On certain correspondences among various coupled-cluster theories for closed-shell systems |
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Authors: | Sourav Pal M Durga Prasad Debashis Mukherjee |
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Affiliation: | (1) Department of Physical Chemistry, Indian Association for the Cultivation of Science, 700 032 Jadavpur, Calcutta, India |
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Abstract: | In this paper certain correspondences have been shown among various formulations of coupled-cluster theories for many electron closed-shell systems. Specifically it is shown that (i) the energy functional using unitary ansatz of the form exp (T−T +) is exactly sameorder by order inT with the size-consistent energy functional 〈ψ|H|ψ〉/〈ψ|ψ〉 recently obtained by us in coupled-cluster framework; (ii) in the framework of unitary ansatz of the form exp (T−T +), both non-variational and variational approaches lead to identical equations upto any given order inT andT + inT∼T 2 approximation; (iii) variational procedure using our size-consistent energy functional or using the functional obtained in the framework of unitary ansatz (as envisaged by Kutzelnigg) leads to energy in both cases, inT∼T 2 approximation, for a total of quadratic powers inT andT +, same as Cizek’s linearised coupled pair many electron theory energy; (iv) in case of practical calculation of the energy through the variational procedures using our size-consistent energy functional and the functional in unitary ansatz framework, there is a loss of upper bound. |
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Keywords: | Coupled-cluster theories many body theory size-consistency atoms molecules |
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