Semiclassical quantization by circuit counting: Application to SO2

Abstract

In this paper a semiclassical quantization method is developed whose formulation and application is simple, general and accurate. We call this method semiclassical quantization by circuit counting (SQCC). SQCC is based upon evaluating the action integral along a trajectory until it undergoes a near recurrence. Several near recurrences are used to obtain a set of independent equations which can then be inverted to yield the actions for the trajectory. Once the actions are obtained a linear extrapolation is used to calculate semiclassical energies. We apply the method to two model systems: (1) three uncoupled Morse oscillators and (2) a realistic three degree of freedom model of SO2. SQCC is found to work very well for these systems. We discuss some of the advantages and disadvantages of SQCC and its application to systems with more than three coupled molecular degrees of freedom.