A compact spin-free cluster expansion formalism for simple open-shell configurations

Jana, Debasis; Mahapatra, Uttam Sinha; Mukherjee, Debashis

doi:10.1016/s0009-2614(01)01500-7

Cited by 12 publications

(23 citation statements)

References 27 publications

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“…There were several limitations of this formalism. The most important among them have been (a) the potential non-termination of the MRCC equations, since the S r operators could be joined in the equations in a chain-like fashion up to arbitrary powers [22,23]: In contrast the normal ordered exponential Ω V or the closed-shell Ωs lead only to a finite power of cluster amplitudes since all cluster operators have to be joined to H; (b) there was no way of factorizing out the S r operators joined to other S r operators and not joined to H to lead to a more compact form of the MRCC equations. This last aspect was a direct consequence of the choice of the Ω V in [28] which allowed powers of S r , but not with the proper factors which would have offered the factorization.…”

Section: Normal Ordered Vs the New Ansatz For ω V And ωmentioning

confidence: 99%

“…Preliminary versions of the formalism for the one-valence case has already been published [22]. A brief account of the general versions has been published already [23].…”

Section: Normal Ordered Vs the New Ansatz For ω V And ωmentioning

confidence: 99%

“…Any S operator in a composite joined either to another S operator via the spectator lines only, or to the H via the spectator lines only must leave some of its inactive orbitals uncontracted, and hence cannot contribute to the closed projection. We call such type of connectivity as 'weak connectivity' [22,23]. The rest of the terms would have S operators joined to H by at least one inactive line and, in addition may generally have contractions among themselves via spectator lines.…”

Section: Emergence Of Strongly Connected Finite Power Mrcc Equationsmentioning

confidence: 99%

“…The rest of the terms would have S operators joined to H by at least one inactive line and, in addition may generally have contractions among themselves via spectator lines. We call these composites 'strongly connected' [22,23]. The above argument shows that H ef f is strongly connected, and thus cannot have more than the powers of S exceeding number of lines in H. We now regroup the various terms of eq.…”

Section: Emergence Of Strongly Connected Finite Power Mrcc Equationsmentioning

confidence: 99%

“…A succinct account of the formulation is about to appear in [23]. In the present paper, we discuss the method in some detail, and illustrate its performance by computing the electron affinity of OH radical, viewed as an IP of the OH − anion at the radical geometry.…”

Section: Introductionmentioning

confidence: 99%

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Use of a New Cluster Ansatz to Treat Strong Relaxation and Correlation Effects: A Direct Method for Energy Differences

Jana

Mahapatra

Mukherjee

2002

IJMS

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Abstract:We have presented in this paper a new cluster Ansatz for the wave operator for open-shell and/or quasidegenerate states, which takes care of strong relaxation and correlation effects in a compact and efficient manner. This Ansatz allows contraction among the various cluster operators via spectator orbitals, accompanied by suitable combinatorial factors. Since both the orbital and the correlation relaxations are treated on the same footing, it allows us to develop a very useful direct method for energy differences for open shell states relative to a closed-shell ground state, where the total charge for the two states may differ. We have discussed a new spin-free coupled cluster (CC) based direct method and illustrated its performance by evaluating electron affinity of a neutral doublet radical. We have also indicated how the scope of the theory can be extended to compute the state energies of simple open shell configurations as well. In that case, the CC equations terminate after the quartic power of cluster operators -exactly as in the closed-shell situation, which is not the case for the current methods.

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Section: Normal Ordered Vs the New Ansatz For ω V And ωmentioning

confidence: 99%

“…Preliminary versions of the formalism for the one-valence case has already been published [22]. A brief account of the general versions has been published already [23].…”

Section: Normal Ordered Vs the New Ansatz For ω V And ωmentioning

confidence: 99%

Section: Emergence Of Strongly Connected Finite Power Mrcc Equationsmentioning

confidence: 99%

Section: Emergence Of Strongly Connected Finite Power Mrcc Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Use of a New Cluster Ansatz to Treat Strong Relaxation and Correlation Effects: A Direct Method for Energy Differences

Jana

Mahapatra

Mukherjee

2002

IJMS

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Identification of the peripheral blood levels of interleukin‐12, interleukin‐10, and transforming growth factor‐β in patients with laryngeal squamous cell carcinoma

et al. 2011

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A compact spin‐free combinatoric open‐shell coupled cluster theory applied to single‐reference doublets

Datta

Mukherjee

2008

Int J of Quantum Chemistry

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ABSTRACT:In this article, we present an explicitly spin-free compact coupled cluster (CC) theory for simple open-shell systems, e.g., doublets, biradicals, which can be described either by a single open-shell determinant or by a configuration state function (CSF) which corresponds to a single spatial configuration but is a linear combination of determinants with different spin allocations. A new cluster expansion Ansatz for the wave-operator is introduced, in which the spin-free cluster operators are either of the form of closed-shell-like n hole-n particle excitations or contain valence excitations, which may involve exchange spectator scatterings. These latter type of operators are allowed to contract among themselves through the spectator orbitals. The novelty of the Ansatz is in the choice of a suitable automorphic factor accompanying each composite of noncommuting operators, ensuring that each such composite appears only once. The resulting CC equations consist of two types of terms: one is direct and the other is folded and the latter involves the effective Hamiltonian operator. We emphasize that while the direct term terminates exactly at the quartic power of the cluster amplitudes, termination of the folded term is dictated by the valence rank of the effective Hamiltonian operator, just as in the spin-free open-shell CC theory with a normal ordered exponential Ansatz. Example applications are presented by computing the core and valence-ionized state energies of H 2 O molecule and comparing the results with benchmark full CI results. The results show the efficacy of the method.

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A compact spin-free cluster expansion formalism for simple open-shell configurations

Cited by 12 publications

References 27 publications

Use of a New Cluster Ansatz to Treat Strong Relaxation and Correlation Effects: A Direct Method for Energy Differences

Use of a New Cluster Ansatz to Treat Strong Relaxation and Correlation Effects: A Direct Method for Energy Differences

Identification of the peripheral blood levels of interleukin‐12, interleukin‐10, and transforming growth factor‐β in patients with laryngeal squamous cell carcinoma

A compact spin‐free combinatoric open‐shell coupled cluster theory applied to single‐reference doublets

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