First principles density functional theory (DFT) calculations are common tools used for the study of bulk materials. Recent advances [1] in numerical methods and computer technology have allowed systems of practical interest to be investigated in this way. Many of these techniques have used a plane wave (PW) basis set expansion of the electronic states as this provides a natural representation for a periodic system. This approach offers a number of advantages. Results may be systematically converged with respect to basis set by variation of a single parameter, the cut-off energy. In addition the use of a PW basis set allows efficient calculation of atomic forces enabling relaxation of atomic structure and dynamical simulation. Although a PW basis set can be very large, the use of optimised pseudopotentials [2,3] significantly reduces the number of plane waves needed to accurately represent the electronic states. PW calculations may only be applied to systems with periodic boundary conditions. However an aperiodic system, eg. a defect, may be modelled using a supercell, provided careful consideration is given to Brillouin zone sampling [4] and electrostatics [5].
One remaining limitation of the use of a PW basis set is that the extended basis states do not provide a natural way of quantifying local atomic properties. Sanchez-Portal et al. describe a technique for the projection of PW states onto a LCAO basis set and show that this may be used to perform population analysis in bulk systems.[6,7] In a previous paper we have applied these techniques to the analysis of molecular systems.[8] We use the formalism due to Mulliken [9] in order to perform the population analysis. These techniques are widely used in the analysis of calculations performed using localised basis sets, particularly in the field of quantum chemistry. However, they have not been routinely applied to PW calculations of bulk systems. It is widely accepted that the absolute magnitude of the atomic charges have little physical meaning as they display an extreme sensitivity to the atomic basis set with which they are calculated.[10,8] In this paper we demonstrate that consideration of relative values of Mulliken populations, in contrast to the absolute magnitudes, can yield useful information.
We have carried out electronic structure calculations using the CASTEP [1] and CETEP [11] codes within the local density approximation (LDA). Section ii presents results for several simple bulk crystals. Previous work by Garcia and Cohen [12,13] considered the link between total valence charge density and measures of ionicity and electronegativity. We discuss the use of Mulliken bond populations and valence charges in this context. Finally, Section iii summarises our conclusions.