On the scaling of semiclassical initial value methods

The semiclassical initial value method of Walton and Manolopoulos, the cellularized frozen Gaussian approximation for the calculation of bound-bound Franck-Condon spectra, has been applied to a series of model problems with up to ten coupled degrees of freedom. The number of classical trajectories required to converge these spectra is found to increase exponentially with the number of degrees of freedom in the model problems. On comparison with earlier applications of the method to the threshold photodetachment spectra of the ArnI- (n=2-6) anions, it appears that the number of trajectories required to converge a Franck-Condon spectrum semiclassically is directly proportional to the number of final quantum states which contribute to the spectrum. (C) 1999 American Institute of Physics. [S0021-9606(99)02038-3].