The Gaussian and augmented-plane-wave density functional method for ab initio molecular dynamics simulations

A new algorithm for density-functional-theory-based ab initio molecular dynamics simulations is presented. The Kohn-Sham orbitals are expanded in Gaussian-type functions and an augmented-plane-wave-type approach is used to represent the electronic density. This extends previous work of ours where the density was expanded only in plane waves. We describe the total density in a smooth extended part which we represent in plane waves as in our previous work and parts localised close to the nuclei which are expanded in Gaussians. Using this representation of the charge we show how the localised and extended part can be treated separately, achieving a computational cost for the calculation of the Kohn-Sham matrix that scales with the system size N as O(N log N). Furthermore, we are able to reduce drastically the size of the plant-wave basis. In addition. we introduce a multiple-cutoff method that improves considerably the performance of this approach. Finally, we demonstrate with a series of numerical examples the accuracy and efficiency of the new algorithm, both for electronic structure calculations and for ab initio molecular dynamics simulations.