the DFT results are strongly functional dependent. In particular, the hybrid
functionals strongly favor the Fe(IV)-oxo-radical form, incorrectly predicting the
Fe(V)-oxo form too high in energy. This observation might be relevant for model-
ing oxidative activity of cytochromes P450 and related enzymes, where the hybrid
functionals are used routinely.
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References
[1] A. Ghosh: Acc. Chem Res 38, 943 (2005).
[2] (a) R. Zhang and M. Newcomb: Acc. Chem. Res. 41, 468 (2008); (b) X. Sheng,
J.H. Horner, M. Newcomb: J. Am. Chem. Soc. 130 13310 (2008).
[3] (a) F. Ogliaro, S.P. de Visser, J.T. Groves, S. Shaik: Angew. Chem. Int. Ed. 40
2874 (2001); (b) H. Chen, J. Song, W. Lai, W. Wu, S. Shaik: J. Chem. Theory
Comput. 6, 940 (2010).
[4] M. Radon, E. Broclawik, K. Pierloot: in preparation (2010).
This work was supported by the Polish State Ministry of Science and Higher
Education, by the Flemish Science Foundation and from the Concerted Research
Actions of the Flemish Government.
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Quantum Chemical Study of the Energetics of Phenolic Compounds
Rimarčík J., Ilčin M., Rottmannová L., Klein E., Lukeš V.
Faculty of Chemical and Food Techology, SUT Bratislava Radlinského 9
SK-81237 Bratislava, Slovakia [email protected]
Hydrogen atom transfer (HAT) represents the generally accepted mechanism of
phenolic compounds (ArOH) antioxidant action. The first step of the mechanism is
phenolic O–H bond cleavage [1]. The main aim of this work is to compute reaction
enthalpies related to this process, i.e. O–H bond dissociation enthalpies (BDE) for
selected phenolic compounds. We have studied polysubstituted phenol with OH, CN or
CH3 groups (Fig 1).
Gaussian 03 program package was employed in this work [2]. Geometries of each
compound and radical were optimized using DFT method with UB3LYP functional
without any constraints using 6-311++G** basis set. Real minima were confirmed using
vibrational analysis (no imaginary frequency). All conformers were calculated and for
next processing were chosen only most stable structures.
We have calculated BDEs of phenol and substituted phenols with two, three, four
and five CN, CH3, or OH groups. We have investigated the effect of various substitutions
on O–H bond dissociation enthalpy. Cyano group was chosen as an electron-withdrawing
substituent. Results for cyano substituted phenols are compiled in table 1. Methyl group
has very low electron-donating character. OH represents an electron-donating group and
there is usual more than one hydroxy group in natural phenolic antioxidants.
Figure 1. Schematic structure of studied molecules. Various mono, di,.tri, tetra and
penta substituted phenols with a) OH, b) CN and c) CH3 groups.
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Table 1. Bond dissociation enthalpies of cyano substituted phenols, in kJ mol-1. Data in parentheses stand for available experimental BDEs.
molecule BDE molecule BDE molecule BDE
F1CNa 353 (368) F2CNe 372 F3CNf 371
F1CNb 358 (374, 393) F2CNf 364 F4CNa 381
F1CNc 356 (377–398) F3CNa 373 F4CNb 376
F2CNa 361 F3CNb 370 F4CNc 372
F2CNb 367 F3CNc 367 F5CNa 382
F2CNc 369 F3CNd 372
F2CNd 368 F3CNe 378 Phenol 347
[1] GUGUMUS, F. Oxidation inhibition in organic materials. Vol. 1. Boca Raton: CRC Press, 1990. Chapter 4, Stabilization of plastics thermal oxidation, p. 156-157. [2] Pople J. A. et al.: GAUSSIAN 03, Revision A.1, Gaussian, Inc., Pittsburgh, PA, 2003.
Acknowledgement
The work has been supported by Scientific Grant Agency (VEGA Project 1/0137/09).
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The Influence of Substituents on the Activity of Half-Titanocene Catalysts for Ethylene Polymerization: Theoretical Study
Agnieszka Rogowska, Artur Michalak, Monika Srebro, Mariusz Mitoraj
the Jagiellonian University, Ingardena 3,
30-060 Krakow, Poland
Polyethenes belong to the most widely used polymers, with annual production of
approximately 80 million metric tons. Due to the growing demand for such materials
there is still a need for development of new organometallic systems revealing the better
catalytic performance in the ethylene polymerization processes. Here, the combined
theoretical and experimental studies are of great importance as they enable to fully
characterize the structure-activity relationship. In this study we would like to present our
latest results on theoretical investigations of a series of the Ti-based organometallic
catalysts, at the density functional theory (DFT) level.
This theoretical study is focused on half-titanocene pentamethylcyclopentadienide
complexes (Figure) with aryloxo-based ligands (R=H, F, OCH3). It was demonstrated in
the recent experimental studies[1] that these type of catalysts could have much better
performance in the high-temperature ethylene polymerization processes even in
comparison with the commonly used in the industry Constrained Geometry Catalyst.
The main goal of the present research was to explore the influence of substituents
on the activity of the half-titanocene catalysts, concerning both, the energy barriers as
well as character of metal-ligand bonding. The Ziegler–Rauk energy-partitioning scheme
(ETS, Extended Transition State)[2] has been used to analyze the electrostatic, Pauli
repulsion, and orbital interaction contribution to the bond energy. The combined ETS-
NOCV (Natural Orbitals for Chemical Valence)[3] analysis was further applied in order
to describe bonding in terms of the contributions to the deformation density originating
from the electron donation (ligand to metal) and back-bonding (metal to ligand).
The 9th Central European Symposium on Theoretical Chemistry
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[1] Kim, T.-J.; Kim, S. K.; Kim, B.-J.; Hahn, J. S.; Ok, M.-A.; Song, J. H.; Shin, D.-H.;
Ko, J.; Cheong, M.; Kim, J.; Won, H.; Mitoraj, M.; Srebro, M.; Michalak, A.; Kang,
S. O. Macromolecules 2009, 42, 6932.
[2] Ziegler, T., Rauk, A. Theor. Chim. Acta 1977, 46, 1; Ziegler, T.; Rauk, A. Inorg.
