A quadratically convergent multiconfiguration–self-consistent field method with simultaneous optimization of orbitals and CI coefficients

Abstract

A quadratically convergent MC–SCF procedure is described which is based on the direct minimization of the energy. In comparison to the Newton–Raphson technique, which has previously been applied by several authors for orbital optimization, the convergence radius is much improved by taking into account in the energy expansion those parts of third and higher order terms which account exactly for the orthonormality constraints imposed on the orbitals. The nonlinear equations which define the improved orbitals are solved iteratively by a simple adaption of the Gauss–Seidel method. The coefficients of the configuration expansion can be optimized simultaneously with the orbitals, a necessary requirement for over-all quadratic convergence. The removal of redundant variables as well as useful approximations for the optimization of core orbitals are discussed. The convergence of the method is demonstrated to be much superior to classical Fock operator techniques and MC–SCF methods which are based on the generalized Brillouin theorem. The formalism is carried down to matrix operations and shows a simple structure.