Many Atoms per Cell

Abstract

The LMTO method has the computational speed and flexibility needed to perform calculations of electron states in molecules and compounds. Therefore in the present chapter we shall generalise the LMTO formalism purely within the atomic-sphere approximation to include the case of many inequivalent atoms per cell. The LMTO method is based on the variational principle in conjunction with energy-independent muffin-tin orbitals but, in addition to this approach, we have also considered the tail-cancellation principle which led to the KKR-ASA condition (2.8). Since the latter has conceptual advantages, we apply the tail-cancellation principle to the simplest possible case of more than one atom, namely the diatomic molecule. After that, we turn to crystalline solids and generalise or sometimes rederive the important equations of LMTO formalism. Hence, in addition to giving the LMTO equations for many atoms per cell, the present chapter may also serve as a short and compact presentation of the crystal-structure-dependent part of LMTO formalism. The potential-dependent part is treated in Chap.3. In the final sections are listed the modifications needed to calculate ground-state properties for materials with several atoms per cell.