Analytic evaluation of energy gradients at the coupled-cluster singles and doubles level using quasi-restricted Hartree–Fock open-shell reference functions

Analytic formulas for the evaluation of energy gradients at the coupled-cluster singles and doubles (CCSD) level for a special class of open-shell quasi-restricted Hartree–Fock (QRHF) reference functions are presented and their computational implementation is discussed. The reference functions considered here are those which are formed from a closed-shell determinant for the molecule in a different ionization state by either adding or removing a single electron. Due to the approximate invariance of the CCSD model with respect to the choice of orbitals, results obtained with QRHF-CCSD closely approximate those from CCSD calculations using unrestricted Hartree–Fock (UHF) or restricted open-shell Hartree–Fock (ROHF) reference functions in cases where the latter references are well behaved. However, in cases where spin contamination (UHF) or symmetry breaking (UHF and ROHF) effects are important, QRHF-CCSD offers an attractive alternative since the resulting wave function is a projected eigenfunction of the spin operator Ŝ2 and transforms as a pure irreducible representation of the molecular point group.