Chem. 1979, 18, 1755;
[3] Mitoraj, M.; Michalak,A; Ziegler, T. J. Chem. Theory Comput., 2009, 5(4), 962;
Mitoraj, M.; Michalak,A; Ziegler, T. Organometallics, 2009, 28 (13), 3727
Acknowledgement to the Foundation for Polish Science MPD Programme co-financed by
the EU European Regional Development Fund.
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A local Coupled Cluster algorithm
Zoltan Rolik, Mihaly Kallay
Budapest University of Technology and Economics (BME)
P.O.Box 91
H-1521 Budapest, Hungary
[email protected], [email protected]
Many methods use localized orbitals to reduce the calculation cost of electron cor-
relation for large molecules utilizing the weak interaction between orbitals localized
far away from each other. In addition, our Coupled Cluster (CC) approach applies
the idea behind the optimized virtual orbitals [1, 2]. Unlike many methods which
divide the molecules into molecular fragments, we divide the CC energy among the
localized occupied orbitals [3]. The partial CC energy contributions belonging to
the occupied orbitals are the quantities that we estimate. For each occupied orbital
a small optimized basis set is determined [4]. Each partial CC energy contribution
is approximated using the optimized basis sets.
The presentation also shows some promising preliminary numerical results.
References
[1] Ludwik Adamowicz, Rodney J. Bartlett, and Andrej J. Sadlej J. Chem. Phys.
88, 5749 (1988).
[2] Pavel Neogrady, Michal Pitonak and Miroslav Urban, Mol. Phys. 103, 2141
(2005).
[3] Wei Li, Piotr Piecuch, Jeffrey R. Gour, and Shuhua Li J. Chem. Phys. 131,
114109 (2009).
[4] Frank Neese, Frank Wennmohs, and Andreas Hansen J. Chem. Phys. 130,
114108 (2009).
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Thermodynamics of homolytic S–H bond dissociation in mono-substituted thiophenols
Lenka Rottmannová, Ján Rimarčík, Erik Klein, Vladimír Lukeš
Institute of Physical Chemistry and Chemical Physics, Slovak University of Technology in Bratislava, Radlinského 9, SK-812 37 Bratislava, Slovak republic
[email protected], [email protected], [email protected], [email protected]
Sulfur-centered radicals represent an important field in chemistry due to their role
in organic synthesis, biochemistry or atmospheric chemistry. Therefore, this study is
devoted to S–H bond cleavage in thiophenols, ArSH → ArS● + H●. This work presents
the study of 14 mono-substituted thiophenols (Fig. 1).
SHX SH
Y Fig. 1 Studied thiophenols, X = OMe, Me, F, Cl, Br, COOMe, CF3, NO2, Y = OMe, Me, Cl, Br, CF3, NO2
Selected compounds and their radicals were studied using DFT/UB3LYP/6-
311++G** approach using Gaussian 03 program package [3]. BDEs were approximated
from total electronic energies.
Calculated BDEs were compared with available experimental values. Bordwell et
al. [1] studied mono-substituted thiophenols employing electrochemical (EC) method that
uses the equilibrium acidity (pKa) and oxidation potential (Eox) values of the conjugated
anion for BDE calculation. Zhu et al. [2] obtained BDEs using thermodynamic cycle
(TDC) method. The method is close to EC method. All experimental values represent
solution-phase values in dimethylsulfoxide (DMSO). Semi-empirical methods do not
provide correct BDE values for thiophenols. However, they reliably reproduce the
substituent effect on BDE. MP2 method overestimates individual BDEs, however
provides the range of substituent induced BDE changes in good agreement with
experiments. Used DFT approach describes BDEs and substituent induced changes in
best accordance to experimental works.
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Tab. 1 BDE values in kJ.mol–1 of substituted thiophenols and Hammett constants.
Substituent ECa TDCb PM3c AM1c DFT MP2c σp,md
— 331 331 377 363 334 352 p-OMe 322 322 372 358 321 345 –0.27 p-Me 328 328 375 361 329 349 –0.17 m-Me 330 330 376 362 333 352 –0.07 p-F 376 359 349 0.06 m-OMe 378 363 356 0.12 p-Cl 331 331 376 362 332 353 0.23 p-Br 332 332 379 363 333 354 0.23 m-Cl 335 335 378 363 337 0.37 m-Br 378 363 0.39 m-CF3 338 338 380 365 340 0.43 p-COOMe 381 368 0.45 p-CF3 383 368 0.54 m-NO2 384 368 0.71 p-NO2 341 341 388 370 347 361 0.78 a Data taken from Ref. [1]. b Data taken from Ref. [2]. c Data taken from Ref. [4]. d Data taken from Ref. [5]. References
[1] Bordwell F.G., Zhang X.-M., Satish A.V., Cheng J.-P.: J. Am. Chem. Soc. 119 (1997)
9125.
[2] Zhu Q., Zhang X.M., Fry A.J.: Polym. Degrad. Stab. 57 (1997) 43.
[3] Pople J. A. et al.: GAUSSIAN 03, Revision A.1, Gaussian, Inc., Pittsburgh, PA, 2003.
[4] Klein E., Lukeš V., Cibulková Z., Polovková J.: J. Mol. Struct. (Theochem) 758, 149
(2006).
[5] Hansh C., Leo A., Taft R. W.: Chem. Rev. 91 (1991) 165.
Acknowledgement
This work was supported by the Scientific Grant Agency of the Slovak Republic
(Projects VEGA 1/0127/09 and 1/0137/09).
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Computational study of weak interactions in the biologically active compounds
Scholtzová Eva and Mach Pavel
Institute of Inorganic Chemistry, Slovak Academy of Sciences,Dúbravská cesta 9
SK-845 36 Bratislava, Slovak [email protected]
Imidazo [2,1-b] thiazoles are intensively studied in the connection with search for
biologically active compounds. The fused rings system of imidazo [2,1-b] thiazoles
exhibits biological activities like antitumor, antitubercular, cardiovascular, herbicidal,
antibacterial, and antihelmintic activity. Presented imidazo [2,1-b] thiazoles are
interesting also due to weak interactions acting in these structures which are on the border
of the weak hydrogen bonds and electrostatic interactions. Because of their non/local
(long-range) character, these dispersion interactions are accurately accounted for only by
correlated wavefunction based methods like MP2, CCSD(T) or DFT-D method, which
adds to the energy special empirical dispersion term. The aim of this study is a detailed
analysis of weak interactions in the presented biologically active structures. The RI-MP2
and DFT-D methods implemented in the TURBOMOLE package were used for
calculation of the interaction energies of the individual weak interactions.
