Semiclassical propagation for multidimensional systems by an initial value method

A semiclassical initial value technique for wave function propagation described by Herman and Kluk [Chem. Phys. 91, 27 (1984)] is tested for systems with two degrees of freedom. It is found that chaotic trajectories cause a serious deterioration in the accuracy and convergence of the technique. A simple procedure is developed to alleviate these difficulties, allowing one to propagate wave functions of a moderately chaotic system for relatively long times with good accuracy. This method is also applied to a very strongly chaotic system, the x²y² or "quadric oscillator" model. The resulting energy spectra, obtained from the autocorrelation function of the wave function, are observed to be in good agreement with the corresponding quantal spectra. In addition, the density of states spectra, computed from the trace of the semiclassical propagator, are found to determine many individual energy levels of this system successfully.