Electronic structure transition metal compounds

Qualitative molecular-orbital analysis of computational results. Rather than employing purely qualitative, symmetry-based theory, we can also perform calculations on solids or clusters and then analyze them using qualitative MO arguments. We will consider two such studies (1) an EHMO study of SiOj in (3-quartz, stishovite, and hypothetical silica-w structures (Burdett and Caneva, 1985), and (2) an MS-SCF-Aa study of electron-rich transition-metal compounds (Tossell and Vaughan, 1981). 

Methods for computing the geometric and electronic structures of metal compounds are advancing rapidly on all fronts. While there is a long way to go before Transition Metal computational chemistry can be described as truly predictive, techniques now exist for computing the structures and reactivities of coordination and organometallic systems to useful accuracy. As such, theory can play a powerful complementary role alongside other physical measurements. 

The critical diameter for change from localized to collective behavior of the d electrons in transition metal compounds is also an important parameter that affects properties and structure, as discussed by Goodenough (Ref. 22, pp. 26-28, 265-266,295-297). 

The general understanding of the electronic structure and the bonding properties of transition-metal silicides is in terms of low-lying Si(3.s) and metal-d silicon-p hybridization. There are two dominant contributions to the bonding in transition-metal compounds, the decrease of the d band width and the covalent hybridization of atomic states. The former is caused by the increase in the distance between the transition-metal atoms due to the insertion of the silicon atoms, which decreases the d band broadening contribution to the stability of the lattice. 

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... 

The dominant features which control the stoichiometry of transition-metal complexes relate to the relative sizes of the metal ions and the ligands, rather than the niceties of electronic configuration. You will recall that the structures of simple ionic solids may be predicted with reasonable accuracy on the basis of radius-ratio rules in which the relative ionic sizes of the cations and anions in the lattice determine the structure adopted. Similar effects are important in determining coordination numbers in transition-metal compounds. In short, it is possible to pack more small ligands than large ligands about a metal ion of a given size. 

In an earlier work, we have proposed a theoretical procedure for the spectroscopy of antiferromagnetically (AF) coupled transition-metal dimers and have successfully applied this approach to the electronic absorption spectrum of model 2-Fe ferredoxin. In this work we apply this same procedure to the [Fe2in - 82) P o - CeH48)2)2 complex in order to better understand the electronic structure of this compound. As in our previous work" we base our analysis on the Intermediate Neglect of the Differential Overlap model parameterized for spectroscopy (INDO/S), utilizing a procedure outlined in detail in Reference 4. 

First we consider the origin of band gaps and characters of the valence and conduction electron states in 3d transition-metal compounds [104]. Band structure calculations using effective one-particle potentials predict often either metallic behavior or gaps which are much too small. This is due to the fact that the electron-electron interactions are underestimated. In the Mott-Hubbard theory excited states which are essentially MMCT states are taken into account dfd -y The subscripts i and] label the transition-metal sites. These... 

Transition metal compounds with ligands of low electronegativity also show deviations, in spite of a d° electron configuration. For example, W(CH3)6 does not have the expected octahedral structure, but is trigonal-prismatic. 

In order to compare the structural options for transition metal compounds and to estimate which of them are most favorable energetically, the ligand field stabilization energy (LFSE) is a useful parameter. This is defined as the difference between the repulsion energy of the bonding electrons toward the d electrons as compared to a notional repulsion energy that would exist if the d electron distribution were spherical. 

I.B. Bersuker, Electronic Structure and Properties of Transition Metal Compounds. John Wiley and Sons, Inc., 1996. 

In contrast to carbon, which forms structures derived from both sp2 and sp3 bonds, silicon is unable to form sp2 related structures. Since one out of four sp3 bonds of a given atom is pointing out of the cage, the most stable fullerene-like structure in this case is a network of connected cages. This kind of network is realized in alkali metal doped silicon clathrate (19), which were identified to have a connected fullerene-like structure (20). In these compounds, Si polyhe-dra of 12 five-fold rings and 2 or 4 more six-fold rings share faces, and form a network of hollow cage structures, which can accommodate endohedral metal atoms. Recently, the clathrate compound (Na,Ba), has been synthesized and demonstrated a transition into a superconductor at 4 K (21). The electronic structure of these compounds is drastically different from that of sp3 Si solid (22). 

We have made one rather obvious omission from our descriptions of molecule electronic structure - the structure of transition-metal ions. This is deliberate since, in spite of the well-developed theories of the electronic spectra (U.V., photo-electron) of these compounds, it is still true to say that there is no theory of the bonding in this important class of molecules. The question of the localised or de-localised nature of the electronic structure of the bonds in these systems has not really been solved historically, there has been some skirmishing about the superiority of the MO or VB methods but the nature of the valence in these molecules has received a disproportionately small amount of attention. Thus any attempt to develop a GHO basis for transition-metal compounds is perhaps premature until more experience has been gained with typical element chemistry. 

The methods used to describe the electronic structure of actinide compounds must, therefore, be relativistic and must also have the capability to describe complex electronic structures. Such methods will be described in the next section. The main characteristic of successful quantum calculations for such systems is the use of multiconfigurational wave functions that include relativistic effects. These methods have been applied for a large number of molecular systems containing transition metals or actinides, and we shall give several examples from recent studies of such systems. 

The electron density in transition metal complexes is of unusual interest. The chemistry of transition metal compounds is of relevance for catalysis, for solid-state properties, and for a large number of key biological processes. The importance of transition-metal-based materials needs no further mention after the discovery of the high-Tc superconducting cuprates, the properties of which depend critically on the electronic structure in the CuOz planes. 

These properties of the d-shell chromophore (group) prove the necessity of the localized description of d-electrons of transition metal atom in TMCs with explicit account for effects of electron correlations in it. Incidentally, during the time of QC development (more than three quarters of century) there was a period when two directions based on two different approximate descriptions of electronic structure of molecular systems coexisted. This reproduced division of chemistry itself to organic and inorganic and took into account specificity of the molecules related to these classical fields. The organic QC was then limited by the Hiickel method, the elementary version of the HFR MO LCAO method. The description of inorganic compounds — mainly TMCs,— within the QC of that time was based on the crystal field... 

J. Demuynck, A. VeiUard. Transition metal compounds. In III H. F. Schaefer, editor, Applications of Electronic Structure Theory, pages 187-222. Plenum Press, New York, London , 1977. 

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).

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