Analytic Energy Gradients for Open-Shell Restricted-Hartree-Fock, Limited Multiconfiguration Scf, and Large Scale Configuration Interaction Wavefunctions.

Analytic derivatives of the energy with respect to nuclear coordinates are exceedingly useful in the optimization of equilibrium and transition state geometries and in the characterization of the stationary points on potential energy surfaces via vibrational analyses (1). However, until quite recently the use of such gradients was somewhat restricted as the gradient method had been developed in detail for only closed-shell single determinant SCF (2) or open-shell unrestricted Hartree-Fock wavefunctions (3). The restriction to these methods would not allow even a qualitatively correct treatment of many reactions such as those for which orbital symmetry considerations suggest a “forbiddenness” due to an orbital crossing or of many unusual free radicals of interest in physical organic chemistry. Within the last two years, the analytic energy gradient approach has been extended to the open-shell restricted Hartree-Fock method (4) to avoid difficulties sometimes encountered with the UHE approach in which the wavefunction is not an eigenfunction of S2 . Certain limited multiconfigu-ration self-consistent-field gradient methods (4,5) have also been developed and applied which allow for a qualitatively correct description of Woodward-Hoffmann forbidden processes and of radicals such as trimethylene.