Transition Metal Oxides with Partially Filled d Bands

Transition Metal Oxides with Partially Filled d Bands 

For transition metal oxides such as NiO the Mott-Hubbard model gives much better agreement with experiment localization of the electrons in this way explains the anh-ferromagnetic ordering observed in NiO and its electrical insulator proper-hes [112]. The terms required to calculate the electron-electron interachon energy on a site, Fmh can be written in terms of the d-electron occupahons, using a UHF approach  

Of course some of these interaction terms are already present in an LSDA calculation and so to incorporate this into a general DFT scheme requires these duplicate contributions to be removed. One way to do this has been proposed by Dudarev and coworkers [113]. They have derived a funchonal incorporating the U and J parameters of the Mott-Hubbard model which is written  

The advantage of this expression is that U and J appear only as their difference (U-J) and so it requires only a single parameter to be determined for any particular transihon metal oxide under considerahon. The J parameter shows little system-to-system variabihty and is taken to be around 1 eV in most cases. Based on a comparison of the calculated DOS and experimental electron energy loss spectra (EELS) the U parameter for NiO was set at 6.2 eV. This gave a ground state in which the Ni spins are aligned within (111) planes and neighboring planes have 

X (units of lattice constant) Figu re 8.20 Charge density difference [LSDA + U] - LSDA (U = S.leN) for bulk NiO taken through a (100) plane of the rock salt cubic unit cell, centered on a Ni ion. Taken from ref [113]. 

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