Acrylonitrile (AN)Cu 9 (100) interfaces: Electron distribution and nature of bonded interactions

Acrylonitrile (AN)–Cu9(100) interfaces: Electrondistribution and nature of bonded interactions

Petar M. Mitrasinovic

Abstract: There is a fundamental interest in the investigation of the interfacial interactions and charge migration pro-cesses between organic molecules and metallic surfaces from a theoretical standpoint. Quantum mechanical (QM) con-cepts of bonding are contrasted, and the vital importance of using combined QM methods to explore the nature of theinterfacial interactions is established. At the one-electron level, the charge distribution and nature of bonded interac-tions at the AN–Cu9(100) (neutral and charged (–1)) interfaces are investigated by both the Becke (B) – Vosko (V) –Wilk (W) – Nusair (N)/DZVP density functional theory (DFT) method and the MP2/6–31+G* strategy within the con-ceptual framework provided by natural bond orbital (NBO) – natural atomic orbital (NAO) population analysis andAtoms-In-Molecules (AIM) theory. By this approach, the interfacial interactions are given physical definitions free ofany assumptions and are visualized by using the topological features of the total electron density. A natural link be-tween the electron density on the one side and the shapes (not energies) of the highest occupied molecular orbital(HOMO) and lowest unoccupied molecular orbital (LUMO) on the other side is clarified. The question of whether thespatial extents of the HOMO and LUMO resemble the corresponding spatial maps of the negative (charge locally con-centrated) and positive (charge locally depleted) Laplacian of the total electron density in [AN–Cu9(100)]–1 is ad-dressed.

Key words: AN–Cu9(100) interfaces, NBO–NAO population, electron distribution, AIM, bonded interactions.

Résumé : D’un point de vue théorique, il existe un intérêt fondamental pour les recherches sur les interactions interfa-ciales et les processus de migration de charge entre des molécules organiques et les surfaces métalliques. On met enrelief les concepts de la mécanique quantique (MQ) de liaison et on démontre l’importance vitale d’utiliser des métho-des de MQ pour explorer la nature des interactions interfaciales. Au niveau d’un électron, on a étudié la distribution dela charge et la nature des interactions de liaison aux interfaces AN–Cu9(100) (neutres ou portant une charge de (–1))par la théorie de la densité fonctionnelle (TDF) de Becke (B) – Vosko (V) – Wilk (W) – Nusair (N)/DZVP ainsi qu’enfaisant appel à la stratégie MP2/6–31+G* dans le cadre conceptuel fournit par l’analyse des populations d’orbitaleliante naturelle (OLN) et d’orbitale atomique naturelle (OAN) ainsi que la théorie des atomes dans la molécule (ADM).Par cette approche, on donne des définitions physiques des interactions interfaciales qui sont exemptes de toute hypo-thèse et qui sont visualisées en faisant appel à des caractéristiques topologiques de la densité totale d’électron. On aclarifié un lien naturel entre d’une part la densité électronique et d’autre part les formes (non pas les énergies) del’orbitale moléculaire haute occupée (OH) et de la basse vacance (BV). On a essayé de déterminer si, dans [AN–Cu9-(100)]–1, les distributions spatiales des orbitales moléculaires OH et BV ressemblent aux cartes spatiales correspondan-tes des laplaciens négatifs (charge ponctuellement concentrée) et positifs (charge ponctuellement appauvrie) de ladensité électronique totale.

Mots clés : interfaces AN–Cu9(100), population OLN–OAN, distribution électronique, ADM, interactions liées.

[Traduit par la Rédaction] Mitrasinovic 554

Introduction

The semiconductor industry is facing difficulties with re-spect to its ultimate goal: to maintain a stable growth of thedensity of packing on a single chip. The permanent trend forreducing the size of conventional MOS (metal–oxide–semi-conductor) components, followed by the significant rise inthe costs needed for producing integrated circuits of a larger

scale, reflects the difficulties in the best possible sense (1).In this context, the potential of molecular electronics to be-come an alternative to the semiconductor industry is grow-ing rapidly. Many experimental and theoretical studies havebeen addressing the question of identifying the functionalabilities of single molecules or molecular self-assemblies tobehave as wires, diodes, transistors, and rectifiers. An exper-iment performed by Reed et al. (2) has shown that phenyl-

Can. J. Chem. 81: 542–554 (2003) doi: 10.1139/V03-043 © 2003 NRC Canada

542

Received 5 September 2002. Published on the NRC Research Press Web site at http://canjchem.nrc.ca on 23 May 2003.

Dedicated to Professor Don Arnold for his contributions to chemistry.

P.M. Mitrasinovic.1 Laboratory for Chemistry of Novel Materials, Center for Research on Molecular Electronics and Photonics,The University of Mons-Hainaut, B-7000 Mons, Belgium, Europe.

1Corresponding author (e-mail: [email protected]).

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ene-based derivatives are capable of behaving as aconducting wire when inserted into a metallic break junc-tion. There are indications that some molecules such as nan-otubes (3) and DNA (4) conduct a current when insertedbetween two metal electrodes. An ancient idea — datingback to Aviram and Ratner (5) — that organic moietieslinked by a saturated spacer between two metallic electrodescan act as a rectifier has recently been verified experimen-tally (6, 7). Mujica et al. (8) have noticed that molecular rec-tification is rare because the interplay between differenttransport regimes (for a specific interface) such as tunneling,hopping, and diffusion is temperature dependent. The au-thors (8) have also indicated that the current of the charge-carrying particles in the coherent tunneling regime dependsstrongly on the following factors: (i) the nature of the mo-lecular bridge and the contacts; (ii) the strength of the sur-face–molecule interaction; (iii) the position of the Fermienergy; and (iv) the profile of the electrochemical potentialacross the interface. The density of states within theHOMO–LUMO gap (HLG) makes the precise position ofthe Fermi energy level sensitive to a small amount of chargetransfer. Thus, the Fermi energy level should be viewed as afitting parameter inside a reasonable range. Several theoreti-cal investigations (9–14) devoted to the understanding of theconducting mechanisms through molecular wires haveshown that the electronic structure of the molecule and thegeometry of the metal–organic interfaces, as well as the na-ture of the chemical interactions, are crucial. By modifyingoriginal contacts between a conjugated molecule and a me-tallic surface by the addition of the sulfur and gold atoms toa terminal carbon of the molecule, Seminario et al. (15) haveshown that the character of the organic–metal interactions islocal. The authors of ref. 1 have stated on p. 10 077:“…there is still a fundamental interest from a theoreticalstandpoint to address separately, at least in the case of longmolecular wires, the charge injection mechanism (i.e., theinterfacial interactions between molecules and metallic sur-faces 32, 33) and the charge migration process…” (1). Thepresent study opens the question of the nature of bonded in-teraction at organic–metal interfaces from a more rigorous(in a physical sense) point of view.

