Time dependent wavepackets and periodic orbit assignment

Abstract

The Kosloff Chebyshev scheme is used to propagate time dependent wavepackets initiated on the various classical periodic orbits of a coupled Morse oscillator system modelled on the stretching vibrational modes of H₂O. It is found that these wavepackets follow parent orbits that are stable for long periods and that the power spectra derived from their autocorrelation functions show simply assignable progressions up to the dissociation limit. By contrast, those initiated on unstable orbits soon break up and, hence, yield more complex power spectra. Eigenvalues extracted from the power spectra by use of an analytically determined lineshape function are in excellent agreement with those determined variationally. Wavefunctions derived from the wavepackets also typically overlap to 99% with their variationally determined counterparts. In addition, an interesting cascade of Fermi resonances associated with highly excited local mode states is identified.