A new approach to the problem of noniterative corrections within the coupled-cluster framework

Abstract

Noniterative corrections to the coupled-cluster (CC) method with singles and doubles (CCSD) due to triple and higher excitations in the cluster operator are investigated. The derivation is based on the standard procedure for evaluating contributions coming from higher excitation rank cluster operators into the CC equations for singles and doubles. The noniterative nature of the approach leads to a direct modification of the CCSD energy through a posteriori corrections, however, unlike previous derivations, we take into account the coupling between the energy and cluster amplitudes in the CC equations. The coupling is not present in the fully iterative CC schemes due to the linked diagram theorem which makes the cluster amplitude equations energy independent. We show, however, that if the problem of unlinked contributions is re-examined in the context of noniterative approaches, then their complete cancellation does not occur. This leads to a partial restoration of the energy dependence. The energy dependence then gives the cluster amplitudes more flexibility in adjusting to the energy changes within the noniterative approach which is especially important in quasidegenerate situations when the standard energy corrections become large. The resulting modifications introduce disconnected contributions to the energy so size-extensivity is no longer preserved. This approach provides a new hierarchy of CC corrections in which the standard corrections, like CCSD[T] or CCSD(T), appear as a natural first step in the derivation. Some of the corrections can be easily identified as analogous to those recently proposed by Kowalski and Piecuch in the context of the method of moments of CC equations. We also suggest new approximations.