Semiclassical initial value representation techniques for chaotic systems

Semiclassical wavefunction propagation for chaotic systems suffer from numerical difficulties due to the chaotic nature of classical trajectories, resulting in reduced accuracy for standard initial value representation (IVR) methods. We compare four recent IVR methods developed to overcome these difficulties (Herman–Kluk with trajectory truncation; stationary-phase Herman–Kluk (SPHK); cellularized frozen Gaussian approximation; stationary-phase Monte Carlo) by computing the Franck–Condon spectrum of the 2-dimensional Henon–Heiles and quartic oscillator systems. The SPHK is found to be the most successful of the four methods. The SPHK is then used to determine the spectrum for collinear CO2 photodissociation.