Analytic gradients for coupled-cluster energies that include noniterative connected triple excitations: Application to cis- and trans-HONO

An efficient formulation of the analytic energy gradient for the single and double excitation coupled-cluster method that includes a perturbational estimate of the effects of connected triple excitations, denoted CCSD(T), is presented. The formulation presented here has a smaller computational cost than any previous formulation, and the algebraic manipulations that lead to the additional savings may be applied generally to the analytic gradient of Møller-Plesset perturbation theory energies. The energy contribution from connected triple excitations scales as n_o ³n _v ⁴ + n_o ⁴n_v ³, and the additional work needed for the gradient scales as 2n_o ³n_v ⁴ + 2n_o ⁴n _v ³, where n_o is the number of doubly occupied orbitals and n_v is the number of unoccupied orbitals. The new formulation has been implemented in an efficient set of programs that utilize highly vectorized algorithms and has been used to investigate the equilibrium structures, harmonic vibrational frequencies, infrared intensities, and energy separation of cis-and trans-HONO.