In the case of two imidazo [2,1-b] thiazoles (A and B) the dispersion interaction is
dominant. In the cluster of (A) structure (Fig. 1) the most tightly bound is 1-3 dimer (-
18.2 kcal/mol) against 2-3 dimer (-8.2kcal/mol) and 1-2 one (-7.1 kcal/mol). For smaller
model of C5-N5C N1 interaction the calculated DFT-D interaction energy at B97-
D/TZVPP (-9.6 kcal/mol) level of theory showed good agreement with more rigorous RI-
MP2 energy extrapolated to the CBS limit (-12.08 kcal/mol). One should keep in mind
that generally MP2 method at CBS limit overestimates dispersion energy, roughly by
20%, so both methods are in harmony.
In the case of (B) structure, there are stacks of parallel molecules, from which we
can singlet out two dimers (Fig. 2): one with C–H O short contacts and another with C–
H N1 contacts. The interaction energy is in the first case -22.5 kcal/mol (B97-D/TZVPP
level) and in the second -21.3 kcal/mol. As standard DFT method (B3LYP) supply for
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these interactions only small bonding energies (-3.9 kcal/mol for the first case) and
slightly repulsive (2.4 kcal/mol in the second case), it is clear that bonding is in high
extend due to the dispersion. In the next step the RI-MP2 method and extrapolation of the
interaction energy to the CBS limit was used for the calculation of the interaction
energies of the individual weak interactions in the both (A) and (B) structures. The
analysis of calculated data showed that both (A) and (B) structures are stabilized mainly
by dispersion energy and also by weak hydrogen bonds of C–H···N> C–H···O> C–H···S
type and C–H···π and π···π stacking type of weak interactions (Table 1).
Tab. 1 Interaction energies for (A) and (B) structures.
ig. 1 Cluster model for examination of dispersion energy
tion of dispersion energy in (B).
cknowledgement: Finantial support for this research by the Slovak Grant Agency (grant no. VEGA /0150/09) is gratefully acknowledged.
D–H···A (A) D–H···A (B)C1–H1B···S1 -1.11 C8–H18···S1 -1.37C5–H5B···N1 -5.38 C20–H20···N1 -3.29C5–H5C···N1 -12.08 C16–H16···O1 -2.52C1–H1C···O1 -2.56 C5–H5C···O1 -3.054x CH···π -6.03 intra CH···π -0.9
F
in (A).
Fig. 2 Cluster models for examina
A2
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TD-DFT investigation of S1 and S2 singlet states of TMPyP(n) and complexes of
TMPyP4 with sulfonated calix[m]arenes
Jakub Šebera1, Stanislav Záliš1, Pavel Kubát1, Kamil Lang2, Tomáš Polívka3
[email protected] J. Heyrovsky Institute of Physical Chemistry, Academy of Sciences of the Czech Republic,
Dolejškova 3, CZ 18223, Prague, Czech Republic 2 Institute of Inorganic Chemistry, v.v.i., Academy of Sciences of the Czech Republic, 250 68
Řež, Czech Republic3 Institute of Physical Biology, University of South Bohemia, Zámek 136, Nové Hrady 37333,
Czech Republic
Photophysical and binding properties predetermine tetrakis (4-N-methylpyridyl)
porphyrin (TMPyP4) as efficient photosensitizer in many artificial light-harvesting systems as
well as in medicine for photodynamic therapy of tumors or bacteria/virus inactivation.
Organizing TMPyP4 molecules through noncovalent host−guest interaction with a range of
guests like nucleic acids/proteins, calixarenes, cyclodextrins, carbon nanotubes, PAMAM
dendrimers, graphene, cucurbituril or their incorporation into micelles, methyl viologen-
hybrid and nafion films, semiconductors, layered silicates, laponite, hydrogels and other solid
materials finds immense importance in creating ordered structures of specific functionality.
Isoelectronic TMPyP2 and TMPyP3 can modulate properties of resulting supramolecular
complexes due to rotational barrier of N-methylpyridyl groups.
Water-soluble p-sulfonatocalixarenes clxm possess the three-dimensional, flexible,
π-electron rich cavities that can adopt different conformations, form complexes with many
compounds and have diverse biomedical applications e.g they can serve as transportation
vehicles for porphyrin drugs. The number of conformations increases with the number of
4-hydroxy-benzenesulfonate units in the system, although this also depends on the solvent
and the nature of the guest.
We have used TD-DFT and DFT calculations to study (photoinduced) charge transfer
in tetrakis(n-N-methylpyridyl)porphyrins TMPyPn (n=2,3,4) and TMPyP4/p-
sulfonatocalix[m]arenes clxm (m=4,6) complexes and to interpret transient absorption
spectroscopy, cyclic voltametry experiments and UV-Vis absorption spectra. Density
functionals MPW1B95 and B3LYP were used. The effect of solvent (water) was described by
Conductor-like Screening Model (COSMO). Excitation of TMPyPn into S1 state is
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accompanied by increasing of electron density at methylpyridyl groups in the following order:
TMPyP2 < TMPyP3 < TMPyP4. Further results on characterization of S1 and S2 singlet states
will be presented. The examples of the investigated complexes are depicted in Figure 1.
Figure 1. DFT optimized geometries of TMPyP4-clx4 (left) and TMPyP4-clx6 (right). Both
systems have partly ionized OH groups.
Acknowledgement: The access to the METACentrum supercomputing facilities is highly
acknowledged. This research was supported by the Czech Science Foundation (No.
P208/10/1678).
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Application of OVOS technique in calculations of small semiconductor clusters.
