• P Raghunathan

      Articles written in Journal of Chemical Sciences

    • The characteristic polynomial approach to the solution of quantum chemical perturbation problems

      P Raghunathan

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      An approach to the solution of finite-dimensional quantum chemical perturbation problems based on the ‘characteristic polynomial’ is developed and discussed. Using the successive derivatives of the polynomial, an ordered perturbation sequence is constructed. From this sequence, perturbation series for individual eigenvalues are determined. Applications of this method are illustrated for cases of non-degenerate eigenvalues, two-fold energy degeneracy lifted in first order, andq-fold energy degeneracy. A re-derivation of the well-known Rayleigh-Schrödinger perturbation formulae from their corresponding characteristic polynomial expressions is presented, and an additional illustration is made of the use of the reduced characteristic polynomial by considering a benzene molecule with three adjacent carbon atoms ‘perturbed’ in some way.

    • Planar ‘coupled water pair’ cluster in disordered solids: Theory of the1H NMR dipolar Hamiltonian

      P Raghunathan S Ray Siddharth

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      The proton NMR dipolar interaction Hamiltonian is set up for the model of planar ‘coupled water pair’ clusters in disordered solids. The Hamiltonian, when analytically solved, leads to interesting predictions of structured dipolar lineshapes when (a) the four protons are tightly coupled and (b) when the dipolar interaction is modulated by water molecules flipping between fixed directions. Detailed features of the line positions and intensities are worked out for both these models, and a suitable formulation is presented for simulating powder lineshapes in a variety of experimental situations.

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