The effect of local approximations on first-order properties from expectation-value coupled cluster theory

Abstract

The accuracy of local approximations has been studied for expectation-value coupled cluster theory restricted to single and double excitations (XCCSD), applied to first-order one-electron molecular properties, such as dipole and quadrupole moments. The analysis has been performed separately for each component of the XCCSD expression, which allows to gauge the sensitivity of various parts of the formula to the localization conditions. The varying impact of local approximations is explained by examining the most important terms in the Moller-Plesset expansion of the first-order XCCSD property formula. It has been found that the contribution from the singly excited cluster operator plays a dominant role in the correlation part of the property, and that the common local settings, which consist in including only strong orbital pairs in the CCSD residual equations, lead to significant errors in the local multipole moments. Fortunately, the Moller-Plesset analysis of the XCCSD method allows to formulate a modified set of local approximations, which is better suited for a description of first-order properties. The new options involve the inclusion of close pairs into the CCSD residual equations and the extension of the strong-pair domains, which considerably improves the agreement of the singles-dependent part of the property with the nonlocal reference value. Additionally, for an accurate description of the part of the XCCSD expression containing the doubly excited cluster operator, it is necessary to include close and weak pairs from local MP2 theory. The mean absolute percent error of the correlation part of the dipole moment for the test set of 31 molecules in the cc-pVDZ basis amounts to 16% with the standard local settings, but can be reduced to only 5%, if the new set of local approximations is utilized instead. The existence of local approximations that are appropriate for local XCCSD opens a possibility to calculate first-order properties for large molecules on the coupled cluster level, without a need to solve an additional expensive set of equations for the zeroth-order Lagrangian multipliers from response coupled cluster theory.