There have been theoretical attempts to rationalize the ex-perimental results that characterize the organic–metal inter-faces. Although useful, there are well-known problemsassociated with such attempts, which have been quite exten-sively reviewed (16). The partitioning schemes of the molec-ular interaction energy used are arbitrary, and the definitionsof additive contributions to the energy are obscure. The divi-sions of the molecular interaction energy into classically in-terpretable segments do not distinguish different aspects ofelectron behavior. The charge transfer and electrostatic com-ponents do not have the usual physical meanings consideredin the Mulliken and Morokuma analyses, respectively(17(a)). The descriptions of bonded interactions have alsobeen sought in orbitals that are not invariant (17(b)). Thisstudy readily makes the distinctions.

Seminario et al. (18, p. 3017) have noticed that most pre-vious work dedicated to the understanding of conductionmechanism has been based on “…the orbital energetics

without considering the spatial extent of the conductionchannels…” (18). To predict the electronic transport of acharged molecule when some unoccupied orbitals of theneutral molecule become occupied following application ofan external voltage, the spatial profile of the LUMO and theHLG have been observed, because the HLG may be viewedas a measure of the hardness of the electron density (18–20).It has been proposed that a prerequisite for a satisfactorycharge transmission through a molecular junction is the de-localization of the LUMO without referring to the total elec-tron density (21). This study is a fundamental reformulationof this qualitative approach for a deeper reason that the suc-cess of frontier molecular orbital theory to rationalize the in-terfacial charge migration process may depend on if thespatial maps of the HOMO and LUMO resemble those de-termined by negative and positive values of the Laplacian ofthe total electron density, which determines the reactivity.2

Becke and Edgecombe (22) have noted that physicallymeaningful descriptions of electron behavior must be soughtin the density matrix (or related functions) and not in theorbitals. Wave functions (or more generally density matri-ces) are therefore indispensable for the interpretation ofelectron behavior. At the one-electron level, the density ma-trix may be diagonalized by using the natural orbitals (NOs)(23, 24). By writing the NOs as linear combinations of theatomic orbitals, an invariant description of electron behaviorcan be related to a localized picture of the atomic orbitals in-volved in bonding. On one hand, NBO analysis (25, 26) isoften in good agreement with such descriptions (27). On theother hand, Bader et al. (28) recognized an alternative or-bital-independent description of electron localization basedon the electron density. A bond path, as defined by Bader inhis AIM theory (29, 30), is a universal indicator of bondedinteractions (31). In this study, the behavior of the electronsin the AN–Cu9(100) complexes in terms of the charge distri-bution and nature of bonded interactions is described by useof the NBO–NAO–AIM strategy.

The plan of this paper is as follows. The theoretical back-ground is given in the following section. The primary inten-tion of this part is to emphasize the importance of usingcombined theoretical methods in investigating the organic—metal bonded interactions. By using NBO–NAO (23) popu-lation analysis and AIM (29, 30) theory, the electron distri-bution and nature of bonded interactions between AN andCu9(100) are explored in the “Electron distribution” and“Nature of bonded interaction” sections, respectively. Theinitial parts of nucleophilic reactions in the complexes arequantitatively expressed by use of the Fukui function f+ (32).In the “[AN–Cu9(100)]–1: Laplacian of total electron densityand spatial extents of HOMO and LUMO” section, the spa-tial extents of the HOMO and LUMO are contrasted to thoseof the negative and positive Laplacian in [AN–Cu9(100)]–1,respectively. Finally, the present qualitative approach is con-trasted to those used in various contributions to this topic.

Background

It is difficult to explore the nature of bonded interactionsat organic–metal interfaces without the concept of bonding

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2 P.M. Mitrasinovic. Unpublished data.



and the association of atoms in molecules. Bonds are im-plicit in the very notion of association. An appropriate ques-tion to be raised, which is not entirely metaphysical, iswhether the bonds hold the atoms together or whether thebonds are the outcome of other processes. In the context ofthis question, the key quantum mechanical concepts ofbonding are contrasted below, indicating the importance ofthe use of NBO analysis and AIM theory to characterizebonded interactions.

Quantum mechanical descriptions of bonding can be clas-sified into three groups. The first is based on the partition ofthe molecular interaction energy (33–39). The strength ofthe arbitrary partitioning schemes to divide the molecular in-teraction energy into classically interpretable segments isless pronounced than their weakness to ignore different as-pects of electron behavior. The determination of electron be-havior is crucial. The second interprets bonding by usingdensity matrices (22, 27, 40). Ruedenberg (40) sought to ex-tract physically meaningful descriptions of bonding, butFulton (27) fully succeeded in his attempt of this kind at theone-electron level. Due to computational costs, the one-electron density matrices of good quality for organic–metalcomplexes are unattainable at the present time. The intentionof this study is, still, to investigate the interfacial interactionsby use of theoretical techniques capable of producing quali-tative interpretations, which are comparable to those rootedin the density matrices. NBO analysis fulfils the requirement(25, 26). The third description of bonding takes advantage ofthe characteristics of the electron density within the mole-cule to interpret bonding (28–31). Note that the electroniccharge density distribution determines the three-dimensionalarrangements of the negative charge of an atom or a mole-cule, the sizes and shapes of molecules, and the electric mo-ments. In other words, the electron density, as a physicallymeasurable quantity, determines all chemical and physicalproperties of atoms and molecules. The actual distribution ofcharge within the molecule allows us to classify ionic andcovalent bonding patterns, but they are given physical defini-tions free of any assumptions. AIM theory (28–31) is of par-ticular interest for characterizing the organic—metal -bonded interactions.

