VSCF in internal coordinates and the calculation of anharmonic torsional mode transitions

The vibrational self-consistent field (VSCF) method assumes separability in normal modes in its usual version. However, the method fails in cases such as soft torsional modes which are better treated by angular variables. We develop VSCF equations based on the assumption of wave function separability in internal coordinates. To test the method, simple illustrative applications to small systems are provided: trans-HONO, cis-HONO, H₂S₂, and H₂O₂. The code directly uses points from ab initio calculations, and the method proves to be accurate for all types of transitions. For typical torsional transitions, the error in the computed frequency is smaller than that of VSCF in normal coordinates. The wave functions for the torsional mode are compared with the corresponding normal mode wave functions. The differences are substantial. The results are encouraging for extension of the model for large polyatomic systems. Work along these lines is in progress.