Use of a convenient size-extensive normalization in multi-reference coupled cluster (MRCC) theory with incomplete model space: A novel valence universal MRCC formulation

Maitra, Rahul; Datta, Dipayan; Mukherjee, Debashis

doi:10.1016/j.chemphys.2008.12.008

Cited by 8 publications

(1 citation statement)

References 83 publications

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“…IMS generalizations of both VUMRCC (Refs. [28][29][30][31] and SUMRCC have been suggested. 32,33 While the VUMRCC theory in IMS has been widely used for computing excitation energies for both non-relativistic and relativistic systems with considerable success, 34 the SUMRCC theory in IMS have been relatively less used either for state energies or for studying potential energy surface (PES).…”

Section: Introductionmentioning

confidence: 99%

Unitary group adapted state-specific multi-reference coupled cluster theory: Formulation and pilot numerical applications

Maitra

Sinha

Mukherjee

2012

The Journal of Chemical Physics

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We present the formulation and the implementation of a spin-free state-specific multi-reference coupled cluster (SSMRCC) theory, realized via the unitary group adapted (UGA) approach, using a multi-exponential type of cluster expansion of the wave-operator Ω. The cluster operators are defined in terms of spin-free unitary generators, and normal ordered exponential parametrization is utilized for cluster expansion instead of pure exponentials. Our Ansatz for Ω is a natural spin-free extension of the spinorbital based Jeziorski-Monkhorst (JM) Ansatz. The normal ordered cluster Ansatz for Ω results in a terminating series of the direct term of the MRCC equations, and it uses ordinary Wick algebra to generate the working equations in a straightforward manner. We call our formulation as UGA-SSMRCC theory. Just as in the case of the spinorbital based SSMRCC theory, there are redundancies in the cluster operators, which are exploited to ensure size-extensivity and avoidance of intruders via suitable sufficiency conditions. Although there already exists in the literature a spin-free JM-like Ansatz, introduced by Datta and Mukherjee, its structure is considerably more complex than ours. The UGA-SSMRCC offers an easier access to spin-free MRCC formulation as compared to the Datta-Mukherjee Ansatz, which at the same time provides with quite accurate description of electron correlation. We will demonstrate the efficacy of the UGA-SSMRCC formulation with a set of numerical results. For non-singlet cases, there is pronounced M(s) dependence of the energy for the spinorbital based SSMRCC results. Although M(s) = 1 results are closer to full configuration interaction (FCI), the extent of spin-contamination is more. In most of the cases, our UGA-SSMRCC results are closer to FCI than the spinorbital M(s) = 0 results.

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Section: Introductionmentioning

confidence: 99%

Unitary group adapted state-specific multi-reference coupled cluster theory: Formulation and pilot numerical applications

Maitra

Sinha

Mukherjee

2012

The Journal of Chemical Physics

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How many‐body perturbation theory (MBPT) has changed quantum chemistry

Kutzelnigg

2009

Int J of Quantum Chemistry

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The history of many-body perturbation theory (MBPT) and its impact onQuantum Chemistry is reviewed, starting with Brueckner's conjecture of a linked-cluster expansion and the time-dependent derivation by Goldstone of such an expansion. A central part of this article is the time-independent formulation of quantum chemistry in Fock space and its diagrammatic representation including the particle-hole picture and the inversion of a commutator. The results of the time-independent derivation of MBPT are compared with those of Goldstone. It is analyzed which ingredients of Goldstone's approach are decisive. The connected diagram theorem is derived both in a constructive way based on a Lie-algebraic formulation and a nonconstructive way making use of the separation theorem. It is discussed why the Goldstone derivation starting from a unitary time-evolution operator, ends up with a wave operator in intermediate normalization. The Møller-Plesset perturbation expansions of Bartlett and Pople are compared. Examples of complete summations of certain classes of diagrams are discussed, for example, that which leads to the Bethe-Goldstone expansion. MBPT for energy differences is analyzed. The paper ends with recent developments and challenges, such as the generalization of normal ordering to arbitrary reference states, contracted Schrödinger k-particle equations and Brillouin conditions, and finally the Nakatsuji theorem and the Nooijen conjecture.

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Unconventional Aspects of Coupled-Cluster Theory

Kutzelnigg

2010

Challenges and Advances in Computational Chemistry and Physics

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Use of a convenient size-extensive normalization in multi-reference coupled cluster (MRCC) theory with incomplete model space: A novel valence universal MRCC formulation

Cited by 8 publications

References 83 publications

Unitary group adapted state-specific multi-reference coupled cluster theory: Formulation and pilot numerical applications

Unitary group adapted state-specific multi-reference coupled cluster theory: Formulation and pilot numerical applications

How many‐body perturbation theory (MBPT) has changed quantum chemistry

Unconventional Aspects of Coupled-Cluster Theory

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