Transition metal compounds, band theory

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... 

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,... 

X-Ray absorption data in combination with atomic theory and solid-state band-structure theory can yield detailed information about the ground-state electronic structure of solids on an energy scale on the order of meV. This holds particularly true for correlated narrow-band systems, such as the rare-earth and transition-metal compounds. In broad-band materials, such as the... 

Finally, lei us use the transition-metal pseudopotential theory to estimate matrix elements between d states and s and p states. These are not so useful in the transition metals themselves since the description of the electronic structure is better made in terms of d bands coupled to free-electron bands, ti k /(2m) d-<01 IT 10>, rather than in terms of d bands coupled to s and p bands. However, the matrix elements and so forth, directly enter the electronic structure of the transition-metal compounds, and it is desirable to obtain these matrix elements in terms of the d-state radius r. We do this by writing expressions for the bands in terms of pseudopotentials and equating them to the LCAO expressions obtained in Section 20-A. 

A pure transition metal is best described by the band theory of solids, as introduced in Chapter 10. In this model, the valence s and d electrons form extended bands of orbitals that are delocalized over the entire network of metal atoms. These valence electrons are easily removed, so most elements In the d block react readily to form compounds oxides such as Fc2 O3, sulfides such as ZnS, and mineral salts such as zircon, ZrSi O4. ... 

Properties of hydrogen Properties of metals Band theory Properties of nonmetals Properties of transition metals Coordination compounds Crystal-held theory Complex ions... 

The electronic spectrum is yet another property which illustrates the similarities between the metallocenes and (7r-ollyl) metal compounds. In Table VI are listed some data for a series of Coin(absorption bands with the small extinction coefficients are probably two of the spin-allowed d-d transitions. Scott (34) has developed an approximate axial ligand field model for the carborane-transition metal complexes and has discussed the optical spectra in relation to this bonding theory. The actual assessment of bonding in the (7r-ollyl) metal compound as well as the metallocenes would be greatly aided by accurate assignments of the electronic spectra. 

Likewise the Hubbard model the periodic Anderson model (PAM) is a basic model in the theory of strongly correlated electron systems. It is destined for the description of the transition metals, lanthanides, actinides and their compositions including the heavy-fermion compounds. The model consists of two groups of electrons itinerant and localized ones (s and d electrons), the hybridization between them is admitted. The model is described by the following parameters the width of the s-electron band W, the energy of the atomic level e, the on-site Coulomb repulsion U of d-electrons with opposite spins, the parameter V of the... 

In the realm of theory also, greater demands will be made. As such studies (37—39) as those of Cu—Ni (Fig. 13) and Ag—Pd (Fig. 14) have shown, the d levels of the two species in transition metal alloys tend to maintain their atomic identities, at least when the levels in the pure components are sufficiently well separated in energy. However, neither calculation nor experiment has been done with refinement sufficient for quantitative testing of a theory, such as the coherent potential approximation, designed to describe the d band behavior. In pure metals and intermetallic compounds, band calculations can be compared directly with experiment if transition probabilities and relaxation effects are understood. With care they can be used also in evaluation of the effective interelectronic terms which enter equations such as (18a). Unfortunately, one cannot, by definition, produce a set of selfconsistent band calculation results for a matrix of specific valence electron snpmdl.. . configurations thus, direct estimates for I of Eq. (18a) or F of Eq. (18b) cannot be made. However, band calculations for a set of systems can indicate whether or not it is reasonable to factor level shifts into volume and electron count terms, in the manner of Eqs. (18a) and (23). When this cannot be done, one must revert to a more general expression for a level shift, such as Eq. (1). 

Early work on pure metals, solid-solution alloys, and intermetallic compounds has been reviewed by Azaroff and Pease (9). Some of the very best X-ray absorption X-edge spectra for 3d transition metals were reported in 1939 by Beeman and Friedman (24), who applied band theory for their interpretation. Up to the early 1960s X-ray band spectra of metals were mainly explained in terms of a density of states multiplied by a transition probability. 

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