The original definition of natural orbitals was given by us-ing the density matrix from a full configuration interaction(CI) wave function (24). The wave function is the best oneconstructed for a given basis set. The idea contained in theNAO and NBO analyses is that the one-electron density ma-trix can be used for defining the shape of the atomic orbitalsin the molecules and for deriving chemical bonds from elec-tron density between atoms (23). The first-order density ma-trix can be diagonalized by the eigenvectors called NOs andthe eigenvalues called Occupation Numbers. The summationof all contributions from orbitals on a specific atom gives theatomic charge. The NAOs usually contribute more than 99%to the electron density, giving a compact expression of thewave function in terms of atomic orbitals. Since the NAOsare defined from the one-electron density matrix, the elec-tron occupation is between 0 and 2, and the NAOs convergeto defined values as the size of the basis set is increased.NAO and NBO analyses may be run for correlated wavefunctions. On the basis of computational considerations, theNAO procedure is an attractive choice for analysis purposes,

involving only matrix diagonalization of small subsets of thedensity matrix.

The charge density distribution in the donor and acceptormolecules and in intermolecular regions can be used to char-acterize weak bonds within AIM theory (28–31). A line ofthe highest electron density linking any bonded pair of at-oms is called a bond path. The existence of a bond path is anecessary and sufficient condition for the existence of abond. The point of a line of the highest electron densitywhere the gradient, ∇

→ρ( )r , of the density ρ(r) is equal to

zero is the bond critical point (CP). The properties of thedensity at this point give quantitative information about thecharacteristics of that bond. A bond path between a pair ofnonchemically bonded atoms is termed an interaction line.The Laplacian of the electron density (∇ 2ρ(r)) indicateswhere the electron density is locally concentrated (∇ 2ρ(r) <0) and depleted (∇ 2ρ(r) > 0) and, therefore, contains a largeamount of chemical information. Note also that the elec-tronic charge operator is simply the negative of the numberoperator (–1 for an electron) in the quantum mechanicalsense. The problem is in the definition of an atom in a mole-cule. The most rigorous division of a molecular volume intoatomic subspaces is given by Bader and co-workers (28–31).

In general, a reaction is followed by a change in the elec-tron density that may be quantified by the Fukui function(32).

[1] f(r) =∂∂ρ(r)N

The Fukui function indicates the change in the electrondensity at a given position when the number of electrons Nis changed. A finite difference of the function associatedwith the addition of an electron is

[2] f+(r) = ρN +1(r) – ρN (r).

The function is expected to be the initial part of a nucleo-philic reaction, and the reaction will probably occur wherethe function is large (41). The function may be written interms of orbital contributions as

[3] f+(r) = φLUMO2 (r) +

∂∂=

∑ φi

ii

rn

2

1

( )N

The last terms become zero in the frozen molecular orbitalapproximation, and the Fukui function contains only thecontribution from LUMO (32).

Electron distribution

In this section, analysis of the charge distribution andcharge-transfer processes at the AN–Cu9(100) interfaces isperformed using the NBO–NAO partitioning scheme. Thenatural charges obtained in this way were shown to be suffi-ciently reliable and stable to computational parameters (23).A two-layer Cu9(100) cluster was used to simulate the actualsurface. The following are recommendations in the litera-ture: that the geometry of AN is not affected by the size ofthe clusters (9 atoms) and that the use of smaller clusters (<9atoms) will affect the binding energy (42). Also, the use oflarger clusters would mimic the density of states of the ac-tual surface (43). The chosen cluster size may be viewed

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both as a compromise among the recommendations and asrepresentative of the problems being addressed. A staticelectric field of –0.015 atomic units (au) was chosen to sim-ulate the driving voltage between the electrode and the mol-ecule. The results reported below are based on calculationsdone at the B-VWN/DZVP(DFT) (44–46) and MP2/6–31+G* levels of approximation. The optimized geometries(Fig. 1) were generated using the program DMol (17, 47,48). The interatomic distances of the Cu9(100) clusters werefrozen at the bulk values (17). The natural population analy-sis was carried out by use of the Gaussian 98 suite of pro-grams (49).

B-VWN/DZVP(DFT)The NBO analysis shows the high percentage (>99%)

contribution of the NAOs to the molecular charge distribu-tion, i.e., 99.58% of 20 in the AN valence, 99.48% of 119 inthe AN–Cu9(100) valence, and 99.52% of 120 in the [AN–Cu9(100)]–1 valence. AN is set as a standard against whichthe changes in the charge distribution caused by the forma-tion of the bonds can be measured. The identified sites be-tween which the bonding occurs are C(1)—Cu(8) andN(7)—Cu(15) in AN–Cu9(100), as well as C(1)—Cu(8) in[AN–Cu9(100)]–1. The NECs of these atomic sites, given inTable 1, contain only those valence NAOs that have beensubstantially modified in terms of the electron distributionby incorporating the isolated AN into the AN–Cu9(100)complexes. In comparison to the standard, the naturalcharges indicate that the C(1) and N(7) sites become morenegative by –0.41 and –0.27 in AN–Cu9(100) and that theC(1) site gains a negative charge of –0.40 in [AN–Cu9(100)]–1. The Cu(8) and Cu(15) atoms have the overallnatural charges of +0.15 and +0.32 in AN–Cu9(100), whilethe Cu(8) site is essentially neutral (slightly negative, –0.08)in [AN–Cu9(100)]–1. The C(1)—Cu(8) and N(7)—Cu(15)bonds in AN–Cu9(100) should be looked upon as being ionic(charge separated) as far as the natural charges are con-cerned. The changes in the electron distribution are mostpronounced in the second shells of C(1) and N(7) and in the3d and 4s NAOs of Cu(8) and Cu(15) in AN–Cu9(100), asgiven in Table 1. By adding an electron to the neutral com-plex AN–Cu9(100), the C(1) site does not experience anysubstantial change while Cu(8) gains a negative charge of–0.23, of which –0.21 is assigned to the 4s. After applyingan electric field to the neutral complex AN– Cu9(100), theN(7) atom in [AN–Cu9(100)]–1 becomes more positive, by+0.14, than N(7) in AN–Cu9(100), of which +0.16 is as-signed to the 2p NAO and –0.02 to the 2s and has an overallnatural charge of –0.45. The Cu(15) atom in [AN–

Cu9(100)]–1 becomes more negative by –0.46 than theCu(15) atom in AN–Cu9(100), of which –0.12 is distributedinto the 3d NAO and –0.34 into the 4s and has an overallnatural charge of –0.14.

