Decoupling of the local mode stretching vibrations of water through rotational excitation. I. Quantum mechanics

Abstract

We demonstrate that in a previously studied model of the stretching modes of the water molecule rotational motion in the plane of the molecule tends to decouple the stretches. For rotational angular momentum near J=18 ℏ, the two local mode stretches are almost entirely decoupled. The source of this decoupling is the centrifugal distortion which stabilizes the asymmetric stretch and effectively cancels the G-matrix coupling. This cancellation is clarified using three different methods: Direct examination of the numerically computed matrix elements, exact analytic matrix elements of an approximate Hamiltonian, and solutions of a Mathieu equation formulation of a classical resonance Hamiltonian. The importance of this result is discussed in light of the fact that strong rotational excitation can occur in infrared multiple photon excitation. If such rotational decoupling occurs in real systems, then intramolecular energy transfer would be diminished thus holding open the possibility of mode specific infrared excitation. The calculations were carried out by numerically evaluating matrix elements between a basis of Morse oscillator eigenstates using an efficient Gaussian quadrature scheme based on associated Laguerre polynomials.