Numerical Evaluation of Energy Levels and Wave Functions for Hindered Internal Rotation

A numerical procedure for the solution of the one-dimensional Schrödinger equation (the finite-difference boundary-value method), especially suited for problems having periodic nature, is presented and applied to the problem of hindered internal rotation. The accuracy of the numerical method, as a function of the number of mesh points, is evaluated by comparing the approximate numerical results with the exact ones, relative to the case of free internal rotation. The hindered rotation in ethane is then examined in detail, and the character of the obtained energy levels is discussed by a comparison with the energy levels of the two limiting cases of torsional vibration and shifted potential free rotation. An approximate procedure for the treatment of internal rotations involving asymmetric tops is also suggested, and applied to the case of 1,2-dichloroethane. The results show a satisfactory agreement with those obtained by the more elaborate method of Chung-Phillips and with the experimental ones