Towards a rigorously defined quantum chemical analysis of the chemical bond in donor–acceptor complexes

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Abstract

The results of an energy decomposition analysis of various classes of donor–acceptor complexes of transition metals and main-group elements are discussed. It is shown that the nature of the chemical bond can be quantitatively identified in terms of Pauli repulsion, electrostatic attraction and covalent bonding. The covalent and electrostatic contributions to the interatomic attraction can be precisely given by using a well defined partitioning method in conjunction with accurate quantum chemical calculations of the geometries and bond energies. This is shown for six classes of donor–acceptor complexes: (a) transition metal carbonyl complexes; (b) transition metal complexes with Group-13 diyl ligands ER (E=BTl); (c) transition metal complexes with phosphane ligands (CO)5TMPX3 (TM=Cr, Mo, W; X=H, Me, F, Cl); (d) main group complexes with phosphane ligands X3BPY3 and X3AlPY3 (X=H, F, Cl; Y=F, Cl, Me, CN); (e) transition metal metallocene complexes Fe(η5-E5)2 and FeCp(η5-E5) (E=CH, N, P, As, Sb); (f) main group metallocenes ECp2 (E=BeBa, Zn, SiPb) and ECp (E=LiCs, BTl).

Introduction

The understanding and the interpretation of the chemical bond in terms of covalent and electrostatic interatomic interactions is one of the most fundamental concepts in chemistry. Numerous chemical models which are based on heuristic arguments or quantum chemical approximations such as the HSAB (hard and soft acids and bases) principle [1], the VSEPR (valence shell electron pair repulsion) model [2], the conservation of orbital symmetry [3] or the frontier orbital method [4], [4](a), [4](b) make use of the distinction between covalent and electrostatic bonding. A related but not exactly identical dichotomy was used by Pauling in his valence bond (VB) interpretation of the chemical bond in terms of ionic and covalent bonding [5]. In his understanding a purely ionic bond is the result of 100% electrostatic attraction between charged atoms while a purely covalent bond is formed between neutral identical atoms. Chemical bonds between unequal atoms AB have covalent and ionic contributions which enforce the attractive interactions relative to the homoatomic bonds AA and BB [5].

Inspection of the chemical literature shows that the discussion in terms of electrostatic (or ionic) and covalent bonding is often made without explicit analysis of the nature of the chemical bond. The arguments are frequently based on considering the electronegativities of the atoms or on calculated atomic partial charges. The use of the latter can be misleading, because partial charges give no information about the topography of the spatial distribution of the charge. The electronic charge distribution of an atom in a molecule is often very anisotropic. An atom which carries an overall positive charge may have a local area of negative charge concentration which can lead to strong charge attraction with another positively charged atom while the partial charges would deceptively predict charge repulsion. Striking examples have recently been found by us in theoretical investigations of donor–acceptor complexes R3EE′R where E, E′ are Group-13 elements BTl [6]. The donor atom E′ of the Lewis base E′R has a positve partial charge but it has a lone-electron pair which yields strong electrostatic attraction with the positively charged acceptor atom E of the Lewis acid ER3. This shows clearly that an estimate of the electrostatic contribution to a chemical bond necessitates a more detailed analysis of the interatomic interactions.

The covalent bond is also frequently a topic of controverse discussions. If the molecule has a mirror plane the molecular orbital interactions which lead to a covalent bond may come from orbitals which have σ or π symmetry. The latter orbitals are responsible for the multiple bond character [7] and thus, the question if a bond should be regarded as single, double or triple bond is often addressed by inspecting the shape and the occupation of the π orbitals or by calculated bond orders which are based on orbital overlap and occupation numbers. However, this may not give a definite answer because the choice of the partitioning method may strongly influence the result and even qualitatively different answers may be found. Recent examples of conflicting interpretations of the multiple bond character are the FeGa bond in (CO)4FeGaAr* and the GaGa bond in Ar*GaGaAr*2− (Ar*=bulky aryl group) [8], [9]. Several theoretical papers have been published which disagree on the question if the bonds should be considered as single or triple bonds [10], [10](a), [10](b), [10](c), [10](d), [11], [11](a), [11](b).