It is also possible to determine the molecule(AN)–clus-ter(Cu9) charge separation by simply summing the appropri-ate natural charges of atoms. The molecule–cluster naturalcharge separation is AN(–0.79)–Cu9(+0.79) in the neutralcomplex. In some respects the C(1)—Cu(8) and N(7)—Cu(15) bonds in AN–Cu9(100) can be considered as chargeseparated, as far as the molecule–cluster natural charge sepa-ration is concerned. The molecule–cluster natural chargeseparation in [AN–Cu9(100)]–1 is AN(–0.67)–Cu9(–0.33).Thus, the AN molecule as a whole becomes more positiveby +0.12 while the Cu9 cluster as a whole becomes morenegative by –1.12, after applying an external voltage to theneutral complex AN–Cu9(100).

Additional information about the nature of bonded inter-actions is provided by Tables 2 and 3, containing the spin-separated NAOs at the interaction sites. The letters “a” and“b” used in the analysis mean “alpha (spin up)” and “beta(spin down)”, respectively. Since the valence electrons tendto be chemically active, the total occupancies of the spin-separated NAOs at the interaction sites in AN–Cu9(100) in-volved in the bonding are 2.33a and 2.31b at C(1), 2.77a and2.74b at N(7), 5.4a and 5.34b at Cu(8), and 5.3a and 5.34bat Cu(15). The occupancies of the σ-bonding and anti-bonding C(1)—Cu(8) NOs of the alpha spin are 0.79 (72.4%at C(1)) and 0.28 (27.6% at C(1)) in AN–Cu9(100). The oc-cupancies of the σ-bonding and antibonding N(7)—Cu(15)NOs of the alpha spin are 0.77 (81.5% at N(7)) and 0.28(18.5% at N(7)) in AN–Cu9(100). Table 3 shows that thevalence occupancies of the spin-separated NAOs are 2.36aand 2.27b at C(1), as well as 5.59a and 5.38b at Cu(8), in

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Fig. 1. Optimized geometries: (a) AN; (b) AN–Cu9(100); (c) [AN–Cu9(100)]–1.

MoleculeAtom(site)

Naturalcharge Configuration

AN C(1) –0.29 2s(1.04)2p(3.24)N(7) –0.32 2s(1.62)2p(3.67)

AN–Cu9(100) C(1) –0.70 2s(1.12)2p(3.53)Cu(8) +0.15 4s(0.84)3d(9.88)N(7) –0.59 2s(1.59)2p(3.96)Cu(15) +0.32 4s(0.81)3d(9.83)

[AN–Cu9(100)]–1 C(1) –0.69 2s(1.13)2p(3.52)Cu(8) –0.08 4s(1.05)3d(9.90)

Table 1. B-VWN/DZVP(DFT): natural charges and electron con-figurations (NECs) at interaction sites.



[AN–Cu9(100)]–1. The occupancies of the σ-bonding andantibonding C(1)—Cu(8) NOs of the “up” spin are 0.96(57.6% at C(1)) and 0.32 (42.4% at C(1)) in [AN–Cu9(100)]–1.

MP2/6–31+G*The NBO analysis shows the high percentage (>99%)

contribution of the NAOs to the molecular charge distribu-tion, that is, 99.40% of 20 in the AN valence, 99.28% of 119in the AN–Cu9(100) valence, and 99.56% of 120 in the[AN–Cu9]

–1 valence. The summary of NO population analy-sis is given in Table 4. By incorporating the isolated AN intothe AN–Cu9(100) complex, the natural charges indicate thatthe C(1) and N(7) sites become more negative by –0.41, ofwhich –0.25 is distributed into 2p and –0.11 into 2s at C(1)and –0.46 into 2p and +0.06 into 2s at N(7). The Cu(8) and

Cu(15) atoms have the natural charges of –0.05 and +0.49 inAN–Cu9(100), respectively. As far as the natural charges areconcerned, the N(7)—Cu(15) bond is charge separated(ionic), while the C(1)—Cu(8) bond is not, in AN–Cu9(100).By adding an electron to the neutral complex, the C(1) sitebecomes slightly more negative by –0.05 while the Cu(8)site gains a negative natural charge of –0.56, of which –0.55is assigned to 4s. In comparison to the neutral complex, thechange of the Cu(8) natural charge of –0.56 is substantial.The overall natural charges of the C(1) and Cu(8) sites in[AN–Cu9(100)]–1 are –0.78 and –0.61, respectively.

By summing the appropriate natural charges of atoms, themolecule–cluster natural charge separation is AN(–0.94)–Cu9(+0.94) in the neutral complex. In some respects theC(1)—Cu(8) and N(7)—Cu(15) bonds in AN–Cu9(100) canbe considered as charge separated, as far as the molecule–

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Atom (site) Atomic orbital Type (atomic orbital)a Occupancy

C(1) s Val (2s)a 0.56121C(1) px Val (2p)a 0.54971C(1) py Val (2p)a 0.58395C(1) pz Val (2p)a 0.64153N(7) s Val (2s)a 0.79381N(7) px Val (2p)a 0.69440N(7) py Val (2p)a 0.62876N(7) pz Val (2p)a 0.68147Cu(8) s Val (4s)a 0.43659Cu(8) dxy Val (3d)a 0.99714Cu(8) dxz Val (3d)a 0.99631Cu(8) dyz Val (3d)a 0.99553Cu(8) dx2y2 Val (3d)a 0.99814Cu(8) dz2 Val (3d)a 0.95938Cu(15) s Val (4s)a 0.39141Cu(15) dxy Val (3d)a 0.99159Cu(15) dxz Val (3d)a 0.96475Cu(15) dyz Val (3d)a 0.99007Cu(15) dx2y2 Val (3d)a 0.99123Cu(15) dz2 Val (3d)a 0.98031C(1) s Val (2s)b 0.56002C(1) px Val (2p)b 0.54942C(1) py Val (2p)b 0.58261C(1) pz Val (2p)b 0.62381N(7) s Val (2s)b 0.79309N(7) px Val (2p)b 0.68505N(7) py Val (2p)b 0.62175N(7) pz Val (2p)b 0.64960Cu(8) s Val (4s)b 0.40603Cu(8) dxy Val (3d)b 0.99695Cu(8) dxz Val (3d)b 0.99246Cu(8) dyz Val (3d)b 0.99374Cu(8) dx2y2 Val (3d)b 0.99420Cu(8) dz2 Val (3d)b 0.95658Cu(15) s Val (4s)b 0.41956Cu(15) dxy Val (3d)b 0.99059Cu(15) dxz Val (3d)b 0.96412Cu(15) dyz Val (3d)b 0.99007Cu(15) dx2y2 Val (3d)b 0.99126Cu(15) dz2 Val (3d)b 0.98030

aa = alpha (spin up); b = beta (spin down); Val = valence.

