Intramolecular vibrational energy transfer: A study of representations

Abstract

In this paper we report a study of possible representations for the description of intramolecular energy transfer. Our ultimate goal is the definition of a scheme suitable to the description of a molecule undergoing dissociation which is valid everywhere along the reaction path. For this reason we study three sets of basis functions for dynamical calculations of intramolecular vibrational energy transfer in one-dimensional, bound or metastable, triatomic molecules having one harmonic and one Morse bond. The different sets result from different definitions of bond coordinates and different methods for separating the bond motions. For Basis Set 1, the two bond coordinates are internuclear distances between adjacent atoms and the interbond coupling is caused by kinetic energy cross-terms. For Basis Sets 2 and 3 the coordinates are the distance between adjacent atoms in the harmonic bond and the distance between the dissociable atom and the remaining diatomic. The separation of coordinates for Basis Set 2 is analogous to the ``static'' resolution of bond motions in collision theory while the separation of coordinates for Basis Set 3 is an adiabatic separation. The nature and mechanism of bond coupling in the adiabatic approximation is analyzed in detail and dominant contributions are identified. We find that the relative merits of the basis functions depend strongly on the masses of the atoms and the harmonic frequencies of the bond. When the vibrational frequency of the harmonic bond exceeds the frequency for small oscillations of the Morse bond, Basis 3 is usually superior to both Bases 1 and 2. When the opposite condition holds and the mass of the central atom is (modestly) large relative to the masses of the other atoms, Basis 1 is usually superior. The conditions which favor the adiabatic separation are similar to those which favor the ``perturbed stationary states'' approximation in collision theory. The weak energy-dependence of the basis sets is explained in terms of a strong dependence of the optimal bond coordinates upon the interatomic distances.