L. Šimováa, P. Neográdya and M. Urbana,b
aDepartment of Physical and Theoretical chemistry, Faculty of Natural
Sciences,Comenius University, Mlynská dolina, 842 15 Bratislava, Slovakia bSlovak University of Technology in Bratislava, Faculty of Materials Science and Technology, Institute of Materials Science, J. Bottu 25, 917 24 Trnava, Slovakia
Following our previous work on small semiconductor clusters Ga2N2, In2N2,
[1,2] we now present CCSD(T) calculations of germanium nitrides and phosphides.
Gallium, Indium and Germanium species are of interest in the semiconductor
materials science and are technologically interesting due to their applications in
optoelectronics and nanotechnologies. Information on the structure, energetics and
molecular properties of small clusters of these species in different spectroscopic
states, can be useful for understanding basic processes in the above mentioned areas.
We hope that accurate CCSD(T) data for small clusters containing Ga, In, Ge,
N, P and C or Si can be eventually exploited as benchmark results for various DFT
techniques, which can be applied for larger clusters related to technological
applications.
Fig.1: Lowest energy structures of 4- and 6- atomic gallium phosphide and
aluminium phosphide clusters.
Clearly, in CCSD(T) calculations of molecules containing Ga, In, or Ge their
subvalence d-shell must be correlated. This requires [2] using large (aug)-cc-pCVXZ
or similar basis sets constructed having in mind correlation of deeper shells of these
elements, which is computationally demanding. We will show that the OVOS
(Optimized Virtual Orbital Space) technique [3] with the virtual space of (aug)-cc-
pCVXZ basis sets reduced to the size corresponding to less extended valence-only
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(aug)-cc-pVXZ bases allows investigations of complexes containing group 13 and 14
elements with no reduction of the accuracy.
References:
[1] M. Kraus, L. Šimová, P. Neogrády, M. Urban, Mol. Phys. 108, 467 (2010);
[2] L. Šimová, D. Tzeli, M. Urban, I. Černušák, G. Theodorakopoulos, I.D. Petsalakis,
Chem. Phys. 349, 98 (2008).
[3] P. Neogrády, M. Pitoňák, J. Granatier, M. Urban, Coupled Cluster Calculations: Ovos As
An Alternative Avenue Towards Treating Still Larger Molecules, in Recent Progress in
Coupled Cluster Methods, Eds. P. Čársky, J. Paldus, J. Pittner, Springer, 2010.
Acknowledgements: The support by the the Slovak Grant Agency VEGA--1/0520/10
and by EURATOM CU assoc., Task 4.2 - P1c is acknowledged.
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Benchmark electron density calculations on
Be-like atoms
R. S�lupskia), J. Komasab), K. Jankowskic), and J. Wasilewskic)
a)Computing Centre, Nicholas Copernicus University,PL-87-100 Torun, Poland
b)Department of Chemistry, Adam Mickiewicz University,PL-60-780 Poznan,Poland
c)Faculty of Physics, Astronomy, and Informatics, Nicholas Copernicus University
PL-87-100 Torun, Poland
Electron densities obtained in the most accurate variational calculations on the
ground state of several members of the beryllium-isoelectronic series are applied in
comparative studies of the performance of several broadly used ab initio methods in
representing electron densities in the presence of varying non-dynamical correlation
effects. The present calculations involved from 4800- to 9000-term exponentially cor-
related Gaussians (ECG) basis functions defined by carefully optimized nonlinear
parameters [1]. The densities for the remaining methods are calculated by means of
GAUSSIAN03 for basis sets partially optimized for the individual ions. To concen-
trate our attention on the correlation effects, we employ a density-based graphical
approach directly hinged on difference radial density (DRD) distributions defined
with respect the Hartree-Fock (HF) radial density in the following way:
dA(r) = DA(r) − DHF (r), (1)
with
DA(r) = 4πr2ρA(r), (2)
where A indicates the method of accounting for correlation effects.
The benchmark DRDs are obtained when using DHF (r) generated for the Froese-
Fischer numerical Hartree-Fock wave function.
It has been demonstrated [2] that, although the impact of correlation effects
on the electron density is relatively weak, the DRD distribution curves provide a
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reliable description of the impact of electron correlation effects both at the WFT
and DFT levels.
To provide the possibility of precise comparison of different results we report also
values of total radial densities for several r-values.
References
[1] J. Komasa, J. Chem. Phys. 110, 790 (1999)
[2] K. Jankowski, I. Grabowski, K. Nowakowski, and J. Wasilewski, J. Chem. Phys.
130, 164102 (2009).
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Comparison of the several correlated OEP
methods in KS-DFT with correct asymptotic
behavior.
Szymon Smiga, Ireneusz Grabowski
Institute of Physics, Nicolaus Copernicus UniversityGrudziadzka 5/7
87-100 Torun, Poland
In recent years, a large emphasis is placed on the development of methods for the
proper inclusion of the electron correlation effects [1, 2] in the Optimized Effective
Potential (OEP) methods and the correct asymptotic behavior of the exchange-
correlation potentials [4, 5]. To show that the inclusion of the additional linear
correction term to OEP exchange potential improves asymptotic behavior of the
OEP potentials, to different types of the ab initio KS–OEP calculations has been
performed for a few atoms (He, Be, Ne). Conventional correlated OEP results,
has been compared with the results obtained with the correlated OEP calculations
where the optimized local potential have the Slater type of asymptotic behavior
In addition to compere KS-OEP result with ab initio wave function theory results,
MP2 and CC calculations has been performed.
The results were compared in the terms of total ground state energies, correlation
energies, exchange–correlation potentials and the electron radial density [3]. Ana-
lysis of the energies, potentials and the electron radial density clearly showed, that
the results obtained in the correlated OEP calculations with linear correction signi-
ficantly improves shape of exchange-correlation potentials while the total energies
remain essentially the same. The highest occupied orbital energies from the asymp-
totically corrected exchange-correlation potentials are found to provide significantly
more accurate approximations to the ionization potential than those without the
asymptotically corrected exchange-correlation potentials.
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Figure.1. Comparison of the exchange-correlation potential of the helium atom
obtained for few KS-OEP methods and MP2, CC calculations.
Literatura
[1] I. Grabowski, S. Hirata, S. Ivanov, and R. J. Bartlett. J. Chem. Phys., 116:4415,
2002.