Table 2. B-VWN/DZVP(DFT): AN–Cu9(100) — spin-separated valence natural atomic orbitals.



cluster natural charge separation is concerned. The mole-cule–cluster natural charge separation in [AN–Cu9(100)]–1 isAN(–0.36)–Cu9(–0.64). Therefore, the AN molecule as awhole becomes more positive by +0.58 while the Cu9 clusteras a whole becomes more negative by –1.58 after applyingan external voltage to the neutral complex AN–Cu9(100).

Additional information about the nature of bonded inter-actions is provided by Tables 5–7, containing the valenceNAOs at the interaction sites in AN and the spin separatedvalence NAOs at the interaction sites in AN–Cu9(100) and[AN–Cu9(100)]–1, respectively. The total occupancies in-volved in the bonding in AN are 4.30 at C(1) and 5.26 atN(7). The total occupancies involved in the bonding in AN–Cu9(100) are 2.53a and 2.13b at C(1), 2.22a and 3.42b atN(7), 5.27a and 5.15b at Cu(8), and 5.18a and 5.06b atCu(15). By bonding AN to Cu9(100), the site C(1) gains abonding NAO occupancy of 0.38a and loses that of 0.02b,while the site N(7) loses a bonding NAO occupancy of 0.41having the “up” spin and gains that of 0.79 having the“down” spin. The occupancies of the σ-bonding and anti-

bonding C(1)—Cu(8) NOs of the alpha spin are 0.73(66.83% at C(1)) and 0.26 (33.17% at C(1)) in AN–Cu9(100), respectively. The occupancies of the σ-bondingand antibonding N(7)—Cu(15) NOs of the alpha spin are0.62 (65.31% at N(7)) and 0.22 (34.69% at N(7)) in AN–Cu9(100), respectively. Table 7 also shows that the valenceoccupancies of the spin-separated NAOs are 1.48a and 3.24bat C(1) and 5.7a and 5.05b at Cu(8) in [AN–Cu9(100)]–1. Byadding an electron to the neutral complex, the C(1) site losesan alpha-bonding occupancy of 1.05 and gains a beta one of1.11, while the Cu(8) site gains an alpha-valence occupancyof 0.43 and loses a beta one of 0.1. The occupancies of theσ-bonding and antibonding C(1)—Cu(8) NOs of spin “up”are 0.6 (36.12% at C(1)) and 0.2 (63.88% at C(1)) in [AN–Cu9(100)]–1.

The AN molecule retains its planarity in AN–Cu9(100)while it becomes distorted after applying an external volt-age, as given in Fig. 1. The C(1)—C(2), C(3)—N(7), andC(2)—C(3) geometric bond lengths (GBLs) in AN are 2.52au, 2.21 au, and 2.66 au, respectively. The C(1)—C(2) and

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C(1) s Val (2s)a 0.57052C(1) px Val (2p)a 0.57445C(1) py Val (2p)a 0.58371C(1) pz Val (2p)a 0.64184Cu(8) s Val (4s)a 0.61215Cu(8) dxy Val (3d)a 0.99702Cu(8) dxz Val (3d)a 0.97963Cu(8) dyz Val (3d)a 0.99810Cu(8) dx2y2 Val (3d)a 0.99138Cu(8) dz2 Val (3d)a 0.99665C(1) s Val (2s)b 0.56195C(1) px Val (2p)b 0.55757C(1) py Val (2p)b 0.58376C(1) pz Val (2p)b 0.57474Cu(8) s Val (4s)b 0.44150Cu(8) dxy Val (3d)b 0.99094Cu(8) dxz Val (3d)b 0.97103Cu(8) dyz Val (3d)b 0.98665Cu(8) dx2y2 Val (3d)b 0.98857Cu(8) dz2 Val (3d)b 0.99678


Table 3. B-VWN/DZVP(DFT): [AN–Cu9(100)]–1 — spin-separated valence natural atomic orbitals.

Spin natural charge

Molecule Atom (site) Natural charge Configurationa Up Down Mulliken chargeb

AN C(1) –0.32 2s(1.00)2p(3.30) –0.16 –0.16 –0.08N(7) –0.28 2s(1.62)2p(3.63) –0.14 –0.14 –0.22

AN–Cu9(100) C(1) –0.73 2s(1.11)2p(3.55) –0.57 –0.16 –0.40Cu(8) –0.05 4s(1.02)3d(9.40)4p(0.44) –0.09 +0.04 –0.28N(7) –0.69 2s(1.56)2p(4.09) +0.25 –0.94 –0.45Cu(15) +0.49 4s(0.71)3d(9.53)4p(0.15) +0.18 +0.31 +0.25

[AN–Cu9(100)]–1 C(1) –0.78 2s(1.13)2p(3.59) +0.49 –1.27 –0.04Cu(8) –0.61 4s(1.57)3d(9.35)4p(0.48) –0.71 +0.10 –0.71

aThe given NAOs have been substantially modified in terms of the charge distribution by incorporating AN into AN–Cu9(100).bThe Mulliken charges are only to be used to demonstrate the arbitrary and unpredictable behavior of this partitioning scheme.

Table 4. MP2/6–31+G*: natural electron charges, natural electron configurations, and Mulliken charges.



