Trace correcting density matrix extrapolation in self-consistent geometry optimization

A linear scaling trace correcting density matrix extrapolation method is proposed for accelerated self-consistency convergence in geometry optimization. The technique is based on nonorthogonal trace correcting purification and perturbation theory. Compared with alternative schemes, extrapolated total energies are often an order of magnitude closer to the self-consistent solution. For insulators, the computational cost is low and it scales linearly with the size of the perturbed region affected by the modified geometry, O(N(pert)). For local perturbations, the computational cost is therefore independent of the total size of the system and scales as O(1).