The LMTO-ASA Method and Band Structures of Layer-Structure Transition Metal Chalcogenides

Abstract

In a band structure calculation, eigenvalues and eigenfunctions of the effective one-electron wave equation can not, in practice, be determined exactly and a number of approximate methods have been proposed. Band structure methods used in the early studies up to 1979, of layer compounds have been reviewed by Fong [1]. In the case of compounds there is a greater need to carry out selfconsistent (SC) calculations since there would be certain charge transfers between the constituent atoms. With the traditional methods described in [1], SC calculations could be a very formidable task. Recently, a number of more efficient linear band methods such as the linear augmented plane wave (LAPW) and the linear muffin-tin orbital (LMTO) methods have been developed. In particular, the LMTO method with atomic sphere approximation (ASA) [2,3] is probably the fastest method available at present, and gives satistfactory results, particularly for close-packed structure materials. This method uses a set of atomic orbital-like muffin-tin orbitals, which are energyindepedent, as bases, and replaces the various integrals over a primitive cell by those over a set of atomic spheres. This is computationally fast since the eigen equation is linear in energy and its dimension is fairly small. The LMTO-ASA method has been successfully used to calculate the SC band structures and ground state properties of a number of close-packed elemental metals and compounds (see [3] chapter 1, and references therein). However, as the ASA approximation is designed for close-packed systems, this method may give rise to inaccuracy for systems with open-structures such as layer compounds. Nevertheless, with suitable modifications the method can still be applied to open structure crystals while exploiting its computational speed. One such modification is the introduction of so-called ‘empty spheres’ into the interstitial sites. This then gives band structures of open structure crystals, such as diamond and Si, with accuracy comparable to those obtained by the computationlly more demanding methods with less stringent assumptions about the form of the potential [4]. Temmerman and coworkers [5] first used the LMTO-ASA method to calculate the SC band structures of TiS₂ and TiSe₂. More recently, we carried out sevaral SC LMTO-ASA band structure calcurations, based on local density functional theory, of layer-structure transition metal chalcogenides such as PtSe₂, PdTe₂ and Hf₂S. In our LMTO-ASA calculations, we introduced artificial ‘empty-spheres’ to interstitial octahedral sites within the so-called ‘van der Waals’ gap. Treating these empty spheres as ‘real’ atoms with zero nuclear charge, the resultant structure looks like that of a close-packed ternary compound. Obviously, this method can be easily extended to calculate the band structures of the intercalate complexes with simple structure such as LiTiS₂, LiNbS₂ and LiTaS₂.