[2] I. Grabowski and V. Lotrich. Mol. Phys., 103:2087, 2005.
[3] I. Grabowski K. Jankowski, K. Nowakowski and J. Wasilewski. J. Chem. Phys.,
130, 2009.
[4] R. Nesbet R. Colle. Optimized effective potential in finite-basis-set treatment.
J. Phys. B, 34(12):2475, 2001.
[5] R. Bartlett S.Ivanov, S. Hirata. Finite-basis-set optimized effective potential
exchange-only method. J. Chem. Phys., 116, 2002.
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Theoretical Study of Ionization and Excitation of
He Gas Exposed to Intense XUV Radiation
Jan Smydke, Petra Ruth Kapralova
J. Heyrovsky Institute of Physical Chemistry, Academy of Sciences of theCzech Republic, v.v.i., Dolejskova 3, 182 23 Praha 8, Czech Republic
andInstitute of Physics, Academy of Sciences of the Czech Republic, v.v.i.,
Na Slovance 2, 182 21 Praha 8, Czech Republic
[email protected], [email protected]
A recent advent of extreme ultraviolet (XUV) and soft X-ray (SXR) lasers enables
investigation of interactions of high-frequency, high-amplitude electromagnetic field
with atomic and molecular gases. A theoretical description of an isolated He atom
in strong femtosecond and nanosecond pulses of 50 nm laser radiation is presented.
The interaction of the field and the atom can be described in a semiclassical
dipole approximation due to the large strength of the field (109−1016 W cm−2) and
relatively small size of the investigated atoms compared to the wavelength of the
radiation, such that the Hamiltonian is given by
H = H0 + Az0 f(t)ε0ω
c(z1 + z2) sinωt
where H0 denotes the field-free Hamiltonian; Az0, the pulse strength at the maxi-
mum; f(t), the pulse modulation (0 < f(t) < 1); ε0, the permitivity of vacuum; c,
the speed of light; ω, the field oscillation; and z1, z2 the electronic coordinates.
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In analogy to the Born–Oppenheimer approximation, the slow pulse modulation
can be adiabatically separated from the fast field oscillation and electronic motion.
In this spirit, the adiabatic states are represented by the quasistationary states |Φk〉
of the Floquet Hamiltonian, which is defined as
HF = H0 + Azε0ω
c(z1 + z2) sinωt− ih
∂
∂t
where Az represents a constant vector potential of a continuous electromagnetic
wave.
Finally, the nonadiabatic time-dependent wavefunction |Ψ(t)〉 is obtained by ex-
panding it in the basis of the quasistationary states
|Ψ(t)〉 =∑
k
|Φk;Az〉χk(t)
and solving the expansion coefficients. (Note the field strength Az = Az0f(t) is a
time-dependent parameter of the basis.)
Due to the ionization effect, which causes the quasistationary states to include an
outgoing part of the ionized electron, we apply the complex scaling transformation of
the Floquet Hamiltonian, which enables to calculate the quasistationary resonances
(i.e. “meta-stable states”). Thus the obtained quasienergies are complex, where
their imaginary parts represent ionization rate constants.
In this contribution, we present the first results, namely the calculated ionization
rate constant as a function of laser strength. These data will be readily useful for an
interpetation of an experiment using long laser pulses, which will be performed at
Institute of Physics. In a subsequent calculation, we are going to provide ionization
yields for short laser pulses.
The calculations are performed with our own codes using a complex scaling Full-CI
method and a (t, t′)-method for the quasistationary states.
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Femtosecond non-adiabatic molecular dynamics: a study of photochemical deactivation of indole
Lukáš Sobek, Jiří Pittner
J. Heyrovsky Institute of Physical Chemistry of the ASCR Dolejškova 2155/3, 182 23 Prague 8, Czech Republic
[email protected] [email protected]
Photochemical behavior of indole can be explained by the presence of polarity
dependent channel of radiationless deactivation attributable to hydrogen predissociation
from NH bond in non-polar non-hydrogen bonding solvents and photoinization in water
as presented in [1]. Our goal is performing the simulation of the deexcitation process with
the quasi-classical molecular dynamics (MD) in which non-adiabatic transitions are
computed by the Tully's fewest switches surface hopping algorithm [2].
We employed the state-averaged complete active space self-consistent field
method (SA-CASSCF) using standard split-valence double zeta Gaussian basis set 6-31
G with polarization functions on carbon atoms and on the hydrogen atom of the NH
group. Correct description of σ* orbital located near NH bond needed s- and p-diffuse
functions (exponent 0.0639) located on the nitrogen atom and s-diffuse function
(exponent 0.036) centered on the adjacent hydrogen atom. The active space involved 10
electrons in 8 orbitals. Four lowest quantum states of indole, i.e. S0, S1 (La), S2 (Lb) (both
of ππ* character) and S3 (σπ*) were treated with weight 0.25 in the state-averaging
procedure.
Potential energy profiles along the NH-bond stretch were computed by means of
coordinate-driven minimum-energy-path approach: for a given value of bond distance all
remaining intramolecular coordinates were optimized with CASSCF analytical gradient.
Initial conditions for the MD simulation were sampled using the Wigner distribution for
temperature 300 K, starting from S2 state (excitation UVc computed wavelength 250 nm).
Total 69 trajectories were run for 500 fs each. We performed exponential fitting of the S2-
state-depopulation curve and obtained the half-time of depopulation of 11.9 fs.
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132
[1] A.L.Sobolewski, W.Domcke: Ab initio investigations on the photophysics of indole,
Chem.Phys.Letters 329 (2000) 130 - 137
[2] J.C.Tully: Mixed quantum-classical dynamics, Faraday Discuss 110 (1998) 407-419
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Theoretical study of radical sites in gallic and protocatechuic acids
Roland Šolc,1 Daniel Tunega,1,2 Martin H. Gerzabek,1 and Hans Lischka2
1 Institute of Soil Research, University of Natural Resources and Applied Life Sciences, Peter-Jordan-Strasse 82b, A-1190 Vienna, Austria,
2 Institute for Theoretical Chemistry, University of Vienna, Währinger Strasse 17, A-1090 Vienna,Austria
e-mail: [email protected]
Humic acids (HA) represent a group of organic macromolecules with high
structural complexity and multiple properties. HAs contain stable organic radical
moieties and are involved in important biochemical and chemical environmental
processes. The high structural heterogeneity and complexity of humic acids leads to
problematic their characterization and interpretation of experimental data. Despite, it is
known that the major part of HAs functional groups include carboxylic (R-COOH),
phenolic (R-OH), and/or carbonyl (C=O) group. Thus, a viable approach is to examine
appropriate small organic molecules as models of humic macromolecules or their
components [1,2]. While simple organic acids do not approach the structural and
functional complexity of real humic acids, detailed studies demonstrated that certain
important features can be remarkably similar [3,4].
