Non-periodic density functional perturbation theory calculations with finite elements

Density functional perturbation theory (DFPT) provides a systematic framework to compute higher-order material behavior based on a ground-state Kohn-Sham density functional theory solution. In this study, Kohn-Sham DFPT is formulated for the first time within the real-space variational framework of the finite element method towards interatomic force constants. The formulation is carried out in a pseudopotential setting for non-periodic systems with the generalized-gradient approximation for the exchange-correlation functional, including nonlinear core correction. The validation process is conducted through comparisons with conventional codes and finite difference schemes applied to perturbed ground-state calculations. For the interatomic force constants, it is demonstrated that one obtains convergence rates which parallel the optimal rates for energy and the observed rates for force.