Configurational forces in density functional theory calculations using orthogonalized enriched finite elements.

Real-space all-electron Kohn-Sham DFT calculations can be efficiently performed using orthogonalized enriched finite element (FE) basis, wherein the classical (standard) FE basis are augmented with atom-centered numerical basis functions (enrichments) that are appropriately orthogonalized with respect to the underlying FE basis. Orthogonalized enriched FE basis improves the numerical conditioning of the basis as well as renders the overlap matrix block-diagonal, greatly simplifying its inversion. In this work, we extend the framework to compute configurational forces which arise from the variational derivative of the Kohn-Sham energy functional with respect to the position of the material point x. This allows us to compute the ionic forces as well as stresses in periodic systems. We establish the accuracy of the formulation, by comparing the computed forces and stresses for various benchmark systems with those obtained from finite-differencing the ground-state energy. We also benchmark our calculations against Gaussian basis for isolated systems and LAPW basis for periodic systems. We finally demonstrate the capability of this approach to obtain relaxed structures for large-scale systems.