Gaussian-basis LDA and GGA calculations for alkali-metal equations of state

Recently there has been renewed interest in implementations of density-functional theory for solids using various types of localized basis sets, including atom-centered Gaussian-type functions. While such methods are clearly well adapted to most insulating and semiconducting systems, one might expect them to give a less-than-optimal description of metals relative to plane-wave-type methods. Nevertheless, several successful applications of local-basis methods to metals have recently been reported. Here, we report an application of our Gaussian linear combination of atomic orbitals (LCAO) code to some extremely free-electron-like metals, namely, the alkali metals Li, Na, and K. In agreement with other calculations (both local and plane wave) we find that the local-density approximation (LDA) lattice constants are relatively poor ($\sim -3\%$ from experiment for the alkali metals versus $\pm 1\%$ for many other solids) and that the LDA bulk moduli are $\sim 30\%$ too high. We find that the Perdew-Burke-Enzerhof (PBE) version of the generalized-gradient approximation (GGA) corrects most of this error, in agreement with earlier calculations using similar GGA functionals. The Becke-Lee-Yang-Parr GGA functional gives similar results for the alkali-metal equations of state but is found to overcorrect the errors of the LDA for the cohesive energies, for which the PBE functional is in better agreement with experiment. Our results indicate that the Gaussian-LCAO method should be able to give accurate results for nearly any crystalline solid, since it succeeds even where it would be expected to have the most difficulty.