Title: Configurational forces in electronic structure calculations using Kohn-Sham density functional theory,
Abstract: We derive the expressions for configurational forces in Kohn-Sham density
functional theory, which correspond to the generalized variational force
computed as the derivative of the Kohn-Sham energy functional with respect to
the position of a material point $\textbf{x}$. These configurational forces
that result from the inner variations of the Kohn-Sham energy functional
provide a unified framework to compute atomic forces as well as stress tensor
for geometry optimization. Importantly, owing to the variational nature of the
formulation, these configurational forces inherently account for the Pulay
corrections. The formulation presented in this work treats both pseudopotential
and all-electron calculations in single framework, and employs a local
variational real-space formulation of Kohn-Sham DFT expressed in terms of the
non-orthogonal wavefunctions that is amenable to reduced-order scaling
techniques. We demonstrate the accuracy and performance of the proposed
configurational force approach on benchmark all-electron and pseudopotential
calculations conducted using higher-order finite-element discretization. To
this end, we examine the rates of convergence of the finite-element
discretization in the computed forces and stresses for various materials
systems, and, further, verify the accuracy from finite-differencing the energy.
Wherever applicable, we also compare the forces and stresses with those
obtained 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 systems
involving a metallic aluminum nanocluster containing 666 atoms and an alkane
chain containing 902 atoms, where the Kohn-Sham electronic ground state is
computed using a reduced-order scaling subspace projection technique (P.
Motamarri and V. Gavini, Phys. Rev. B 90, 115127).