Research into using quantum computers for electronic structure theory has brought about a renewed interest in unitary coupled cluster (UCC) theory.  Here, we consider the linear methods which emerge from the second-order Taylor expansion in the t-amplitudes of both the traditional and disentangled UCC energy functionals.  These linear methods closely resemble the coupled electron pair approximation (CEPA) and have received limited attention in the past.  We offer numerical evidence that they have similar performance to CEPA, and suffer from the same pathological divergence in the presence of singularities.  We go on to propose and characterize improved methods which include a subset of the terms in the third-order truncation of the UCC functionals.  These methods are shown to help treat pathological singularities in diatomic bond-breaking and in modestly-sized organic molecules, at a cost which is comparable to the shifted CEPA variants.

Developments in truncating the unitary coupled cluster functional

ACS Fall 2021

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