a Study of Vibrating-Rotating Motions of Polyatomic Molecules.

Exact vibration-rotational eigenstates for the ground electronic state of HCN were obtained by solving the time-independent Schrodinger equation. The Hamiltonian of the system was expressed in both rectilinear and curvilinear coordinates, Potential energy surfaces were obtained from fitting either ab initio or experimental data points by a series expansion of convenient functions in the same coordinates as the kinetic energy operator. We have formulated the problem such that the variables are separable and hence the dimension of the problem is reduced to one. The energy levels were obtained variationally by using harmonic oscillator, Kratzer oscillator, and pendulum functions as basis functions. Our approach is computationally efficient and our results agrees with those published in the literature.