Configurational forces in electronic structure calculations using Kohn-Sham density functional theory

摘要

We derive the expressions for configurational forces in Kohn-Sham densityfunctional theory, which correspond to the generalized variational forcecomputed as the derivative of the Kohn-Sham energy functional with respect tothe position of a material point $\textbf{x}$. These configurational forcesthat result from the inner variations of the Kohn-Sham energy functionalprovide a unified framework to compute atomic forces as well as stress tensorfor geometry optimization. Importantly, owing to the variational nature of theformulation, these configurational forces inherently account for the Pulaycorrections. The formulation presented in this work treats both pseudopotentialand all-electron calculations in single framework, and employs a localvariational real-space formulation of Kohn-Sham DFT expressed in terms of thenon-orthogonal wavefunctions that is amenable to reduced-order scalingtechniques. We demonstrate the accuracy and performance of the proposedconfigurational force approach on benchmark all-electron and pseudopotentialcalculations conducted using higher-order finite-element discretization. Tothis end, we examine the rates of convergence of the finite-elementdiscretization in the computed forces and stresses for various materialssystems, and, further, verify the accuracy from finite-differencing the energy.Wherever applicable, we also compare the forces and stresses with thoseobtained from Kohn-Sham DFT calculations employing plane-wave basis(pseudopotential calculations) and Gaussian basis (all-electron calculations).Finally, we verify the accuracy of the forces on large materials systemsinvolving a metallic aluminum nanocluster containing 666 atoms and an alkanechain containing 902 atoms, where the Kohn-Sham electronic ground state iscomputed using a reduced-order scaling subspace projection technique (P.Motamarri and V. Gavini, Phys. Rev. B 90, 115127).