Hydroxybenzoic acid derivatives such as gallic acid (GA) or protocatechuic acid
(PA) represent very suitable models for a study of radical sites in HAs [5]. In this work,
a theoretical investigation of the radical stability of GA and PA is presented. All
calculations were performed by means of a density functional theory approach (DFT).
In the first step, all possible radical, anion, and radical-anion structures were generated
and the full geometry optimization was performed on them at the B3LYP/TZVP level of
theory. The solvent effect on the radical stability and geometry was investigated as well.
The EPR and NMR parameters were calculated using the B3LYP/EPRII approach, both
for gas phase and solvent optimized geometries. Calculated EPR and NMR values were
compared with available experimental data.
[1] Kummert, R., Stumm, W., J. Colloid Interface Sci. 75, 373 (1980).
[2] Banaya, L., Garnier, J.-M., Environ. Sci. Technol. 33, 1398 (1999).
The 9th Central European Symposium on Theoretical Chemistry
134
[3] McBride, M. B.,Wesselink, L. G., Environ. Sci. Technol. 22, 703 (1988).
[4] Boily, J.-F., Fein, J. B., Chem. Geol. 148, 157 (1998).
[5] Giannakopoulos, E., Stathi, P., Dimos, K., Gournis, D., Sanakis, Y., Deligiannakis,
Y., Langmuir, 22, 6863, (2006).
Acknowledgment - We are grateful for the financial support from the Austrian Sciences Fund (project P20893-N19), and the German Research Foundation, the priority program SPP 1315 (project GE1676/1-1). The authors also acknowledge the technical support and computer time at the Vienna Scientific Cluster.
The 9th Central European Symposium on Theoretical Chemistry
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Charge Sensitivity Analisys in Force Field Atoms Resolution
Anna Stachowicz and Jacek Korchowiec
Jagiellonian University, Department of Theoretical Chemistry ul. R. Ingardena 3, 30-060, Kraków, Poland
[email protected], [email protected]
Charge Sensitivity Analysis (CSA) was formulated in the nineties [1]. The formalism
is rooted in Density Functional Theory (DFT) and can be applied at different resolutions: local,
molecular orbital, atoms-in-molecule (AIM), fragment and global. It refers to such concepts
as electronegativity and hardness/softness data; all of them are rigorously defined within DFT.
CSA provides a thermodynamic-like description of the system’s equilibrium charge distribution
and allows to describe its response to external potential and/or electron population perturbations.
It has normally been used as a method complementary to ab initio calculations but it can likewise
be treated as an independent semi-empirical method. One of the realizations of CSA
is Electronegativity Equalization Method (EEM) for evaluating the charge distribution
in a molecule at global equilibrium [2].
EEM is a very fast method and is usually adopted in AIM resolution in Molecular
Mechanics/Dynamics (MM/MD) software for computing initial charge distribution. It should
be expected that by extending CSA to force field atom resolution the area of its application will
be enlarged, e.g., to polarizable force fields. To enable this the atomic hardnesses and
electronegativities have to be parameterized. This is the goal of our work. The AMBER force
field has been employed here and the set of parameters for all standart atom types of the force
field has been determined by fitting to the ab initio charge distribution of a set of test molecules.
Ab initio charges were obtained via two methods, namely Mulliken Population Analysis (MPA)
and charges derived from electrostatic potential fitting procedure. The optimization was
performed with an evolutionary algorithm on a population of 50 entities.
The results obtained were satisfactory. The agreement between ab initio and EEM charges was
good, especially for MPA charges. The correlation coefficient R2=0.9699 was obtained,
which is accurate enough to start applying EEM in the MM/MD calculations.
The 9th Central European Symposium on Theoretical Chemistry
136
[1] R. F. Nalewajski, J. Korchwiec, Charge Sensitivity Approach to Electronic Structure and
Chemical Reactivity, Word Scientific Co. Pte. Ltd., Singapore, 1997
[2] W. J. Mortier, S. K. Gosh, S. Shankar, J. Am. Chem. Soc., 108 (1986) 4315
The 9th Central European Symposium on Theoretical Chemistry
137
Cold electron collisions with nonpolar molecules
M. Sulc, R. Curık
J. Heyrovsky Institute of Physical Chemistry
Dolejskova 3
182 23 Prague 8, Czech Republic
We investigate collisions of cold electrons (incident energy below 1 eV) with di-
atomic nonpolar molecules by combination of the body frame rigid rotor approxima-
tion with the adiabatic frame transformation [1, 2]. Electron-molecule interaction is
in case of e−–N2 process described for benchmarking purposes in an ab-initio man-
ner by the static-exchange plus polarisation (SEP) model similar to [3]. Even this
approximation leads to an acceptable agreement with experimental data measured
at the ASTRID laboratory [4]. The reactance matrix is further parametrised with
a few quantities. Their energy dependence is then determined from the experimental
data by fitting of the total and backward scattering cross-sections. This information
makes consequently the physical description within our approach complete and we
can in principle predict individual rotational state-to-state cross-sections and thus
separate the (rotationally) elastic and inelastic processes, which is experimentally
unachievable. Obtained theoretical results therefore find application especially in
plasma related fields such as astrophysics, physics of interstellar media as well as
semiconductors (micro-devices) production [5]. Results are compared to data avail-
able in literature [6] and also to predictions based on the Modified Effective Range
Theory (MERT) models [7].
Acknowledgements
We gratefully appreciate the substantial financial support of the Grant Agency of the
Czech Republic (grant no. 202/08/0631), the Grant Agency of the Czech Academy of
Sciences (grant no. KJB400400803) and the Grant Agency of the Charles University
in Prague (grant no. 113210).
