Coupled-cluster methods with noniterative triple excitations for restricted open-shell Hartree–Fock and other general single determinant reference functions. Energies and analytical gradients

A new, noniterative triples correction to the coupled-cluster singles and doubles (CCSD), method, for general single determinant reference functions is proposed and investigated numerically for various cases, including non-Hartree–Fock (non-HF) reference functions. It is correct through fourth-order of perturbation theory for non-HF references, and unlike other such methods, retains the usual invariance properties common to CC methods, while requiring only a single N7 step. In the canonical Hartree–Fock case, the method is equivalent to the usual CCSD(T) method, but now permits the use of restricted open-shell Hartree-Fock (ROHF) and quasirestricted Hartree–Fock (QRHF) reference determinants, along with many others. Comparisons with full configuration interaction (FCI) results are presented for CH2, CH2+, CH3, NH2, and SiH2. The paper also reports the derivation and initial computational implementation of analytical gradients for the ROHF-CCSD(T) method, which includes unrestricted Hartree–Fock (UHF) CCSD(T) and RHF-CCSD(T) as special cases. Applications of analytical gradients are presented for HOO, the CN radical, which is highly spin contaminated at the UHF level, and HCO, the latter with several large basis sets. With these developments of analytical gradients, these highly accurate generalized CCSD(T) methods can be widely applied.