Intrinsic convergence in closed-shell SCF calculations. A general criterion

Abstract

It is shown that the intrinsic convergence of the classical SCF algorithm for closed shells is governed by the eigenvalues of a supermatrix Q whose elements involve orbital excitation energies and electron repulsion integrals over occupied and virtual orbitals. In general, the SCF process is intrinsically convergent if all eigenvalues of Q have absolute values less than unity, and intrinsically divergent if one ore more is greater than unity. It is also shown how the symmetry preserving features of the SCF algorithm enable one to avoid certain divergences provided one starts a calculation with symmetry adapted orbitals. In cases of intrinsic convergence it is proved that the ratio of successive energy increments produced by the SCF algorithm is equal to the square of the largest eigenvalue of Q. The implications of the theory are illustrated by calculations on linear H8, on the cyclic planar ion S4N3+, and on model Q matrices filled with random numbers over the interval (−0.5,0.5).