The Electronic Structure of Transition Metal Compounds

Fachbereich Chemie, Philipps-Universitat Marburg, Hans-Meerwein-StraBe, D-35032 Marburg 

Pauling always favored the Valence Bond (VB) theory over the Molecular Orbital (MO) theory for the description of the electronic structure of molecules, because the VB model resembles more the pre-quantum theoretical models of chemical bonding. However, modem quantum chemistry is dominated by MO theory, which has clearly prevailed in the computational applications. Nevertheless, a number of terms and concepts of VB theory still play an important role when it comes to the interpretation of the results of a quantum chemical calculation. 

The understanding of the bonding in transition metal compounds presents a special challenge for theoretical chemistry. Just as in the case of the main group elements,8 it could be shown that a classification of the bonds between a transition metal and a ligand into 

The geometry optimizations have been carried out at the MP2 level of theory17 using effective core potentials (ECPs)18 for the heavier elements. Hydrogen and the first and second row elements B, C, N, O, Na, Mg, Al and Si were described by standard all electron 6-31G(d) basis sets.19 For tungsten we used the relativistic ECP developed by Hay and Wadt and the corresponding (441/2111/21) split-valence basis set.20 A pseudopotential with a (31/31/1) valence basis set was used for Cl, Ga, In and Tl.21 This basis set combination is our standard basis set II.22 

The sum of the orbital contributions d, bj and r, yields the total amount of donation (d), backdonation (b) and repulsion (r), respectively. 

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Electron correlation plays an important role in determining the electronic structures of many solids. Hubbard (1963) treated the correlation problem in terms of the parameter, U. Figure 6.2 shows how U varies with the band-width W, resulting in the overlap of the upper and lower Hubbard states (or in the disappearance of the band gap). In NiO, there is a splitting between the upper and lower Hubbard bands since IV relative values of U and W determine the electronic structure of transition-metal compounds. Unfortunately, it is difficult to obtain reliable values of U. The Hubbard model takes into account only the d orbitals of the transition metal (single band model). One has to include the mixing of the oxygen p and metal d orbitals in a more realistic treatment. It would also be necessary to take into account the presence of mixed-valence of a metal (e.g. Cu ", Cu ). 

Figure 6.52 Schematic electron addition and removal spectra representing the electronic structure of transition-metal compounds for different regimes of the parameter values (a) charge-transfer insulator with U > A (b) Mott-Hubbard insulator A> U (From Rao et al, 1992).

Analysis of the valence-band spectrum of NiO helped to understand the electronic structure of transition-metal compounds. It is to be noted that th.e crystal-field theory cannot explain the features over the entire valence-band region of NiO. It therefore becomes necessary to explicitly take into account the ligand(02p)-metal (Ni3d) hybridization and the intra-atomic Coulomb interaction, 11, in order to satisfactorily explain the spectral features. This has been done by approximating bulk NiO by a cluster (NiOg) ". The ground-state wave function Tg of this cluster is given by,... 

This very short intermezzo on the electronic structure of transition metal compounds had as its main purpose to illustrate that bonding is very similar to that in molecular co-ordination compounds. Hence their chemical reactivity can be understood using the same concepts. 

In this article we have shown that the electronic structures of transition metal compounds based on a cubic architecture can be rationalized, by use of results obtained from molecular orbital calculations, leading to some interesting extensions of the electron-counting PSEP rules. Indeed, the cluster topology of the different cubic cluster categories is highly dependent on several parameters which can be calibrated. 

Vibrational fine structure in the electronic spectra of transition metal compounds an experimental survey. M. Cicslak-Golonka, A. Bartecki and S. P. Sinha, Coord. Chem. Rev., 1980, 31, 251-288... 

Even though both Hohenberg-Kohn and Kohn-Sham papers have been subsequently recognized as extremely important for Chemistry, that recognition came late in the community of theoretical chemists. Meanwhile, the MS-Xa method received much more attention. Por example, in 1970, Johnson and Smith addressed polyatomic molecules such as perchlorate and sulphate ions for the first time [13]. A landmark application of MS-Xa was the first investigation by Johnson and Smith of the electronic structure of a coordination compound, namely the permanganate ion [22]. The interest in the MS-Xa method for calculating the electronic structure of transition metal complexes increased rapidly and realistic results were soon obtained [23-25]. 

Later developments of linear methods have been in the direction of self-consistent calculations of ground-state properties utilising local spin-density-functional formalism [1.51,52] for exchange and correlation. The basis of the self-consistency procedure was given in papers by Madsen et al. [1.53], Vouisen et al. [1.54] and Andersen and Jepsen [1.55], and was soon followed by results for the magnetic transition metals [1.56], the noble metals [1.57], some lanthanides [1.58], the actinides [1.59,60], and the 3d transition metal monoxides [1.61,62]. In this context one should also mention calculations of the electronic structure in transition metal compounds [1.63,64], A15 compounds [1.65,66], rare-earth borides [1.67], Chevrel... 

Molecular symmetry and ways of specifying it with mathematical precision are important for several reasons. The most basic reason is that all molecular wave functions—those governing electron distribution as well as those for vibrations, nmr spectra, etc.—must conform, rigorously, to certain requirements based on the symmetry of the equilibrium nuclear framework of the molecule. When the symmetry is high these restrictions can be very severe. Thus, from a knowledge of symmetry alone it is often possible to reach useful qualitative conclusions about molecular electronic structure and to draw inferences from spectra as to molecular structures. The qualitative application of symmetry restrictions is most impressively illustrated by the crystal-field and ligand-field theories of the electronic structures of transition-metal complexes, as described in Chapter 20, and by numerous examples of the use of infrared and Raman spectra to deduce molecular symmetry. Illustrations of the latter occur throughout the book, but particularly with respect to some metal carbonyl compounds in Chapter 22. 

The nature of this group of phases has been associated with the characteristic feature of the electronic structure of transition metal atoms [6,7] d electrons which do not participate in the formation of Me-Si bonds. It was concluded that the d states are discrete only in CrSi2 and do not have any appreciable effect on the transport properties of the compound. 

The MNDO/d parametrization for the transition metals has proven to be more difficult than for the main-group elements. This is mostly due to the more complicated electronic structure of transition metal compounds, and partly also to the lack of reliable thermochemical reference data. During the parametrization, the proper reproduction of the lowest electronic states of a given transition metal was enforced by a suitable choice of the one-center parameters, and some bond-specific a parameters were introduced for fine tuning. In spite of these measures, the results for elements in the middle of a transition... 

The ZSA phase diagram and its variants provide a satisfactory description of the overall electronic structure of stoichiometric and ordered transition-metal compounds. Within the above description, the electronic properties of transition-metal oxides are primarily determined by the values of A, and t. There have been several electron spectroscopic (photoemission) investigations in order to estimate the interaction strengths. Valence-band as well as core-level spectra have been analysed for a large number of transition-metal and rare-earth compounds. Calculations of the spectra have been performed at different levels of complexity, but generally within an Anderson impurity Hamiltonian. In the case of metallic systems, the situation is complicated by the presence of a continuum of low-energy electron-hole excitations across the Fermi level. These play an important role in the case of the rare earths and their intermetallics. This effect is particularly important for the valence-band spectra. 

The development of electronic structure theories for metal complexes has always been closely linked with electron spectroscopy of transition metal compounds. We shall in the following describe both DFT and wave function methods that have been used in the study of excited states. We shall also discuss their application to the tetroxo systems. 

McClure, D. S. (1961) Electronic structure of transition metal complex ions. Advances in the Chemistry of coordination compounds, p. 498 ed. Kirshner, S. New York McMillan and Co. 

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