Gradient techniques for open-shell restricted Hartree–Fock and multiconfiguration self-consistent-field methods

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Abstract
Formulas for the analytical first derivatives of the potential energy have been derived for five specific cases of complexity beyond that of the closed‐shell single‐determinant self‐consistent‐field (SCF) approximation. The first four cases encompass most open‐shell systems of chemical interest, namely, the conventional restricted SCF wave functions for doublets, triplets, open‐shell singlets, and quartets. The final case considered is the two‐configuration SCF (TCSCF) wave function required to describe singlet diradicals and orbital symmetry forbidden reaction pathways. An explicit example of the latter procedure is provided by the least motion insertion of CH(2Π) into H2 (1Σ+g) to yield the methyl radical. This doublet (S=1/2) TCSCF wave function is fairly typical of those required to theoretically explore problems in the physical chemistry of organic free radicals. Geometry optimization for the equilibrium structures of radical cations is illustrated by gradient calculations on H2CO+.