The 9th Central European Symposium on Theoretical Chemistry
138
References
[1] W.M. Huo and F.A. Gianturco. Computational methods for Electron-Molecule
Collisions. Plenum Press, New York, 1995.
[2] U. Fano and S. Chang. Theory of electron-molecule collisions by frame transfor-
mations. Phys. Rev. A, 6:173–185, 1972.
[3] S. Telega and F.A. Gianturco. Electron–molecule scattering in gases at very
low energies: a comparison of theory and experiment for the nitrogen target.
Mol. Phys., 104(November):3147–3154, 2006.
[4] S.V. Hoffmann, S.L. Lunt, N.C. Jones, D. Field, and J.-P. Ziesel. An undulator-
based spherical grating monochromator beamline for low energy electron-
molecule scattering experiments. Rev. Sci. Instrum., 73:4157–4163, 2002.
[5] M.A. Morrison. The physics of low-energy electron-molecule collisions (a guide
for the perplexed and the uninitiated). Aust. J. Phys., 36:239–286, 1983.
[6] M.J. Brunger and S.J. Buckman. Electron-molecule scattering cross-sections I –
experimental techniques and data for diatomic molecules. Phys. Rep., 357:215–
458, 2002.
[7] W.A. Isaacs and M.A. Morrison. Modified effective range theory as an alternative
to low-energy close-coupling calculations. J.Phys. B, 25:703–725, 1992.
The 9th Central European Symposium on Theoretical Chemistry
139
OVOS technique with controlled accuracy in noniterative triples calculations
Martin Šulka, Michal Pitoák, Miroslav Urban, Pavel Neogrády
Department of Physical and Theoretical Chemistry, Faculty of Natural Sciences, Comenius University Mlynská dolina CH1
84215 Bratislava, Slovakia [email protected]
Performance of optimized virtual orbital space (OVOS) technique with controlled
accuracy approach, introduced by Kraus et al. [1], was studied. They have shown that
there is roughly linear dependence between the Y2,MP2 correction and post-MP2
corrections (Y2,CCSD, Y2,T3) in coupled cluster CCSD(T) method in logarithmic scale. This
fact opens up the possibility to control the accuracy of the whole calculation via the
Y2,MP2 correction.
Eight molecules from S22 series [2] were chosen in our calculations. For four of
them, dependence between post-MP2 corrections and Y2,MP2 correction is shown in
Figure 1.
Figure 1 Dependence between log(Y2,MP2) and log(Q), where Q is Y2,CCSD and Y2,T3
The 9th Central European Symposium on Theoretical Chemistry
140
We can see that both post-MP2 corrections are nearly linearly dependent on Y2,MP2
and at the same time the triples correction is much smaller than CCSD correction. From
the controlled accuracy point of view, it is optimal to perform calculation of all
contributions with the same level of accuracy. Since the error introduced by triples step in
CCSD(T) is smaller than that introduced at CCSD level, we can make some profit from
additional reducing of virtual space just before the triples step, up to such extension at
which we reach the same level of accuracy (expressed in terms of Y2,CCSD and Y2,T3
corrections) in both CCSD and T3 steps. In our calculations we wanted to evaluate the
measure of possible reduction before the triples step in CCSD(T). Table 1 summarizes
our results, where the final dPOVOS results in eventual additional reduction before the
triples step.
Table 1 Reductions of virtual space at CCSD and T3 levels at the same level of accuracy
(POVOS) and their difference (dPOVOS)
Average possible reduction in our case was about 32 percent. Since the triples step is the
most demanding step in CCSD(T) calculation (scales with N7), this would mean
considerable saving of computational time.
[1] Kraus, M. Pitoák, P. Hobza, M. Urban, P. Neogrády – To be published
[2] P. Jureka, J. Šponer, J. erný, P. Hobza; Phys Chem Chem Phys 8, 1985-1993, 2006
Acknowledgement
This work was supported by the Slovak Research and Development Agency, contracts
No. APVV-20-018405, APVV-LPP-0155-09, and the Slovak Grant Agency VEGA under
contract No. 1/0428/09.
The 9th Central European Symposium on Theoretical Chemistry
141
Substituent effect on OH- addition to substituted benzocyclobutene-1, 2-diones: A DFT study
Nargis Sultana and Walter M. F. Fabian
Institut für Chemie, Karl-Franzens-Universität Graz Heinrichstrasse 28/I 8010 Graz, Austria
A DFT study on the reaction route and chemical reactivity for the addition of OH- (a
nucleophile) to substituted (poly) carbonyl compounds is carried out by using [B3LYP/6-31+G (d, p)].
1,2-dicarbonyls undergo three types of reaction following addition of OH–, (1) benzyl–benzilic acid
rearrangement (path A); (2) fission of the α-carbon – carbonyl carbon bond (path B); and (3) fission of
the carbonyl carbon – carbonyl carbon bond (path C).1
In all cases, the primary element of such reactions is the formation of tetrahedral adduct (2) as an
intermediate. In this study, the extremes of substituent effect on the formation of (2)resulting from the
attack of OH- as a nucleophile on the substituted benzocyclobutene-1,2-dione (I) leading toadduct (2)
has been explored. The model systems used in the calculations contains [OH (H2O)4]– + [I.(H2O)2],
Y=-OCH3 and -NO2 groups. The investigation of chemical reactivity has been accomplished by
conventional density functionaltheory2; electrophilicity indexes.
O
O O
OH
OH
OCOOH
OHCOO
COO
O
OHR1 R2
R2R1
_
1 2
R1
R2
R1
R2
_path A
path BR1
_+
4
path C
3
+ R2H
5 6
R1CHO + R2COO_
7 8
O
O
Y
Benzocyclobutene-1,2-dione (I)
Y= -OCH3, -NO2
[1] Bwden, K.; Fabian, W.M.F. J. Phys. Org. Chem. 2001, 14, 794.
[2] Fuentealba, P., Contreras, R.R., Reviews of Modern Quantum Chemistry, World
Scientific, 2002, Volume II.
