The multiconfiguration self-consistent field (MCSCF) method offers the most general approach to the computation of chemical reactions and multiple electronic states. This review discusses the design of MCSCF wavefunctions for treating these problems and the interpretation of the resulting orbitals and configurations. In particular, localized orbitals are convenient both for selection of the appropriate active space and for understanding the computed results. The computational procedures for optimizing these wavefunctions and the techniques for recovery of dynamical correlation energy are reviewed.

The construction and interpretation of MCSCF wavefunctions.

A quadratically convergent MCSCF method is described which allows one to optimize an energy average of several states with arbitrary weight factors. An analysis of the problems connected with the variational determination of excited states is given and it is concluded that the averaging method is a natural solution to these problems. In the energy expansion minimized in each iteration, certain cubic and higher order terms can be included. It is demonstrated that this greatly facilitates convergence in cases where the Hessian matrix of second energy derivatives has many negative eigenvalues. Several approximations to the exact quadratically convergent scheme, which are useful when calculating potential surfaces, are discussed.

A quadratically convergent MCSCF method for the simultaneous optimization of several states

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.

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

Matrix‐Formulated Direct Multiconfiguration Self‐Consistent Field and Multiconfiguration Reference Configuration‐Interaction Methods

Valence and Rydberg excitations, ionizations, and inner-valence ionizations of CO 2 and N 2 O, which are isoelectronic, are studied by the SAC and SAC CI theories. We have given a systematic assignment of the electronic spectra of these molecules, though there were some controversial situations in the assignment of the spectra. The broad and overlapping features of the spectra of the inner-valence ionizations are due to the existence of a large number of ionization-excitation states mixing with the singly ionized states. The theoretical origins of the similarities and differences in the photoelectron spectra of CO 2 and N 2 O are clarified.

Cluster expansion of the wavefunction, valence and rydberg excitations, ionizations, and inner-valence ionizations of CO2 and N2O studied by the sac and sac CI theories

An exact MCSCF theory is proposed for excited states belonging to the same symmetry species and is illustrated by actual application to some of the excited states of the CN radical.

G. Das

Papers

Multiconfiguration self-consistent field (MCSCF) theory for excited states