Torsional energy levels and wave functions

A numerical method for solving the approximate Schrödinger equation (SE) for a single internal motion is presented. In the SE the reduced moment of inertia I(ϕ) and potential energy V(ϕ) are expressed as functions of the torsional angle ϕ. Molecular examples include ethane, chloroethane, and 1,2‐dichloroethane for which I(ϕ) and V(ϕ) have been derived from the HF/6‐31G* optimized geometries and energies at ϕ increments of 30°. The resulting potential energy curves, energy levels, and wave functions are shown graphically. The calculated fundamental torsional frequencies are found to fall within 10 cm−1 of the experimental values. Approximations for the off‐diagonal energy matrix elements, and numerical accuracy of torsional energy levels, are shown to be satisfactory. Attention is called to the computer programs developed for this work and their applications to torsional studies in relevant areas of spectroscopy, thermodynamics, and reaction rates.