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C(1) s Val (2s)a 0.56951C(1) px Val (2p)a 0.58950C(1) py Val (2p)a 0.61067C(1) pz Val (2p)a 0.76383N(7) s Val (2s)a 0.75370N(7) px Val (2p)a 0.53719N(7) py Val (2p)a 0.32182N(7) pz Val (2p)a 0.61095Cu(8) s Val (4s)a 0.53980Cu(8) dxy Val (3d)a 0.95956Cu(8) dxz Val (3d)a 0.96381Cu(8) dyz Val (3d)a 0.96291Cu(8) dx2y2 Val (3d)a 0.95701Cu(8) dz2 Val (3d)a 0.89262Cu(15) s Val (4s)a 0.43380Cu(15) dxy Val (3d)a 0.96544Cu(15) dxz Val (3d)a 0.90644Cu(15) dyz Val (3d)a 0.96552Cu(15) dx2y2 Val (3d)a 0.96028Cu(15) dz2 Val (3d)a 0.95151C(1) s Val (2s)b 0.54128C(1) px Val (2p)b 0.54188C(1) py Val (2p)b 0.60240C(1) pz Val (2p)b 0.44503N(7) s Val (2s)b 0.80284N(7) px Val (2p)b 0.86106N(7) py Val (2p)b 0.89021N(7) pz Val (2p)b 0.86922Cu(8) s Val (4s)b 0.47945Cu(8) dxy Val (3d)b 0.94021Cu(8) dxz Val (3d)b 0.93111Cu(8) dyz Val (3d)b 0.95569Cu(8) dx2y2 Val (3d)b 0.95266Cu(8) dz2 Val (3d)b 0.88607Cu(15) s Val (4s)b 0.27714Cu(15) dxy Val (3d)b 0.96607Cu(15) dxz Val (3d)b 0.92352Cu(15) dyz Val (3d)b 0.97039Cu(15) dx2y2 Val (3d)b 0.96129Cu(15) dz2 Val (3d)b 0.96313


Table 6. MP2/6–31+G*: AN–Cu9(100) — spin-separated valence natural atomic orbitals.


C(1) s Val(2s) 1.00396C(1) px Val(2p) 1.14970C(1) py Val(2p) 1.11966C(1) pz Val(2p) 1.02730N(7) s Val(2s) 1.61634N(7) px Val(2p) 1.14945N(7) py Val(2p) 1.40741N(7) pz Val(2p) 1.07615


Table 5. MP2/6–31+G*: AN — valence natural atomic orbitals at the C(1) and N(7) sites.



C(3)—N(7) GBLs in both AN–Cu9(100) and [AN–Cu9(100)]–1 are 2.7 au and 2.27 au, while those of theC(2)—C(3) bonds are 2.57 au and 2.59 au, respectively. Theelongation of the C(1)—C(2) and C(3)—N(7) bonds and theshortening of the C(2)—C(3) bonds with reference to ANconfirm electron transfer from Cu9 to AN. The calculatedvalue of the ionization potential (IP) of 4.43 electron volts(eV) for Cu9 confirms recent measurements of 4.2 eV,which is comparable with the IPs of Na (5.14 eV) and K(4.34 eV) (50). A similar electron transfer in NO populationhas been reported for an AN molecule with an Na atom, aswell as for an acrolein molecule with an Na atom (51, 52).

Nature of bonded interactions

In this section, the nature of the AN–Cu9(100) interfacialinteractions is investigated by use of AIM theory at the B-VWN/DZVP(DFT) and MP2/6–31+G* levels of theory. Thecalculations pertaining to the topological features of theelectron density were performed by use of the programEXTREM (53). The figures were created by use of the pro-gram MOLDEN (54).

B-VWN/DZVP(DFT)The Bader (AIM) (29, 30) analysis shows the existence of

the C(1)—Cu(8) and N(7)—Cu(15) through-space interac-tions in AN–Cu9(100), as well as that between the C(1) andthe Cu(8) in [AN–Cu9(100)]–1; that is, bond paths — lines ofthe highest electron density linking the pairs of the atoms —exist. The total bond path lengths (TBPLs) are in agreementwith the geometric bond lengths. For example, the TBPLs ofthe C(1)—Cu(8) and the N(7)—Cu(15) in AN–Cu9(100) are3.9223 au and 3.5795 au, while the corresponding GBLs are3.9204 au and 3.5779 au, respectively. Also, the TBPL of theC(1)—Cu(8) bond in [AN–Cu9(100)]–1 is 4.1189 au while theC(1)—Cu(8) GBL is 4.1172 au. The bond critical point is

determined by the condition that the gradient of the electrondensity is equal to zero, and the properties of the density atthis point provide quantitative characteristics of a bond. Thebond CPs have a small electron density of 0.0829 ea0

–3 be-tween C(1) and Cu(8) and of 0.1093 ea0

–3 between N(7) andCu(15) in AN–Cu9(100), as well as of 0.0669 ea0

–3 betweenC(1) and Cu(8) in [AN–Cu9(100)]–1. The positions of thebond CPs are clear as pronounced minima of the electrondensity in the regions between the corresponding nuclei inFig. 2. The Laplacian (the second derivative of the density)of the bond CPs has values of +0.1189 (C(1)—Cu(8)) and+0.3184 (N(7)—Cu(15)) in AN–Cu9(100) and of +0.1095(C(1)—Cu(8)) in [AN–Cu9(100)]–1, characteristic of a do-nor–acceptor bond.

Applying an external voltage to the neutral complexcaused a change in the number of electrons, from 289 inAN–Cu9(100) to 290 in [AN–Cu9(100)]–1. The Fukui func-tion f+ has values of –0.43 at C(1), +0.39 at Cu(8), –0.02 atN(7), and +30.18 at Cu(15), respectively. The changes of theelectron density at C(1), Cu(8), and N(7) are not substantial,and therefore, a nucleophilic reaction may not be expectedto occur in the vicinity of the interaction sites. Such a reac-tion may be possible in the vicinity of Cu(15).