The 9th Central European Symposium on Theoretical Chemistry
142
Calculations of fine-structure resolved collisional
rates for NH(X3Σ−)-He system
Robert Tobo�la1, Fabien Dumouchel2, Jacek K�los3, Francois Lique2
1Faculty of Chemistry, University of Warsaw,
Pasteura 1,
02-093 Warsaw, Poland
2LOMC - Universite du Havre,
25 Rue Philippe Lebon,
BP 540 - 76 058 Le Havre Cedex, France
3Department of Chemistry and Biochemistry - University of Maryland,
College Park,
20742-2021 Maryland, USA
We present the first to date fine-structure-resolved collisional rate coefficients for
NH(X3Σ−)-He van der Waals complex. The calculations are based on the state-of-
the-art potential energy surface of Cybulski at al. [H. Cybulski, R. V. Krems, H.
R. Sadeghpour, A. Dalgarno, J. K�los, G. C. Groenenboom, A. van der Avoird, D.
Zgid, and G. Cha�lasinski, J. Chem. Phys. 122, 094307 (2005)]. Close-coupling cal-
culations of the collisional excitation cross sections of the fine-structure levels of NH
by He are calculated for total energies up to 3500 cm−1, which yield, after thermal
average, rate coefficients up to 350 K. The fine-structure splitting of rotational levels
is taken into account rigorously. The propensity rules between fine-structure levels
are reported, and it is obvious that F -conserving cross sections are much larger
than F -changing cross sections, as expected from theoretical considerations. The
calculated rate coefficients are compared with available experimental measurements
at room temperature and a fairly good agreement is found between experimental
and theoretical data. The agreement confirms the relatively good quality of the
scattering calculations in this work.
The 9th Central European Symposium on Theoretical Chemistry
143
Wetting of clay mineral surfaces – molecular dynamics simulation
Daniel Tunega,1,2 Roland Šolc,1 Hasan Pašalić,2 Martin H. Gerzabek,1 and Hans Lischka2
1 Institute for Soil Science, University of Natural Resources and Applied Life Sciences, Peter-Jordan Strasse 82b, A-1190 Vienna, Austria
2 Institute for Theoratical Chemistry, University of Vienna, Währingerstrasse 17, A-1090 Vienna, Austria
e-mail: [email protected]
Wettability of minerals is primarily related to an energetic characteristic of surfaces
affecting processes as adhesion, friction, detergency, biofilm growth, etc. The wetting
ability of a solid surface is mainly determined by its chemical composition, structure and
topography [1]. The solid-liquid contact angle method is often used to characterize
wettability of surfaces and to determine its surface free energy.
Clay minerals represent a group of geochemically and industrially important
materials. They also belong to a substantial part of inorganic soil matter and significantly
affect overall properties of soils. Owing to compositional variability ad structural
complexity various clay minerals behave considerably differently with respect to wetting.
In order to elucidate structural and compositional factors affecting
hydrophilic/hydrophobic character of clay minerals, interactions of water nanodroplets
with basal surfaces of selected clay minerals (particularly kaolinite and phlogopite) were
investigated by means of classical molecular dynamics simulations at room temperature.
From the evolution and shape of the nanodroplet on the surfaces it was possible to
characterize hydrophobic/hydrophilic character of studied surfaces. In case of the
kaolinite octahedral surface formed from surface hydroxyl groups, the water droplet was
completely spread and a monomolecular network of hydrogen-bonded water molecules
was formed. In opposite, the tetrahedral surface, which is formed from basal oxygen
atoms, is less interacting with the water nanodroplet and the shape of the droplet is
partially preserving. The molecular simulations clearly showed a difference between both
basal surfaces of kaolinite. While the octahedral surface is clearly hydrophilic, the
tetrahedral surface has partially hydrophobic character. Structural and energetic aspects
of both surfaces are obtained as well.
The 9th Central European Symposium on Theoretical Chemistry
144
Fig. 1 Water density profile (in g/cm3) of water
nanodroplet on tetrehadral kaolinite surface.
(500 water molecules, 2 ns MD, 300K).
[1] Bachmann, J. et al., (2000) Soil Sci. Soc. Am. J., 64, 564-567.
Acknowledgement - We are grateful for the financial support from the Austrian Sciences
Fund (project P20893-N19), and the German Research Foundation, the priority program
SPP 1315 (project GE1676/1-1). The authors also acknowledge the technical support and
computer time at the Vienna Scientific Cluster.
The 9th Central European Symposium on Theoretical Chemistry
145
Optimalizations of the molecular clusters by the evolutional algorithms method
Lucie Zárubová, Karel Oleksy
Department of Physics, Faculty of Science, University of Ostrava 30. dubna 22
70103 Ostrava, Czech Republic [email protected]
This work focuses on searching for suitable parametrs in our computer programme
based on genetic algorithms. We tested various parameters – for Lennard-Jones clusters with
10 and 30 molecules we tested dependence of number of optimizations on the number of
processors used; for water clusters (H2O)n of n = 2-13 molecules we tested dependence of
energy evolution during the program progress, which was confronted with [1]; and for water
cluster with 11 molecules we tested suitability of various evolution operators (probability of
genotype mutation, phenotype mutation, cut by plane, crossover coordination, crossover
cluster) used.
0 10 20 30 40
4,30
4,32
4,34
4,36
4,38
4,40
4,42
4,44
4,46
Optimalization number
Ene
rgy
[eV]
0.2 1.0 0.8 0.6 0.4
Figure: Dependence of energy for water cluster (H2O)11 on probability of cut by plane (0.2-1.0) used
The 9th Central European Symposium on Theoretical Chemistry
146
[1] Wales, D.J. a Hodges, M.P. Chem. Phys. Lett., 286, 65. 1998. [2] Hartke, B. Global Geometry Optimalization of Molecular Clusters: TIP4P Water Zeitschrift für Phys. Chemie, 214, 9 1251-1264. 2000. [3] Cartwright, H. M. An introduction to Evolutionary Computation and Evolutionary Algorithms Springer-Verlag Berlin Heidelberg. 2004. Acknowledgement
Grant Agency of the Academy of Sciences of the Czech Republic, grant No. IAA401870702;
University of Ostrava, Students Grant Competition, grant No. SGS7/PřF/2010.