Analytic Interatomic Forces in the Random Phase Approximation

The random phase approximation (RPA) is a perturbational approach to evaluate the ground state energy of matter. It is growing popular recently as it describes many systems more realistically than density functional theory (DFT). However, in condensed matter simulations, forces beyond DFT have been rarely available, thus limiting the application of other methods like the RPA. Here we present our recent advances on the computation of interatomic forces in the RPA, including the work in PRL 118, 106403 (2017). There we show that the first derivative of the RPA energy with respect to the Green's function is the self-energy in the G⁰W⁰, which allows us to write compact equations for the RPA forces and calculate them efficiently. Furthermore, position dependent overlap operators are incorporated in the present framework, allowing us to implement the RPA forces in the projector augmented wave (PAW) formalism. We also sketch that our approach could be easily adapted for other methods like second-order Møller-Plesset (MP2) perturbation theory. Finally we give examples of recent applications, e.g. assesing the quality of different density functionals with RPA molecular dynamics [PRL 119, 145501 (2017)].