Understanding the nature of the bonding in transition metal complexes: from Dewar's molecular orbital model to an energy partitioning analysis of the metal–ligand bond

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Abstract

The results of an energy partitioning analysis of three classes of transition metal complexes are discussed. They are (i) neutral and charged isoelectronic hexacarbonyls TM(CO)6q (TMq=Hf2−, Ta, W, Re+, Os2+, Ir3+); (ii) Group-13 diyl complexes (CO)4FeER (E=B, Al, Ga, In, Tl; R=Cp, Ph), Fe(ECH3)5 and Ni(ECH3)4; (iii) complexes with cyclic π-donor ligands Fe(Cp)2 and Fe(η5-N5)2. The results show that Dewar's molecular orbital model can be recovered and that the orbital interactions can become quantitatively expressed by accurate quantum chemical calculations. However, the energy analysis goes beyond the MO model and gives a much deeper insight into the nature of the metal–ligand bonding. It addresses also the question of ionic versus covalent bonding as well as the relative importance of σ and π bonding contributions.

The bonding model suggested for metal–olefin complexes, which was suggested by Dewar 50 years ago, is found by an energy partitioning analysis to be a valid description of the bonding in transition metal complexes with ligands CO, Group-13 diyl species ER (E=B, Al, Ga, In, Tl; R=Cp, Ph, CH3) and with cyclic π-donor ligands Cp and cyc-N5 in Fe(Cp)2 and Fe (η5-N5)2.

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Introduction

The history of chemistry knows a small number of chemical models which were first suggested in order to rationalise a single puzzling phenomenon but then they became the paradigmatic ground for a whole new area in chemistry. Classical examples are Kekulé's bonding model for benzene [1] and its quantum chemical explanation given by Hückel [2] which is the theoretical foundation of aromaticity and aromatic compounds [3] and the Woodward–Hoffmann/Fukui orbital symmetry rules [4], [4](a), [4](b) which gave an understanding for the reaction mechanism of pericyclic and other organic reactions [5]. Another equally important bonding model, which is now ubiquitously used in transition metal (TM) chemistry, was suggested by Dewar, who introduced in 1951 the concept of metal–ligand orbital interactions in terms of ligand→metal σ-donation and metal→ligand π-backdonation [6]. Dewar suggested the molecular orbital model to describe the bonding of an olefin coordinated to Ag(I) or Cu(I). A peculiar aspect of the groundbreaking idea is that Dewar apparently was not very interested in the field of TM chemistry and probably was not aware of the huge impact of his suggestion to the field. It was the famous paper by Chatt and Duncanson [7] who used Dewar's model for a systematic description of metal–olefin complexes which led to the breakthrough of Dewar's MO model in TM chemistry. This is the reason that the bonding model of donation and backdonation between a metal and a ligand is now termed the CDC model after Dewar, Chatt and Duncanson.

The DCD model has become the standard model not only for metal–olefin bonds but also for all kinds of transition metal–ligand bonds (TM–L). Textbooks of inorganic and organometallic chemistry and chemical bonding theory usually show the relevant molecular orbitals of the ligand and the metal or metal fragment and then discuss the bonding in terms of ligand→metal donation and metal→ligand backdonation [8], [8](a), [8](b), [8](c), [8](d). This is done in a qualitative and heuristic way. The results are frequently compared with experimental values such as bond lengths, bond strengths and vibrational frequencies. Calculations at the EHT level particularly by Hoffmann supported the DCD model [9]. EHT calculations have been used to discuss the bonding situation in numerous TM compounds providing the basis for a qualitative bonding model based on approximate quantum chemical methods [10].

The last decade has seen an enormous progress in quantum chemical methods for calculating TM compounds and other heavy atom molecules with high accuracy. This became possible because gradient corrected DFT, effective core potentials and new methods for calculating relativistic effects have been introduced at standard levels of theory which were proven to give accurate geometries, energies and other important properties of molecules [11]. Progress has also been made in the development of methods for analysing the electronic structure of the calculated species. New techniques were suggested for partitioning the electronic charge and the bonding energy of molecules. The natural bond orbital (NBO) method by Weinhold [12] and the topological analysis of the electron density distribution by Bader [13] are powerful tools which provide detailed insight into the bonding situation in a molecule. The charge decomposition analysis (CDA) is particularly interesting in the context of the DCD bonding model [14]. It is a charge partitioning method which calculates the amount of electronic charge of the ligand→metal donation and the metal→ligand backdonation for each orbital. The analysis of the bonding situation of many TM complexes showed that the DCD model of metal–ligand bonds can be quantitatively expressed using the results of the CDA calculations [15], [15](a), [15](b), [15](c), [15](d), [15](e), [15](f), [15](g), [15](h), [15](i).

