K -edge absorption spectra of selected vanadium compounds

Publisher Summary This chapter discusses statistical exchange-correlation in the self-consistent field. There are two sides to a self-consistent field calculation: the determination of the potential and the solution of Schrodinger's equation for the one-electron problem. The solution of Schrodinger's equation has fortunately advanced far enough through the application of the electronic digital computer so that it can be regarded for most purposes as being a standardized technique. The main point of the method of Gaspar, Kohn, and Sham is that they derive the approximate exchange correction from an approximate Hamiltonian for the system by varying the spin-orbitals to minimize the average value of this Hamiltonian for the ground state. The approximate Hamiltonian has many important and valuable features that are described in the chapter.

Statistical Exchange-Correlation in the Self-Consistent Field

Transition metal sulfides

An attempt has been made to illuminate the intricacies of the Mott transition as applicable to binary transition metal compounds. This has been done in the light shed by recent experimental and theoretical developments taken over a wide field. The position of Mott transition has been considered with regard to the full array of binary materials offered, and the possibilities for several new systems have been indicated. The properties of materials close to either side of the transition are discussed.

Systematics of the breakdown of Mott insulation in binary transition metal compounds

An account is given of some of the mechanisms which can lead to a transition from a metallic to a nonmetallic state, when a parameter such as the interatomic distance or temperature is varied. The simplest of these is the band overlap or Wilson transition, which occurs when a conduction band overlaps a valence band; this is discussed in § 2 and for noncrystalline systems in § 15. These transitions can be described in the Hartree-Fock approximation. If the insulating property is due essentially to the repulsion between electrons (e2/r12), then the nonmetallic state is normally antiferromagnetic. The possibility of describing it by normal band theory with a spin-dependent potential is discussed in § 5. It is emphasized that antiferromagnetism can exist in the metallic state, and that the conditions for the appearance of conductivity and the disappearance of antiferromagnetism are not always the same. The nonmetallic behaviour, that is the existence of a Hubbard gap, normally persists above the Neel temperature (as in NiO), as does the gap in some metals, but not in chromium. Disordered systems, such as doped semiconductors, are discussed; here in the metallic state we suggest that the two Hubbard bands overlap, and that the metal-nonmetal transition can be described as an Anderson transition (§ 16). This model gives a simple explanation of the negative magnetoresistance. In some materials a transition occurs which does not involve magnetic moments or structural change, and for d bands, following Halperin and Rice, and Weger, we introduce the concept of an `orbital orientation wave' in degenerate d bands (§§ 5, 19.3, 19.4). A number of specific materials are discussed.

https://iopscience.iop.org/article/10.1088/0034-4885/33/3/302/pdf

The metal-nonmetal transition

Energy bands are calculated for hexagonal NiS using lattice constants and crystal potential appropriate to the metallic phase. Group theoretic results for $s$, $p$, and $d$ bands in the NiAs structure are obtained, and the calculation is performed using a first-principles tight-binding method. The energy band structure is characterized by a $3d$ band about 3 eV wide, hybridized with a broad $s\ensuremath{-}p$ band, indicating $s\ensuremath{-}d$-type conductivity. The Fermi energy lies just below the top of the $d$ bands and the density of states exhibits a strong sharp peak about 1 eV below the Fermi energy. Since the energy bands suggest considerable structure in the low-energy region of the reflectivity, selection rules, polarizations, and energies for some of the spectra are presented. The band structure is discussed in terms of the metal-to-semiconductor transition which has been observed for hexagonal NiS.

Energy Bands of Hexagonal NiS

A tight-binding calculation of the energy bands of VO has been performed for several different atomic configurations using all the valence and core orbitals from vanadium and oxygen as bases. All tight-binding integrals are accurately evaluated and all sums carried to convergence. Energy bands are found to be sensitive to the particular core states included and to the degree of ionicity assumed. Results for the band structure indicate that $d$ bands are about 7 eV wide, lying below the vanadium $4s$ band, so that conductivity in VO is attributed primarily to $d$ electrons. The Fermi energy falls in the $d$ bands at a large peak in the density of states.

J. L. Fry

Papers

Energy Bands of Hexagonal NiS

Energy Bands of VO

Tight-Binding Calculations fordBands