Covalent and electrostatic bonding are energy terms and the most straightforward methods to address the question about the size of the two contributions should be based on a plausible definition of partitioning the interaction energy rather than the charge distribution between two chemically bonded atoms or fragments. Several conditions must be fulfilled if the results of the partitioning shall be meaningful. It must be a rigorously defined energy partitioning which can be used in conjunction with any quantum chemical method. The results of the method should not significantly change with different levels of theory. The calculated numbers cannot be compared with experimental data but they should be obtained with a plausible partitioning scheme which is mathematically well defined. It should also be possible to give a physical interpretation of the terms which are calculated with the partitioning device.

A method which fulfills the above criteria is the energy partitioning scheme which is available in the program package ADF (Amsterdam density functionals) [12], [12](a), [12](b). It is based on ideas presented first in 1971 by Morokuma [13], [13](a), [13](b) who suggested an energy partitioning procedure for Hartree-Fock (HF) calculations. A very similar energy partitioning method was introduced in 1977 by Ziegler [14] who showed that DFT calculations of interatomic interaction energies can be analyzed and interpreted in terms of physically meaningful contributions to the chemical bond. The advantage of DFT as against HF calculations is that the Kohn-Sham orbitals include correlation effects while HF orbitals do not [12], [12](a), [12](b). The fundamental steps of the Morokuma/Ziegler energy partitioning are given in Section 2.

Two years ago we started a research program which has the goal to give an understanding of the chemical bond in terms of rigorously defined and physically meaningful contributions which are given by partitioning the results of accurate quantum chemical calculations. We have chosen the partitioning method of ADF because the energy terms can be identified with three main components of the chemical bond, i.e. Pauli repulsion, electrostatic attraction and covalent interaction. The latter term can be broken down into contributions which come from orbitals with different symmetry. Thus, the calculated data may be directly used to address the question if π interactions are important in a chemical bond. The answer to the question is then given together with the information about the relative contributions of covalent and electrostatic interactions to the chemical bond. The latter term is often neglected in qualitative discussions of single versus multiple bond character. Thus, the results of the energy partitioning analysis give a comprehensive picture of the nature of the chemical bond in terms of familiar concepts of traditional bonding models. This is the goal of our research program: to build a bridge between the results of accurate quantum chemical calculations and traditional bonding models.

This paper gives a first summary of the research projects which have been finished until now. We investigated the nature of the chemical bond in donor–acceptor complexes of transition metal complexes with carbonyl ligands, Group-13 diyl ligands ER (E=BTl) and phosphane ligands PR3, in sandwich complexes of transition metals and main group elements with carbocyclic and heterocyclic ligands, and in complexes between borane and alane Lewis acids with phosphane Lewis bases. The results are very promising and we plan to extend the work to other classes of compounds. We will also analyze the chemical bonding between open-shell fragments.

Section snippets

Methods

The geometries and bond energies of the complexes which shall not be discussed here have been calculated with gradient corrected DFT methods (B3LYP [15], [15](a), [15](b), [15](c) and/or BP86 [16], [16](a), [16](b)) using valence basis sets of DZP or TZP quality. Details of the methods and the results can be found in the original publications which are cited below. Relativistic effects have been considered by the zero order regular approximation (ZORA) [17], [17](a), [17](b), [17](c), [17](d),

Transition metal-carbonyl complexes

The chemical bonding between a transition metal and a CO ligand in carbonyl complexes is usually described in terms of donor–acceptor interactions between the occupied orbitals of the ligand and the empty orbitals of the metal and vice versa. The generally accepted bonding model which is based on the orbital interaction scheme that was first suggested by Dewar [19], [19](a), [19](b) is shown in Fig. 1.

