Applications of ETS-NOCV method in description of varioustypes of chemical bonds

Mariusz Mariusz P. P. MitorajMitoraj

Jagiellonian UniversityCracow, Poland

Department of Theoretical Chemistry

ADF webinar, Kraków-rest-of-the-world, 28th Feb., 2014

Examples of theoretical quantities for visualization of chemical bond

ADF webinar, Kraków-restoftheworld, 28th Feb., 2014

Formation of chemical bond in H2 – based picture

H H

H2

HH 22 Deformation density (Differential density)

(1) qualitative databy inspection of the signof : negative (outflow),positive (inflow) of densitydue to bond formation

H H

1. Start from promolecular state (atom/fragments)

H=1s2 H=1s2

ADF webinar, Kraków-restoftheworld, 28th Feb., 2014

The Natural Orbitals for Chemical Valence (NOCV)The Natural Orbitals for Chemical Valence (NOCV)

NOCV’s also decompose the deformation density :

useful qualitative databy inspection of the signof : negative (outflow),positive (inflow) of density

M

1k

2kk )r(ψv)r(ρ

Mitoraj, M.; Michalak, A. Organometallics 2007, 26(26); 6576., Michalak, A.; Mitoraj, M.; Ziegler, T. J. Phys. Chem. A. 2008, 112 (9), 1933, Mitoraj, M.; Michalak, A. J. Mol. Model., 2008, 14, 681, Mitoraj,

M.; Zhu, H.; Michalak, A.; Ziegler, T. 2008, International Journal of Quantum Chemistry, DOI: 10.1002/qua.21910., Mitoraj, M.; Michalak, A. J. Mol. Model. 2008, 14, 681.

NOCV’s ( ) diagonalize the deformation density matrix:

PCi v iCi ; i =1,M

where P=P-P0 , density matrix of the combined molecule,P0- density matrix of the considered molecular fragments.

i

iiji λ*Cψ

(r) vk[ k2 (r) k

2

k1

M / 2

(r)] k (r)k1

M / 2

NOCV’s are in pairs:

Radoń, M. Theor Chem Account 2008, 120,337.

backdonation

donation

backdonation

The contours of the deformation density (The contours of the deformation density () and the contributions) and the contributionsfrom the pairs of complementary orbitals for the heme/CO systemfrom the pairs of complementary orbitals for the heme/CO system

rr i

n

ii

2

1

)(

q = 0.74q = 1.04

-De=Etotal= Edist + Eelstat + EPauli + Eorb ETS:

λ μ

TSλμ

orbλμorb FPE

2/M

k

korb

TSk

2/M

1k

TSkkorb E]FF[vE Energetic estimation

of k

A combination of ETS and NOCV - (ETS-NOCV)A combination of ETS and NOCV - (ETS-NOCV)

NOCV:

2/N

1kk

2/N

1k

2k

2kk

orb )r(ρ)]r(ψ)r(ψ[v)r(ρ

2/N

1k

orbk

2/N

1k

TSk,k

TSk,kk

TSorbTSorborb E]FF[v)CFCCPC(Tr)FPTr( E

ETS-NOCV:

Mariusz P. Mitoraj, Artur Michalak and Tom Ziegler „A combined charge and energy decom-

Position scheme for bond analysis” J. Chem. Theory Comput., 2009, 5 (4), pp 962–975.

electronic factor

Dative bonds – systems with symmetry Dative bonds – systems with symmetry

(CO)5Cr=CH2

donation

backdonation

:CN- > PH3 > NH3 > C2H4 > CS > CO > N2 > NO+

:NO+ > CS > CO > N2 > C2H4 > PH3 > CN- > NH3

for Ni(NH3)3 X complexes:Donor/acceptor properties of ligands

Mitoraj Mariusz, Michalak A (2007) „ Donor-Acceptor Properties of Ligands from the Natural Orbitals for Chemical Valence” Organometallics, 26, 6576-6580

