Theoretical techniques for electronic structure determination

Various theoretical methods have been used to determine the electronic structure of insulating oxides. We will review here only those which treat 

Density functional methods The density functional theory reduces the search of the many-body ground state to the resolution of an effective one-electron variational Hamiltonian, which includes a Hartree potential, which is a function of the mean charge distribution, an exchange term, due to the Pauli s principle and a correlation term. 

The local density approximation (LDA) replaces the exchange and correlation potential, which is non-local, by a local potential. This latter is constructed from an approximate expression of the exchange-correlation energy xc( ) of an homogeneous electron gas. At each point r of the system, the uniform electron density n in xc( ) is functionally replaced by the actual density n f). The Hamiltonian and the Poisson s equation are then solved in a self-consistent manner. There have been various applications of these methods to oxides  

The calculations based on the DFT theory yield the band dispersion, the charge density around the atoms, and the gap width if states are expanded on an over-complete basis set. Yet, in the standard LDA approximation, the calculated band gaps are always narrower than measured ones. New methods for treating the excited states better, such as the so-called GW approximation, are now being developed to overcome this discrepancy (Hybertsen and Louie, 1986 Godby et al, 1988 von der Linden and Horsch, 1988 Hott, 1991 Bechstedt et al, 1992 Del Sole et al, 1994), but, aside from NiO (Aryasetiawan et al, 1994) and LiNbOs (Gu and 

1994 Ching et ai, 1994), their use has, until now, been restricted to semi-conductors. In the density functional methods the total energy is also calculated and, provided that a search of the energy minimum as a function of structural degrees of freedom is simultaneously performed, the gound state atomic configuration at 0 K may be determined. 

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