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 H20. 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 ft'om 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.

Bifurcation Analysis of Higherm:nResonance Spectroscopic Hamiltonian†

“…Example: The 3:2 Resonance. The 3:2 resonance is an important resonance between normal modes in the system of two kinetically coupled Morse oscillators, − ,− which is a prototype for interesting molecular systems such as the strongly coupled stretch local modes in CO 2 or CS 2 . The 3:2 resonance is strongly implicated (in association with other nearby resonances) with the onset of classical chaos in the coupled Morse system. − The 3:2 resonance of course can be important in other molecular spectroscopic systems with an accidental 3:2 frequency degeneracy.…”

“…We now present a host of catastrophe maps for additional m : n resonance systems, leaving out the detailed description of dynamics in the last two sections. The resonances that we focus on are those that are most important in the dynamics of the normal modes in the system of two kinetically coupled Morse oscillators. − ,− Because of the symmetry of the system, n is limited to even numbers. These resonances are not limited to the coupled Morse system and may occur in general molecular spectroscopic systems.…”