Dative Bond NHDative Bond NH33BHBH3 3 - Calculations- Calculations

• Define closed shell fragments, NH3 and BH3

• Run SP calculations to get the fragment MO’s• Run SP ETS-NOCV calculations for whole molecule in the basis of previously calculated fragment MO’s

Dative Bond NHDative Bond NH33BHBH3 3 - Calculations- Calculations

M.Mitoraj J. Phys. Chem. A, 2011, 115 (51), pp 14708–14716

Crystal of Ammonia Borane, NHCrystal of Ammonia Borane, NH33BHBH33

M.Mitoraj J. Phys. Chem. A, 2011, 115 (51), pp 14708–14716

Inter-Molecular-Hydrogen BondsInter-Molecular-Hydrogen Bonds

Adenine-Thyminekcal/mol,

(BP86/TZ2P)A-T

Eint -13.0

Eorb -22.0

EPauli 38.7

Eprep 2.1

Eelstat -31.9

Etotal-experiment99 -12.1

Etotal – other

theoreticalresults

-13.2

Eorb=-22.0

Rafał Kurczab, Mariusz P. Mitoraj, Artur Michalak and Tom Ziegler J. Phys. Chem. A,2010, 114, 8581.

N*(H-N)

H-N covalency!

O-H

O*(H-N)

Hydrogen Bond A-T CalculationsHydrogen Bond A-T Calculations

• Define closed shell fragments, Adenine and Thymine• Run SP calculations to get the fragment MO’s• Run SP ETS-NOCV calculations for whole molecule in the basis of previously calculated fragment MO’s

ADF webinar, Kraków-restoftheworld, 28th Feb., 2014

Covalent bondsCovalent bonds

CHCH33-CH-CH33 CHCH22=CH=CH22GeHGeH22=GeH=GeH22 HH33CCCCCCHCCH33

Quadruple bond; ReQuadruple bond; Re22ClCl882-2-

[-1.3 kcal/mol]

1[-65.5 kcal/mol]

2[-65.5 kcal/mol]

[-84.3 kcal/mol]

Etotal=-31.3kcal/molEorb=-242.7Esteric=211.4

Cr2, formally sixtuple bond, bCr2-Nal = 6.01

Eorb=-242.7 kcal/mol

Typical-Multiple bonds-TMTypical-Multiple bonds-TM

J. Chem. Theory Comput., 2009, 5 (4), pp 962–975.

Ethane Built from two methyl radicalsEthane Built from two methyl radicals

1. Define CH3 regions (uneven number of electrons);2. Run SP RESTRICTED ! Calculations for CH3 fragments to get the fragment MO’s; (1/2 + 1/2 electrons for SOMO of CH3)3. Use fragoccupations keyword in order to keep the right occupations for each CH3

fragoccupations f1 A 5 // 4 subend f2 A 4 // 5 subend End

4. Run SP ETS-NOCV calculations for whole molecule in the basis of previously calculated fragment MO’s -alpha-and beta-NOCV’s

Etotal=-31.3kcal/molEorb=-242.7Esteric=211.4

Cr2, sextuple bond, bCr2-Nal = 6.01

Eorb=-242.7 kcal/mol

Typical-Multiple bonds-TMTypical-Multiple bonds-TM

J. Chem. Theory Comput., 2009, 5 (4), pp 962–975.

CrCr22 Built from two Cr Built from two Cr++CrCr

1. Define Cr regions (uneven number of electrons);2. Run SP RESTRICTED ! Calculations for Cr fragments using OCCUPATION keyword (A 18 1 1 1 1 1 1);Should be like CrShould be like Cr but it is Cr 6* but it is Cr 6* (1/2 + 1/2) so we must:3. Use fragoccupations keyword in order to keep the right occupations for each Cr.

