DISCRETE VARIABLE REPRESENTATIONS OF DIFFERENTIAL-OPERATORS

By making use of known properties of orthogonal polynomials the discre te variable representation (DVR) method [J. C. Light, I. P. Hamilton, and J. V. Lill, J. Chem. Phys. 82, 1400 (1985)] has been rederived. Si mple 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, ge neralized Laguerre, Legendre, and Jacobi polynomial bases and to the L anczos basis for Morse oscillator, that is, to basis sets often used i n calculating rovibrational energy levels, have been discussed.