• Debashis Mukherjee

      Articles written in Journal of Chemical Sciences

    • Orthonormality-constrained orbital optimisations in MC-SCF theory

      Debashis Mukherjee

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      A simple algorithm for the direct solution of the MC-SCF orbital equations of McWeeny is proposed and its performance is compared with those of two gradient optimisation methods currently in use. This method has been found to possess good convergence property and is suited to treat a variety of multi-configuration wave functions. Some possible modes of useful applications of the method are suggested.

    • Use of cluster expansion techniques in quantum chemistry. A linear response model for calculating energy differences

      Somnath Ghosh Debashis Mukherjee

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      In this paper we have reviewed the theoretical framework of the coupled-cluster (cc) based linear response model as a tool for directly calculating energy differences of spectroscopic interest like excitation energy (ee), ionisation potential (ip) or electron affinity (ea). In this model, the ground state of a many-electron system is described as in a coupled cluster theory for closed shells. The electronic ground state is supposed to interact with an external photon field of frequencyw, and the poles of the linear response function as a function ofw furnish with the elementary excitations of the system. Depending on the general form of the coupling term chosen, appropriate difference energies like ee, ip or EA may be generated. Pertinent derivations of the general working equations are reviewed, and specific details as well as approximations for ee, ip or ea are indicated. It is shown that the theory bears a close resemblance to the equation of motion (eom) method but is superior to the latter in that the ground state correlation is taken to all orders and may be looked upon as essentially a variant of renormalisedtda. A perturbative analysis elucidating the underlying perturbative structure of the formulation is also given which reveals that the theory has a hybrid structure: the correlation terms are treated akin to an open shellmbpt, while the relaxation terms are treated akin to a Green function theory. A critique of the methodvis-a-vis other cc-based approaches for difference energies forms the concluding part of our review.

    • Applications of a novel algorithm for the calculation ofMCSCF wavefunction: a look into possible avenues of convergence acceleration

      Kalyan Das Kumar Debashis Mukherjee Sankar Prasad Bhattacharyya

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      The efficacy of a method based on the direct inversion in the iterative subspace (DIIS) in accelerating the approach to self consistency in the calculation of theMCSCF wavefunction using a novel algorithm developed earlier, is compared with that of a simple damping technique. Although the ‘damping’ turns out to be ineffective in the ‘quadratic region’, it accelerates remarkably in the rate of descent on the energy hypersurface in the early stages of the iterative process which leads to an impressive overall increase in the rate of approach to self consistency. TheDIIS based procedure turns out to be ineffective when coupled to the present method and is plagued by ill conditioning problems. Calculations are done to compute the equilibrium geometrical parameter, charge density on different atoms, and dipole moment of HNO molecule in the lowest1,3nπ* states at theINDO/2-MCSCF level.

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