LINEAR-DEPENDENCE IN BASIS-SET CALCULATIONS FOR EXTENDED SYSTEMS

The problem of linear dependence in basis-set calculations for extended systems is discussed. We show that the problem is intrinsic in three-dimensionally extended systems, but is not as serious in systems with extension in fewer dimensions. The possibility of choosing suitable basis sets that avoid linear dependence is discussed. It is shown that for systems extended in three dimensions in which the orbitals near the Fermi-level are well described by plane waves a mixed atomic-orbital/plane-wave (AO-PW) basis set with tight orbitals to describe the cores avoids the problem in the most efficient way. Numerical experiments with ls Slater-type orbitals and plane waves on a simple cubic lattice are presented for illustration.