MP2/6–31+G*The Bader analysis shows that the total bond path lengths

are in agreement with the geometric bond lengths (i.e., AN–Cu9(100): C(1)—Cu(8) TBPL = 3.9265 au, GBL = 3.9205;N(7)—Cu(15) TBPL = 3.5809 au, GBL = 3.5779 au; [AN–Cu9(100)]–1: C(1)—Cu(8) TBPL = 4.1214 au, GBL =4.1172). The bond CPs have a small total electron density of0.0805 ea0

–3 between C(1) and Cu(8) and of 0.1076 ea0–3

between N(7) and Cu(15) in AN–Cu9(100), as well as of0.0657 ea0

–3 between C(1) and Cu(8) in [AN–Cu9(100)]–1.The values of the spin electron densities at the bond CPs are

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C(1) s Val (2s)a 0.46816C(1) px Val (2p)a 0.42184C(1) py Val (2p)a 0.56532C(1) pz Val (2p)a 0.01859Cu(8) s Val (4s)a 0.9988Cu(8) dxy Val (3d)a 0.95234Cu(8) dxz Val (3d)a 0.90209Cu(8) dyz Val (3d)a 0.95399Cu(8) dx2y2 Val (3d)a 0.94188Cu(8) dz2 Val (3d)a 0.95919C(1) s Val (2s)b 0.65702C(1) px Val (2p)b 0.71899C(1) py Val (2p)b 0.65700C(1) pz Val (2p)b 1.20373Cu(8) s Val (4s)b 0.40021Cu(8) dxy Val (3d)b 0.94093Cu(8) dxz Val (3d)b 0.88619Cu(8) dyz Val (3d)b 0.92084Cu(8) dx2y2 Val (3d)b 0.93905Cu(8) dz2 Val (3d)b 0.95498


Table 7. MP2/6–31+G*: [AN–Cu9(100)]–1 — spin-separated valence natural atomic orbitals.



0.0414 ea0–3 (C(1)—Cu(8)) and 0.0554 ea0

–3 (N(7)—Cu(15)) in AN–Cu9(100), as well as 0.0338 ea0

–3 (C(1)—Cu(8)) in [AN–Cu9(100)]–1. The Laplacian of the bond CPshas values of +0.0892 (C(1)—Cu(8)) and +0.3704 (N(7)—Cu(15)) in AN–Cu9(100) and of +0.0867 (C(1)—Cu(8)) in[AN–Cu9(100)]–1, characteristic of a donor–acceptor bond.

The Fukui function f+ has values of –0.49 at C(1), +133.2at Cu(8), +2.84 at N(7), and +172.17 at Cu(15), respectively.The changes of the electron density of the Cu(8) and Cu(15)sites are substantial, indicating that a nucleophilic reactionmay be expected to occur in the vicinity of the interactionsites.

[AN–Cu9(100)]–1: Laplacian of total electrondensity and spatial extents of HOMO andLUMO

In this section, the Laplacian of the electron density is an-alyzed and contrasted to the spatial extents of the HOMOand LUMO in [AN–Cu9(100)]–1.

The Laplacian itself contains features such as bonds andlone pairs, which are not observable in the density itself. Thecut of the Laplacian of the electron density is given inFigs. 3 and 4. From left to right, the nuclei in the plane ofthe cut are N(7), C(1), and Cu(8). The electron density is lo-cally concentrated in spatial regions determined by a nega-tive Laplacian and locally depleted in those regionsdetermined by a positive Laplacian. Having a slightly posi-tive value of the Laplacian, the position of the bond criticalpoint is nicely visible in the region between C(1) and Cu(8).

In most previous work, the HLG has been observed as acrucial parameter for understanding conductance mecha-nisms through molecular junctions. The ability of a moleculeto rearrange its electron density under the presence of an ex-ternal electron underlies such observations. If the ability isnot that pronounced, the molecular admittance to the incom-ing electron is less recognizable and, therefore, a molecule ismore stable. As the first consequence, by employing theelectronegativity equalization theorem and a relative align-ment of the Fermi energy level with respect to the HLG (20,55–59), the barrier to electron transfer is proportional to theHLG to the first approximation. As the second consequence,the size of the HLG may be regarded as a measure of thehardness of the electron density. The relative alignment of

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Fig. 2. Electron density. B-VWN/DZVP(DFT). (a) AN–Cu9(100); (b) [AN–Cu9(100)]–1.

Fig. 3. [AN–Cu9(100)]–1 — Laplacian of electron density. B-VWN/DZVP(DFT).

Fig. 4. [AN–Cu9(100)]–1 — Laplacian of electron density.MP2/6–31+G*.



the Fermi energy level is strongly dependent upon the den-sity of states within the HLG and is sensitive to a smallamount of charge transfer. Thus, the physical essence is con-tained in the electron density distribution.

Electron transfer, from Cu9 to AN, leads to substantialchange in the molecular structure according to the nature ofthe LUMO in AN. Electrons occupy some unoccupiedorbitals of the neutral complex after the action of an externalvoltage. An area with locally concentrated electron densityis susceptible to attack by an electrophile while an area withlocally depleted electron density is susceptible to attack by anucleophile. In general, it has been found that a map of neg-ative values of the Laplacian of the total electron density re-sembles a spatial extent of the HOMO while that of positivevalues of the Laplacian resembles a spatial extent of theLUMO (60). The spatial extent of the LUMO or, more con-ceivably, the extent of its electron delocalization may be em-ployed to describe electronic molecular transport of acharged molecule qualitatively if and only if (according tothis study) a spatial extent of the LUMO resembles a map ofpositive values of the Laplacian of the total electron density.What do the spatial extents of the HOMO and LUMO in[AN–Cu9(100)]–1 indicate?

B-VWN/DZVP(DFT)The cut of the HOMO in [AN–Cu9(100)]–1 is given in

Fig. 5. The plane of the cut is the same as that of theLaplacian in Fig. 3. Note the contour map of the negativeLaplacian (Fig. 3). The contours encompass C(1) and N(7),showing roughly circular curvatures, but those around C(1)are not fully closed. Note the contour lines of the HOMO re-siding in the same regions in Fig. 5. In its immediate vicin-ity, C(1) is encompassed by the negative contours. Thecontours are also shifted behind C(1) where the correspond-ing lines of the Laplacian are not fully closed. In the vicinityof N(7), the negative contours encircle N(7) towards C(1)but not fully behind the N(7) nucleus, in Fig. 5. Regardlessof the qualitative differences, the area determined by nega-tive values of the Laplacian spreads roughly in the same spa-tial regions as that of the HOMO.

