Linear scaling first-principles molecular dynamics with controlled accuracy

In our quest for accurate linear scaling first-principles molecular dynamics methods for pseudopotential DFT calculations, we investigate the accuracy of real-space grid approaches, with finite differences and spherical localization regions. We examine how the positions of the localization centers affect accuracy and the convergence rate in the optimization process. In particular we investigate the accuracy of the atomic forces computation compared to the standard O(N³) approach. We show the exponential decay of the error on the energy and forces with the size of the localization regions for a variety of realistic physical systems. We propose a new algorithm to automatically adapt the localization centers during the ground state computation which allows for molecular dynamics simulations with diffusion processes. The combination of algorithms proposed lead to a genuine linear scaling First-Principles Molecular Dynamics method with controlled accuracy. We illustrate our approach with examples of microcanonical molecular dynamics with localized orbitals.