Calculations, band theory

Like Rh and Ir, all three members of this triad have the fee structure predicted by band theory calculations for elements with nearly filled d shells. Also in this region of the periodic table, densities and mps are decreasing with increase in Z across the table thus, although by comparison... 

We have carried out impurity calculations for a zinc atom embedded in a copper matrix. We first perform self consistent band theory calculations on pure Cu and Zn on fee lattices with the lattice constant of pure Cu, 6.76 Bohr radii. This yields Fermi energies, self consistent potentials, scattering matrices, and wave functions for both metals. The Green s function for a system with a Zn atom embedded in a Cu matrix... 

It was pointed out in my 1949 paper (5) that resonance of electron-pair bonds among the bond positions gives energy bands similar to those obtained in the usual band theory by formation of Bloch functions of the atomic orbitals. There is no incompatibility between the two descriptions, which may be described as complementary. It is accordingly to be expected that the 0.72 metallic orbital per atom would make itself clearly visible in the band-theory calculations for the metals from Co to Ge, Rh to Sn, and Pt to Pb for example, the decrease in the number of bonding electrons from 4 for gray tin to 2.56 for white tin should result from these calculations. So far as I know, however, no such interpretation of the band-theory calculations has been reported. 

Many solid-state physicists discuss the structure and properties of metals and alloys with use of the band theory, in its several modifications. This theory is also a quantum mechanical theory, which starts with a solution of the wave equation for a single electron, and introduces electron-electron correlation in one or another of several ways. The resonating-valence-bond theory introduces electron-electron correlation in several stages, one of which is by the formation of covalent bonds between adjacent atoms, and another the application of the electroneutrality principle to restrict the acceptable structures to those that involve only M+, M°, and M-. It should be possible to find a relationship between the band-theory calculations and the resonating-covalent-bond theory, but I have been largely unsuccessful in finding such a correlation. I have, for example, not been able to find any trace of the metallic orbital in the band-theory calculations, which thus stand in contrast to the resonating-valence-bond theory, in which the metallic orbital plays a predominant role."... 

The earliest band theory calculations for conjugated polymers were focussed on rrans-polyacetylene (t-PAc). It was the first system in which metallic levels of electrical conductivity were observed (Shirakawa et al., 1977) and has by far the simplest molecular structure of this class of polymers. There are two possible structures, either ... 

The delocalized (right-hand) side of Fig. 1.1 involves some form of calculation on the full lattice such as a band-theory calculation. Again, the Hartree-Fock wave function may be employed in an ab initio method or some approximate method such as Huckel band theory, or the local-exchange approximations employed leading to augmented-plane-wave or ab initio pseudopotential (PP) methods. As an alternative to band theory, the development of the ionic approach using pair potentials or modified electron-gas (MEG) theory has proved effective for certain crystalline species. 

With the growing interest in polysilane polymers, calculations have been carried out using several other approaches95,105,106. Band theory calculations are especially useful they support assignment of the electronic transition as mainly even for arylpolysil-... 

Although SrTiOs, which undergoes a spontaneous distortion at low temperature, has received recent attention in band theory calculations (see Section VII. B), few of these interesting systems have yet been thoroughly investigated by many of the techniques described in this article. 

KNiFs has been subject to both extensive molecular orbital and to thorough band theory calculations. Newmancrystal field splitting may be derived from the calculations of Mattheiss and the value found is about 20% below the experimental figure—a situation indeed comparable to the localized electron calculations< 5) jt jg interesting that the LCAO interpretation of the band theory calculations for the monoxides< i > indicates that oxygen 2s-2p interaction with the metal and Ap orbitals may cause a greater charge redistribution than the interaction with the M orbitals. 

Magnetization can be calculated from first principles by band theory. Calculation methods are usually separated into (i) scalar-relativistic calculations and (ii) full-relativistic calculations. The scalar-relativistic calculations can predict the occurrence of ferromagnetism, the value of the spin moment, and several nonmagnetic properties. The fuU-relativistic calculations are additionally able to determine the magnetocrystalline anisotropy and the induced orbital moment. The most common approach uses the formalism of local density approximation (LDA) to the density functional theory (DFT) [10]. 

---