Efficient Fock matrix diagonalization by a Krylov-space method

Abstract

The solution of the Hartree–Fock equations involves the iterative construction of the Fock matrix based on approximate molecular orbitals and the diagonalization of that Fock matrix to obtain new approximations to those orbitals. A significant portion of this work is unnecessary, however, because the occupied molecular orbitals, which are required to construct the Fock matrix, represent a small fraction of the total number of orbitals that are obtained in the diagonalization, and furthermore, typically change little in each iteration. In this paper we introduce a new method which significantly accelerates diagonalization of the Fock matrix by avoiding the unnecessary calculation of the virtual orbitals. Using the occupied orbitals from the previous iteration as an initial guess, accurate updated orbitals are obtained through a combination of diagonalization in the subspace spanned by the occupied orbitals and the mixing of virtual orbital character into the occupied orbitals using a single-vector Lanczos algorithm. Calculations are presented which demonstrate up to 15-fold acceleration of the Fock matrix diagonalizations in a typical problem of 430 orbitals.