Discrete variable representations of differential operators

By making use of known properties of orthogonal polynomials the discrete variable representation (DVR) method [J. C. Light, I. P. Hamilton, and J. V. Lill, J. Chem. Phys. 82, 1400 (1985)] has been rederived. Simple analytical formulas have been obtained for the matrix elements of DVRs of differential operators which may appear in the rovibrational Hamiltonian of a molecule. DVRs corresponding to Hermite, Laguerre, generalized Laguerre, Legendre, and Jacobi polynomial bases and to the Lanczos basis for Morse oscillator, that is, to basis sets often used in calculating rovibrational energy levels, have been discussed.

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