Least‐squares numerical Rayleigh‐Ritz and minimum‐variance methods for molecular calculations

Abstract

AbstractA general method is presented to find in a least‐squares sense a set of orthogonal eigenfunctions and their eigenvalues from local energy and numerical integration methods or by any other dissymmetric approach to solve the eigenvalue problem of a Hermitian operator. By this method a generalization of the minimum variance method to more than one eigenfunction is obtained, which is a variant of Scott's method. Also a new method is derived—called the minimum‐overlap method—that is a least‐squares numerical version of the standard Rayleigh‐Ritz method. Test calculations on the atoms Be and Tm and the molecules H2 and CO have been performed with both numerical Hartree‐Fock and Hartree‐Fock‐Slater methods. The least‐squares solutions are an improvement over other methods in the case of accurate basis sets. Numerical Hartree‐Fock calculations of moderate accuracy are found to be considerably faster than the analytic method.