Electronic Structure of Metals and Atomic Parameters

Homogeneous alloys of metals with atoms of similar radius are substitutional alloys. For example, in brass, zinc atoms readily replace copper atoms in the crystalline lattice, because they are nearly the same size (Fig. 16.41). However, the presence of the substituted atoms changes the lattice parameters and distorts the local electronic structure. This distortion lowers the electrical and thermal conductivity of the host metal, but it also increases hardness and strength. Coinage alloys are usually substitutional alloys. They are selected for durability—a coin must last for at least 3 years—and electrical resistance so that genuine coins can be identified by vending machines. 

So far we have assumed that the electronic structure of the crystal consists of one band derived, in our approximation, from a single atomic state. In general, this will not be a realistic picture. The metals, for example, have a complicated system of overlapping bands derived, in our approximation, from several atomic states. This means that more than one atomic orbital has to be associated with each crystal atom. When this is done, it turns out that even the equations for the one-dimensional crystal cannot be solved directly. However, the mathematical technique developed by Baldock (2) and Koster and Slater (S) can be applied (8) and a formal solution obtained. Even so, the question of the existence of otherwise of surface states in real crystals is diflBcult to answer from theoretical considerations. For the simplest metals, i.e., the alkali metals, for which a one-band model is a fair approximation, the problem is still difficult. The nature of the difficulty can be seen within the framework of our simple model. In the first place, the effective one-electron Hamiltonian operator is really different for each electron. If we overlook this complication and use some sort of mean value for this operator, the operator still contains terms representing the interaction of the considered electron with all other electrons in the crystal. The Coulomb part of this interaction acts in such a way as to reduce the effect of the perturbation introduced by the existence of a free surface. A self-consistent calculation is therefore essential, and the various parameters in our theory would have to be chosen in conformity with the results of such a calculation. 

A theoretical foundation for understanding these correlations is found in the calculated bulk electronic structures of the first- and second-row TMS. The electronic environment of the metal surrounded by six sulfur atoms in an octahedral configuration was calculated, using the hypotheses that all the sulfides could be represented by this symmetry as an approximation. There are several electronic factors that appear to be related to catalytic activity the orbital occupation of the HOMO (Highest Occupied Molecular Orbital), the degree of covalency of the metal-sulfur bond, and the metal-sulfur bond strength. These factors were incorporated into an activity parameter (A2), which correlates well with the periodic trends (Fig. 16) (74, 75). This parameter is equal to the product of the number of electrons contained in the... 

The principle aim of the reported studies was to model structures, conformational equilibria, and fluxionality. Parameters for the model involving interactionless dummy atoms were fitted to infrared spectra and allowed for the structures of metallocenes (M = Fe(H), Ru(II), Os(II), V(U), Cr(II), Cofll), Co(ni), Fe(III), Ni(II)) and analogues with substituted cyclopentadienyl rings (Fig. 13.3) to be accurately reproduced 981. The preferred conformation and the calculated barrier for cyclopentadienyl ring rotation in ferrocene were also found to agree well with the experimentally determined data (Table 13.1). This is not surprising since the relevant experimental data were used in the parameterization procedure. However, the parameters were shown to be self-consistent and transferable (except for the torsional parameters which are dependent on the metal center). An important conclusion was that the preference for an eclipsed conformation of metallocenes is the result of electronic effects. Van der Waals and electrostatic terms were similar for the eclipsed and staggered conformation and the van der Waals interactions were attractive 981. It is important to note, however, that these conclusions are to some extent dependent on the parameterization scheme, and particularly on the parameters used for the nonbonded interactions. 

---