Semiclassical inversion of torsional vibration energy levels: Method,and application to acetaldehyde

An RKR-based semiclassical inversion procedure for restricted rotation potentials is developed, tested, and applied to the torsional vibration of acetaldehyde. The method is based on a semiclassical quantization of the problem which in higher-order approximations is shown to yield eigenvalues of extremely high accuracy. Two-phase integral functions are extracted from the torsional eigenvalue spectrum, one of which depends on the potential well and the other on the potential barrier, and these two functions are then subjected to RKR manipulation. The model potential is reproduced within a few per cent in all regions of the potential and the height of the barrier of acetaldehyde, V₃ = 406.1 cm^?1, is in excellent agreement with the quantum mechanical results.