Noniterative energy corrections through fifth-order to the coupled cluster singles and doubles method

Perturbation corrections through fifth order in the many-body perturbation theory energy with respect to a coupled cluster singles and doubles reference have been derived and analyzed. The formulas employ the T${}_1$ and T${}_2$ amplitudes obtained as a solution of the coupled cluster singles and doubles equations. Four different energy functionals have been considered as a starting point in the derivation: the regular coupled cluster energy expression, the coupled cluster functional incorporating $\Lambda$ amplitudes, the one constructed via an expectation value coupled cluster method, and that obtained on the basis of the extended coupled cluster method. The proposed corrections have been applied to several small molecules to test their performance compared to full configuration interaction. The fourth-order $\Lambda$ -based formulas improve upon CCSD(T), (coupled cluster singles and doubles with noniterative triples), while the best fifth-order formulas reduce the fourth-order error by about two-thirds. We also introduce a factorized evaluation of connected T${}_4$ in fifth order, which reduces its calculation from an $n^9$ algorithm to $n^7$ . This permits T${}_4$ to be included at approximately the same cost as CCSD(T).