The cut of the LUMO in [AN–Cu9(100)]–1 is given inFig. 6. The plane of the cut is the same as that of theLaplacian in Fig. 3. Focus on the region between C(1) andCu(8). The contour lines of the LUMO in this region arenegative, spreading both toward the left and the right withrespect to the C(1)—Cu(8) bond line. In contrast to it, thecontour lines of the Laplacian in the same region are posi-tive. It is clear that the spatial extent of the LUMO does notresemble that of the positive Laplacian.

MP2/6–31+G*The cut of the HOMO in [AN–Cu9(100)]–1 is given in

Fig. 7. The plane of the cut is the same as that of theLaplacian given in Fig. 4. The negative contours of theHOMO show a circular curvature in the immediate vicinityof C(1), which spreads right under the C(1)—Cu(8) inter-nuclear axis. In contrast to the Laplacian, there are somepositive contours of the HOMO in the immediate vicinity ofC(1), which are still edged by the negative ones right abovethe C(1)—Cu(8) interaction line. The N(7) site is also sur-rounded by two concentric spatial profiles of the negative

contours, of which the outer one is substantially extendedboth toward the left and the right with respect to N(7). Re-gardless of the qualitative differences, the area determinedby negative values of the Laplacian spreads roughly in thesame spatial regions as that of the HOMO.

The cut of the LUMO in [AN–Cu9(100)]–1 is given inFig. 8. The plane of the cut is the same as that of theLaplacian in Fig. 4. Focus on region between C(1) andCu(8). It is clear that the map of the LUMO resembles thatdetermined by positive values of the Laplacian conspicu-ously.

The fundamental question related to the essential origin ofthe electron distribution in the AN–Cu9 systems is not yetresolved.

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Mitrasinovic 551

Fig. 5. [AN–Cu9(100)]–1 — HOMO. B-VWN/DZVP(DFT).

Fig. 6. [AN–Cu9(100)]–1 — LUMO. B-VWN/DZVP(DFT).



Discussion

Most results related to the characterizations of the interfa-cial interactions are strongly dependent on the molecular ge-ometries used. The first aspect is that considerable effects ofthe increase of the cluster size and the choice of metal sur-face on the molecular properties are well known. The secondaspect is that methods chosen to generate the optimized ge-ometries need to be computationally efficient with respect tothe number of atoms involved in such calculations. The thirdaspect is that a satisfactory basis set is required, providingthat the structure is qualitatively correct. In contrast to theCu9 cluster, the problems associated with the clusters havingthe open-shell characters are well known. The strong de-pendence of degenerate open-shell atomic energies on theoccupancy of the atomic orbitals within DFT is associatedwith the different densities of the degenerate atomic orbitals.The degenerate atomic orbitals can be populated in differentways. It is difficult to reproduce the exact degeneracy ofthese states within the average thermo chemical accuracy(2 kcal mol–1) by using approximate exchange-correlationfunctionals that depend on density gradient (61). There arerecommendations that the local spin-density (LSD) approxi-mation, in combination with some improved optimization al-gorithms (62, 63), is capable of generating reliableadsorption structures of adsorbates (64, 65).

The questions that have been previously addressed regard-ing the nature of the organic—metal-bonded interactions canbe summarized as follows (17, 66–68). Where is the energet-ically preferable adsorption site for a molecule on differentmetal surfaces? How are the structures for a molecule at dif-ferent adsorption sites on different metal surfaces? What arethe different contributions to the bond between interactionsites? What are the differences for the adsorption of a mole-cule to different metal surfaces? The extraction of orbitalsimportant in the bonding to the metal surfaces has been thekey objective, but simplified structures have been needed forthe construction of the orbitals. The simplified structures

sometimes had all atoms except those in the top layer re-moved (66). There are two reasons for these implications.First, the energetic requirements are based on the arbitrarypartition of the molecular interaction energy. Second, the de-scriptions of bonded interactions are sought in orbitals. Thephysics underlying these results is not clear for two primaryreasons. In a pure physical sense, the general trend contra-dictory to the investigations is to have the clusters of largersizes involved in calculations to mimic the density of statesof the actual surface. If the analysis of tracing bond pathsbetween the atoms in the AN–Cu9 systems is carried out in agreater detail, it is possible to intuitively predict the direc-tions of “hypothetical” bond paths linking the atoms of theorganic molecule to those of a “hypothetical” cluster pos-sessing a size that is larger or smaller than the actual one. Inother words, the existence of possible bond paths is physi-cally independent of increasing or decreasing the clustersize. This is the essence of the understanding that the bondpath is a universal indicator of bonded interactions, as notedby Bader in 1990 when his AIM theory was released (29).

The question raised at the very end of the previous sectionis fundamentally profound. Possible DFT analyses of thedensity of states and band structures would probably indi-cate that the origin of the electron distribution in this systemis more complicated than that based solely on classical inter-pretations. The first quantitative measurement of the 2Dband structure at a self-assembling interface between athiolate and a silver surface by use of two-photon photo-emission may be an appropriate guidance for some futurework (69). Experimental and theoretical investigations con-verging to the same answer are worth being pursued.

Summary

The electron distribution around the nuclei and the natureof bonded interactions at the AN–Cu9 interfaces need to beinvestigated by combining different quantum mechanicalmethods. The QM methods include ab initio electron corre-

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Fig. 7. [AN–Cu9(100)]–1 — HOMO. MP2/6–31+G*. Fig. 8. [AN–Cu9(100)]–1 — LUMO. MP2/6–31+G*.



lation effects and lead toward the invariant descriptions ofthe interfacial interactions.

The success of frontier molecular orbital theory to ratio-nalize the organic–metal charge migration process may de-pend on whether the spatial extents of the HOMO andLUMO support the corresponding topological features of thetotal electron density, which determines the reactivity.

The essential origin of the electron transfer in the AN–Cu9 system is not yet described.

The message of this study is best described by C.A.Coulson, “In a profound sense the description of the bondsin a molecule is simply the description of the distribution ofelectrons around the nuclei”, as quoted from p. 2 of ref. 34.

Acknowledgments

This work in Mons, Belgium was supported by the Euro-pean Commission project SANEME (IST-1999–10323).

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