Alternative ansätze in single reference coupled-cluster theory. III. A critical analysis of different methods

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Abstract
There are several important formal requirements that should be satisfied if a quantum chemical method is to offer a widely applicable approach. This paper considers a variety of potential exponential ansätze, and assesses their attributes pertaining to different desiderata, in particular satisfaction of a symmetric generalized Hellmann–Feynman theorem, exactness of the method in the untruncated limit and finiteness of the equations. The ansätze are the standard coupled-cluster (CC); the expectation value (XCC); symmetric expectation value (SXCC); unitary (UCC); and the extended (ECC) coupled-cluster approaches. ECC satisfies most specified desiderata, but it does not satisfy a symmetric GHF theorem. SXCC is shown to be a symmetrized approximation to ECC, which does satisfy a symmetric GHF theorem, but SXCC is not exact in the untruncated limit. A new alternative ansatz, strongly connected SC-XCC is proposed which satisfies all desiderata except that the equations are nonterminating. Considering the necessity of approximation for all high level alternative CC methods, the nonfiniteness of the energy functional and stationary equations might not be a major limitation.