fragoccupations

Region_1

A 15//9

subend

Region_2

A 9//15

subend

End

4. Run SP ETS-NOCV calculations for whole molecule in the basis of previously calculated fragment MO’s

CrCr

CrCr

Better Fragment MO’s from unrestriced run:Better Fragment MO’s from unrestriced run: advanced ’manual’ usageadvanced ’manual’ usage

1. Run open shell calculations for a given fragment;

2. Save tape21 ascii (dmpkf) copy the final MO’s(from the section Eig-CoreSFO_A, MO’s expressed in SFO);

3. Run fragment calculations by setting SCF=0 wrong MO’ssave tape21asciifind Eig-CoreSFO_A section, then:

4. Take MO’s and occupations, energies, from step 2 and paste them toTape21 from step 3…..it gives you right fragment MO’sTransform asciibinary(udmpkf);

ADF uses in principle only ‚rectricted’ fragments, however, one might cheat him

5. Rerun final ETSNOCV calculations (do not recalculate the fragments!)

Agostic intramolecular RH---Metal interactionAgostic intramolecular RH---Metal interaction

Ni-diimine cationic Brookhart model catalyst

Mariusz P. Mitoraj, Artur Michalak and Tom Ziegler „On the Nature of the Agostic Bond between Metal Centers and -Hydrogen Atoms in Alkyl Complexes. An Analysis Based on the Extended Transition State Method and the Natural Orbitals for Chemical Valence Scheme (ETS-NOCV)”

Organometallics, 2009, 28 (13), pp 3727

Ni-C

C-Hpolarization

C-C

ETSNOCV(red-outflow,blue-inflow) -8.3 kcal/mol

Halogen Bonding CFHalogen Bonding CF33I---NHI---NH33 from ETS-NOCV perspective from ETS-NOCV perspective

N

H

H

H

I CF

FF

N-I covalency

N*(C-F)

charge accumulation, increase s-character (pointed out by prof. Grabowski)

Charge outflow, increase positive charge

Grabowski S. Chem. Rev., 2011, 111 (4), pp 2597–2625

Domination of the electrostatic factor is due to the presense of σ-holeon iodine atom:

FF

F I

Halogen Bonding CFHalogen Bonding CF33I---NHI---NH33 from ETS-NOCV perspective from ETS-NOCV perspective

(Politzer P, Lane P, Concha MC, Ma Y, Murray J (2007) JMolModel, 13, 305, „An Overview of Halogen Bonding”

Halogen Bonding CFHalogen Bonding CF33I---NHI---NH33 from ETS-NOCV perspective from ETS-NOCV perspective

Prof. Politzer, „Program & Book of Abstracts”, MIB 2011,„….The weakness of this interpretation (electrostatic) is that it is simple and straightforward, and therefore is viewed by some with suspicion.

C

F

F

F

I

FF

F I

Electrostatic potential picture

ETS-NOCV picture

(C-F) bond

-hole

Charge Anisotropy

Can ETS-NOCV discriminate between halogen and hydrogenCan ETS-NOCV discriminate between halogen and hydrogen bonding within the same molecule?bonding within the same molecule?

Anion receptor based on urea, which involve hydrogen and halogenBonding at the same time|:

Chudzinski, et all, JACS, 2011, 133, 10559

Can ETS-NOCV discriminate between halogen and hydrogenCan ETS-NOCV discriminate between halogen and hydrogen bonding within the same molecule?bonding within the same molecule?

-22.3 kcal/mol -6.3 kcal/mol

Yes: ETS-NOCV can separate halogen and hydrogen connections

Cl- / restCl- / rest

• Define closed shell fragments, Cl minus + rest of the complex• Run SP calculations to get the fragment MO’s• Run SP ETS-NOCV calculations for whole molecule in the basis of previously calculated fragment MO’s

ADF webinar, Kraków-restoftheworld, 28th Feb., 2014

Thank You very much for Thank You very much for Your Attention! Your Attention!

ADF webinar, Kraków-restoftheworld, 28th Feb., 2014