Solution of the Rovibrational Schrodinger Equation of a Molecule Using the Volterra Integral Equation

By using the Rayleigh-Schrodinger perturbation theory the rovibrational wave function is expanded in terms of the series of functions phi(0), phi(1), phi(2), ... phi(n), where phi(0) is the pure vibrational wave function and phi(i) are the rotational harmonics. By replacing the Schrodinger differential equation by the Volterra integral equation the two canonical functions alpha(0) and beta(0) are well defined for a given potential function. These functions allow the determination of (i) the values of the functions phi(i) at any points; (ii) the eigenvalues of the eigenvalue equations of the functions phi(0), phi(1), phi(2), ... phi(n) which are, respectively, the vibrational energy E-v, the rotational constant Bv, and the large order centrifugal distortion constants D-v, H-v, L-v ..... Based on these canonical functions and in the Born-Oppenheimer approximation these constants can be obtained with accurate estimates for the low and high excited electronic state and for any values of the vibrational and rotational quantum numbers v and J even near dissociation. As application, the calculations have been done for the potential energy curves: Morse, Lenard Jones, Reidberg-Klein-Rees (RKR), ab initio, Simon-Parr-Finlin, Kratzer, and Dunhum with a variable step for the empirical potentials. A program is available for these calculations free of charge with the corresponding author.