### 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.

Original language | English |
---|---|

Pages (from-to) | 281-298 |

Number of pages | 18 |

Journal | The Journal of Chemical Physics |

Volume | 103 |

Issue number | 1 |

Publication status | Published - 1995 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*The Journal of Chemical Physics*,

*103*(1), 281-298.

**Alternative ansätze in single reference coupled-cluster theory. III. A critical analysis of different methods.** / Szalay, P.; Nooijen, Marcel; Bartlett, Rodney J.

Research output: Contribution to journal › Article

*The Journal of Chemical Physics*, vol. 103, no. 1, pp. 281-298.

}

TY - JOUR

T1 - Alternative ansätze in single reference coupled-cluster theory. III. A critical analysis of different methods

AU - Szalay, P.

AU - Nooijen, Marcel

AU - Bartlett, Rodney J.

PY - 1995

Y1 - 1995

N2 - 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.

AB - 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.

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UR - http://www.scopus.com/inward/citedby.url?scp=36449002268&partnerID=8YFLogxK

M3 - Article

VL - 103

SP - 281

EP - 298

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 1

ER -