Towards Translational Invariance of Total Energy with Finite Element Methods for Kohn-Sham Equation (Communications in Computational Physics, 2018)
Numerical oscillation of the total energy can be observed when the Kohn-Shamequation is solved by real-space methods to simulate the translational move ofan electronic system. Effectively remove or reduce the unphysical oscillation is crucialnot only for the optimization of the geometry of the electronic structure, but also forthe study of molecular dynamics. In this paper, we study such unphysical oscillationbased on the numerical framework in [G. Bao, G. H. Hu, and D. Liu, An h-adaptive finite element solver for the calculations of the electronic structures, Journal of ComputationalPhysics, Volume 231, Issue 14, Pages 4967-4979, 2012], and deliver some numericalmethods to constrain such unphysical effect for both pseudopotential and all-electroncalculations, including a stabilized cubature strategy for Hamiltonian operator, and an a posteriori error estimator of the finite element methods for Kohn-Sham equation. Thenumerical results demonstrate the effectiveness of our method on restraining unphysicaloscillation of the total energies.