A perhaps even more important question concerns the energies which are associated with the ligand→metal donation and the metal→ligand backdonation. Energy partitioning methods such as the extended transition state (ETS) method developed by Ziegler and Rauk [16], [16](a), [16](b), [16](c) and the related energy decomposition analysis (EDA) which was earlier suggested by Morokuma [17] are available which give well defined energy terms for the donation and backdonation. Thus, accurate quantum chemical calculations at the DFT or ab initio level may be used to obtain energy values which give the strength of the ligand→metal donation and the metal→ligand backdonation. The energy analysis may even be used in such a way that it goes beyond the DCD model. The first and perhaps most detailed investigation was made 10 years ago by Davidson et al. who analysed the chemical bonding in Cr(CO)6 [18]. We could show in recent investigations that the partitioning of the total energy of a transition metal complex into energies of the bonding fragments may lead to expressions which can be interpreted only in terms of donation and backdonation [19], [20], [21], [22]. While the latter considers only the orbital interactions as components of the TM–L bonds the energy partitioning also gives information about the relative strength of the electrostatic and orbital interactions. We proposed that the latter term may be considered as a measure of the covalent bonding while the former term gives the strength of the ionic bonding. The progress which has been made in the understanding of the chemical bond in transition metal complexes has recently been reviewed [23].

In this paper we compare recent results of the EDA of three classes of transition metal complexes. The data which were obtained in these studies show that, although the original bonding model which was suggested by Dewar 50 years ago is beautifully recovered and quantitatively supported by modern quantum chemical methods, other terms than donation and backdonation need to be considered for a full understanding of the chemical bond. The analysis shows that the metal–ligand interactions can be divided into three physically meaningful components whose strength can be quantitatively estimated. They are the attractive electrostatic interaction (ionic bonding), the attractive orbital interactions (covalent bonding) and the repulsive interactions between occupied orbitals of the fragments which arise from the Pauli repulsion. The DCD model is then given by the relative strength of the orbital interactions between occupied ligand orbitals and empty metal orbitals (donation) and between occupied metal orbitals and empty ligand orbitals (backdonation). Although the absolute values of the latter terms may not be the largest ones they often (but not always!) determine the trend of the bond strength. The three classes of TM complexes are: (i) carbonyls for which the isoelectronic series TM(CO)6q (TMq=Hf2−, Ta, W, Re+, Os2+, Ir3+) was chosen; (ii) carbonyl complexes with Group-13 diyl ligands (CO)4FeER (E=B, Al, Ga, In, Tl; R=Cp, Ph) and homoleptical Group-13 diyl complexes Fe(ECH3)5 and Ni(ECH3)4; (iii) complexes with cyclic π-donor ligands Fe(Cp)2 and Fe(η5-N5)2. We will compare the most important results of the EDA. Further results such as the geometries and bond energies and a more detailed discussion of the bonding analysis are given in the original publications [20], [21], [22].

Section snippets

Methods

The calculations have been performed at the gradient corrected DFT level using the exchange functional of Becke [24] and the correlation functional of Perdew [25] (BP86). Relativistic effects have been considered in case of the carbonyls and for the complexes with cyclic π-donor ligands Fe(Cp)2 and Fe(η5-N5)2 by the zero-order regular approximation (ZORA) [26], [26](a), [26](b), [26](c), [26](d), [26](e). The Group-13 diyl complexes (CO)4FeER have been calculated using the Pauli formalism [27]

Metal–CO bonding in TM(CO)6q (TMq=Hf2−, Ta, W, Re+, Os2+, Ir3+) [20]

The choice of the fragments for the analysis of the TMCO bonding in the isoelectronic hexacarbonyls which are experimentally known was done in two different ways. One way was by analysing the interactions of a single CO ligand with the remaining TM(CO)5q fragment. The other choice was by taking the metal atom as one fragment and the (CO)6 ligand cage as the other fragment. We begin with the bonding analysis of one CO with TM(CO)5q. Fig. 1 shows the DCD model of the orbital interactions between

Complexes with Group-13 diyl ligands (CO)4FeER (E=B, Al, Ga, In, Tl; R=Cp, Ph) [21]

While carbonyls were the first TM complexes which have been synthesised [36], molecules with Group-13 ligands ER (E=Group-13 element B-Tl) belong to the youngest classes of TM complexes. The first TM Group-13 diyl complex characterised by X-ray structure analysis which is not stabilised by additional donor ligands is (CO)4FeAlCp* which has been reported by Weiss et al. in 1997 [37]. The first homoleptical diyl complex Ni(InC(SiMe3)3)4 was synthesised by Uhl et al. in 1998 [38]. The DCD model

Complexes with cyclic π-donor ligands Fe(Cp)2 and Fe(η5-N5)2 [22]

In the final paragraph we compare the results of an ETS analysis of ferrocene with the data of the isoelectronic iron bispentazole. The former compound was already synthesised in 1951 [46], [46](a), [46](b). Soon after the sandwich structure of Fe(Cp)2 was recognised [47], [47](a), [47](b), [47](c) the metal–ligand bonding was discussed in terms of the DCD donor–acceptor interactions between Fe2+ and 2 Cp shown in Fig. 12. Although the cyclopentadienyl ligands of ferrocene in the gas phase are

Summary

The discussion of the results which have been obtained for three different classes of TM complexes demonstrate how much progress has been made in the development of methods which give insight into the nature of the metal–ligand bonding situation. The molecular orbital model suggested by Dewar 50 years ago which has become a standard model for a qualitative understanding of the structure and bonding of TM compounds is quantitatively supported by the ETS results. However, the picture which

Acknowledgements

This work was supported by the Deutsche Forschungsgemeinschaft and by the Fonds der Chemischen Industrie. Excellent service by the Hochschulrechenzentrum of the Philipps-Universität Marburg is gratefully acknowledged. Additional computer time was provided by the HLRS Stuttgart, HHLRZ Darmstadt and HRZ Frankfurt.

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