Isogeometric analysis, environment-reflecting separable pseudopotentials and Hamiltonian rank-m updates in the evaluation of Hellman-Feynman forces

Abstract: Technical details of a newly developed ab-initio computational method focused on non-periodic structures are presented. The method is based on density functional theory, finite-element method / isogeometric analysis, and environment-reflecting separable pseudopotentials. A weak form of Kohn-Sham equations is used and Hamiltonian matrix is assembled, incorporating completely non-local separable pseudopotentials, in the form of a series of rank-m updates being added to a sparse matrix coming from local Hamiltonian terms. Thus, Kohn-Sham equations are transformed into symmetric rank-m-update generalized eigenproblem that is solved by iterative block Lanczos and block Jacobi-Davidson eigenvalue solvers. The derivatives of the total energy of a system (Hellmann-Feynman forces) require in this case, because of computational reasons, the discretized charge density and wave functions having continuous second derivatives in the whole solution domain. An implementation based on a spline modification of the finite element method, the isogeometric analysis, is shown.