ALMOST VARIATIONAL COUPLED-CLUSTER THEORY

The energy expectation value of coupled-cluster theory can be formulat ed as the sum of the energy expression of traditional coupled-cluster (TCC) theory plus a correction term. The latter is simplified if the s tationarity conditions of TCC hold. It is then of O(S-4), where S is t he coupled-cluster amplitude. The leading error contribution agrees wi th the leading term of the difference between the TCC energy and the e nergy expression of extended coupled-cluster (ECC) theory. It is sugge sted to evaluate this routinely at the end of any TCC calculation as a check of the reliability of the latter. The error of the ECC energy e xpression with respect to an expectation value is of O(S-6). The error of traditional CCSD with respect to an expectation value is not affec ted by the inclusion of triple excitations in CCSDT. Approximations to CCSDT are also discussed. A hierarchy of approximations starting from TCC and ending at variational coupled-cluster (VCC) theory, alternati ve to the previously proposed improved coupled-cluster (ICC) method is presented.