Spin-projected coupled-cluster theory with single and double excitations

Coupled-cluster (CC) theory including single (S) and double (D) excitations and carried out with a spin-unrestricted Hartree-Fock (UHF) reference wave function is free from S + 1 spin contamination as can be confirmed by an a nalysis of the expectation value of the spin operator, (S) over cap (2). Co ntamination by the S + 2 contaminant can be projected out by an approximate procedure (APCCSD) with a projection operator, (P) over cap, represented b y the product of the spin annihilation operators (A) over cap (s+1) and (A) over cap (s+2). The computational cost of such a projection scales with O( M-6) (M is the number of basis functions). The APCCSD energy obtained after annihilation of the S + 2 contaminant can be improved by adding triple (T) excitations in a perturbative way, thus leading to APCCSD(T) energies. For the 17 examples studied, the deviation of the UHF-CCSD(T) energies from th e corresponding full configuaration interaction values is reduced from 4.0 to 2.3 mhartree on the average as a result of annihilating the S + 2 contam inant in an approximate way. In the case of single-bond cleavage, APCSSD le ads to a significant improvement of the energy in the region where the bond ing electrons recouple from a closed shell to an open shell singlet electro n pair.