• Debashis Mukherjee

      Articles written in Pramana – Journal of Physics

    • An ab-initio derivation of the pi-electron hamiltonian by a nonperturbative open-shell formalism

      Debashis Mukherjee Raj Kumar Moitra Atri Mukhopadhyay

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      A method for generating a pi-electron hamiltonian in an ab-initio manner using the non-perturbative open-shell many-body formalism recently developed by us is presented. The π-hamiltonian thus derived is energy-independent, and is also proved to be spin-independent. A recipe is given with the help of which Goldstone—like matrix-elements ofHπ can be extracted up to three body terms. It has been demonstrated that the use of diagrammatics considerably simplifies the algebra and allows one to keep track of the various quantities involved. Up to a given order of approximation, an explicit form ofHπ containing up to the three body terms has been given, and some of the important physical effects embedded in the hamiltonian are discussed. A comparative analysis of the various formalisms currently in use forms the concluding section of the paper.

    • On the hierarchy equations of the wave-operator for open-shell systems

      Debashis Mukherjee

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      Starting with the open-shell analogue of the Gell Mann-Low theorem of many-body perturbation theory, a non-perturbative linear operator equation is derived for the linked part of the wave-operatorW for open-shell systems. It is shown that, for a proper treatment of the linked nature of the wave-operator, a separation into its connected and disconnected components has to be made, and this leads to a hierarchy of equations for the various connected components. It is proved that the set of equations can be cast into a form equivalent to the non-perturbative equations of the wave-operator recently derived by Mukherjee and others in a coupled-cluster or exp(T) type formalism if a consistent use is made of a ‘core-valence separability’ condition introduced earlier. A comparison of the coupled-cluster representation ofW with the perturbative representation reveals that various alternative forms ofW in the coupled-cluster representation are possible and these reflect alternative ways of realising the core-valence expansion of the wave-operator. In particular it is emphasised how the use of Mandelstam block-ordering simplifies the coupled-cluster theories to a considerable extent and a comparison is made with coupled-cluster methods for open-shells put forward very recently by Ey and Lindgren. Finally, it is shown how difference energies of interest may be derived in a compact manner using the Mandelstam block-ordering of the wave-operator.

    • Symmetry-adapted many-body perturbation theory: use of the wave operator matrix elements

      Debashis Mukherjee Dipan Bhattacharyya

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      In this paper we develop a simple method for adapting the closed-shell many-body perturbation theory to an arbitrary point group symmetry taking account of various classes of diagrams exactly to all orders. The method consists in deriving a linear operator equation for the closed-shell wave-operatorW which is then symmetry-adapted to the pertinent point groupG. It is shown that the system of equations thus derived enables one to include orbital-diagonalh-h, p-p andh-p ladders to all orders in a perturbative framework. The way to generalise the method through inclusion of a larger classes of diagrams to all orders is also indicated. Finally, the connection of the present mode of development with the non-perturbative coupled-cluster formalisms is briefly indicated.

    • On certain correspondences among various coupled-cluster theories for closed-shell systems

      Sourav Pal M Durga Prasad Debashis Mukherjee

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      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 (TT+) 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 (TT+), both non-variational and variational approaches lead to identical equations upto any given order inT andT+ inTT2 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, inTT2 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.

    • A hermitian open-shell many-body perturbation theory for treating intruder states

      Azizul Haque Debashis Mukherjee

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      In this paper we have formulated an open-shell many-body perturbation theory (mbpt) that applies to an incomplete model space. The effective HamiltonianHeff generated in our theory is hermitian. We follow the resolvent-operator based time-dependent formulation ofmbpt of Banerjeeet al, and show quite generally that, by classifying the various determinants spanning the Hilbert space as model valence spaceP, virtual valence spaceR and virtual spaceQ, a diagrammaticmbpt satisfying size consistency can be developed. The chief new features of the theory are (i) manifest hermiticity ofHeff; (ii) presence of disconnected diagrams no part of which is a legitimate diagram (irreducible disconnected diagrams); (iii) presence of folded diagrams with components that may be irreducible disconnected diagrams; (iv) a consistent treatment of the variousn-valence sectors of the Hilbert space that may be interacting throughHeft if valence-holes are present—in particular a modified treatment of the core-valence separation. The generalisation afforded by the theory offers useful conceptual as well as computational advantages because the convergence difficulty encountered in a complete valence space formulation may be bypassed here by keeping the offending valence space determinants out of the model space. A brief critique of the developmentvis-a-vis the only other general model space development leading to a nonhermitianHeff is also given.

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