The dominant contributions come from: (i) the electron donation of the CO σ HOMO which is

Transition metal complexes with Group-13 diyl ligands ER (E=BTl)

Unlike the TMCO bonding in carbonyl complexes which was undisputed in the literature, the nature of the donor–acceptor interactions between a transition metal and a Group-13 diyl ligand ER (E=BTl) has been controversially discussed for several years. The first complex with a ligand ER which was characterized by X-ray structure analysis was (CO)4FeAlCp* [26], [26](a), [26](b). The FeAl bond was interpreted in terms of σ donation and π backdonation between the interacting ligand and metal

Transition metal complexes with phosphane ligands (CO)5TMPX3 (TM=Cr, Mo, W; X=H, Me, F, Cl)

The interpretation of the chemical bonding in TM phosphane complexes in terms of donor–acceptor interactions focuses often on the strength of the TM→PR3 π backdonation [34]. Numerous theoretical and experimental studies have been carried out in order to analyze the nature of the TMPR3 bond [34]. Different methods have been used to estimate the π acceptor strength of different phosphanes PR3 but the results led to controversial discussions particularly with regard to PCl3. The interpretation of

Main group complexes with phosphane ligands X3BPY3 and X3AlPY3 (X=H, F, Cl; Y=F, Cl, Me, CN)

The chemical bonds of phosphanes as Lewis bases was also investigated by us in complexes with main group Lewis acids of aluminum and boron. To this end we calculated the structures and bond energies of the alane and borane complexes X3BPY3 and X3AlPY3 (X=H, F, Cl; Y=F, Cl, Me, CN) [41] The Lewis base P(CN)3 was of particular interest because, until today, there is no stable complex of P(CN)3 known. Part of the theoretical work was to find out if P(CN)3 is a particularly weak Lewis base, and

Transition metal metallocene complexes Fe(η5-E5)2 and FeCp(η5-E5) (E=CH, N, P, As, Sb)

We recently analyzed the metal ligand bonds in ferrocene (FeCp2) and in the isoelectronic all-nitrogen analogue iron bispentazole Fe(η5-N5)2 which has not yet been synthesized [43]. In a subsequent paper we extended the investigations to the Group-15 elements Fe(η5-E5)2 and the ‘semiheterocyclic’ species FeCp(η5-N5) (E=NSb) [44].

Fig. 14 shows the orbital correlation diagram for ferrocene and related molecules which is found in many textbooks of inorganic and organometallic chemistry [24], [45]

Main group metallocenes ECp2 (E=BeBa, Zn, SiPb) and ECp (E=LiCs, BTl)

The bonding situation in the ubiquitous metallococene complexes ECp2 has also been studied by us for main group elements E where E is a Group-2 (BeBa) or -14 element (SiPb) or Zn. A comparison of the energy analysis with the results of ferrocene should give insight into the difference between the ECp2 bonding of a transition metal and main group elements. We also investigated the metalCp bonding in the ‘half sandwich’ complexes ECp of Groups 1 (LiCs) and 13 (BTl) [46].

We first discuss the

Summary and conclusion

The results of the energy partitioning analysis of a variety of donor–acceptor complexes of transition metals and main-group elements demonstrates that it is possible to examine the nature of a chemical bond not only qualitatively but quantitatively [53]. This is possible for two reasons. One reason is that the geometries and energies of heavy-atom molecules can be accurately calculated with modern quantum chemical methods. The second reason is that the interaction energies between atoms or

Acknowledgements

We want to thank both reviewers who forced us with their thoughtful comments, questions and suggestions to state our arguments more precisely and on this way helped to improve the paper. The work was supported by the Deutsche Forschungsgemeinschaft and by the Fonds der Chemischen Industrie. G.F. thanks Matthias Bickelhaupt and Evert-Jan Baerends for helpful comments and stimulating discussions. V.M.R. thanks the Secretarı́a de Estado de Educación y Universidades (MECD-Spain) for support via

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