A second order multiconfiguration SCF procedure with optimum convergence

TLDR

The authors present an MCSCF method that directly minimizes a second‑order accurate, periodic energy expression with respect to orthonormal orbitals. The method fully optimizes CI coefficients and incorporates higher‑order coupling between orbital rotations and CI coefficients, including additional transformations of internal orbitals and their integrals to treat internal rotations beyond second order. These enhancements yield rapid convergence—typically within three iterations—and super‑quadratic energy convergence even when the initial Hessian contains many negative eigenvalues, greatly improving overall efficiency.

Abstract

An MCSCF procedure is described which is based on the direct minimization of an approximate energy expression which is periodic and correct to second order in the changes in the orthonormal orbitals. Within this approximation, the CI coefficients are fully optimized, thereby accounting for the coupling between orbital rotations and CI coefficients to higher order than in previous treatments. Additional transformations among the internal orbitals and their associated one- and two-electron integrals are performed which amounts to treating the rotations among internal orbitals to higher than second order. These extra steps are cheap compared to the four index transformation performed in each iteration, but lead to a remarkable enhancement of convergence and overall efficiency. In all calculations attempted to date, convergence has been achieved in at most three iterations. The energy has been observed to converge better than quadratically from the first iteration even when the initial Hessian matrix has many negative eigenvalues.