The Yearn to be Hermitian

Abstract

In this work we analyze hermitian aspects of methods which can offer improved numerical approximations, simpler computational evaluations or other benefits. There is a route toward approximations to the correlation problem that is neither purely perturbative, nor infinite order as is Coupled Cluster (CC), and this has certain hermitian aspects that are of interest. As perturbation theory (PT) is hermitian, we consider CCPT. The CCPT approach might be offered as an alternative to the infinite order CC approach for the reference state correlation problem itself with some advantages like, potentially, e.g., a more rapid convergence to a satisfactory answer in low order. The CCPT methods up to fifth order with the inclusion of the connected quadruple excitations have been formulated and implemented. We illustrate its results by comparison with several full configuration interaction values. For comparison purposes we also compare our new results with results obtained using the standard CC and MBPT variants like: CCSD, CCSD(T), CCSDT, CCSDTQ, MBPT2, MBPT3, MBPT4, MBPT5 and MBPT6.