Efficient formalism for large-scale ab initio molecular dynamics based on time-dependent density functional theory

A new "on the fly" method to perform Born-Oppenheimer ab initio molecular dynamics (AIMD) simulations is presented. Inspired by Ehrenfest dynamics in time-dependent density functional theory, the electronic orbitals are evolved by a Schrödinger-like equation, where the orbital time derivative is multiplied by a parameter. This parameter controls the time scale of the fictitious electronic motion and speeds up the calculations with respect to standard Ehrenfest dynamics. In contrast with other methods, wave function orthogonality needs not be imposed as it is automatically preserved, which is of paramount relevance for large-scale AIMD simulations.