Approximate constants of motion for vibrational spectra of many-oscillator systems with multiple anharmonic resonances

Abstract

A theory of approximate dynamical constants of motion is presented for vibrational (and implicitly, rovibrational) spectra of polyatomics with multiple nonlinear resonances. The formalism is developed in terms of simple vector algebra. The theory is applied to Hamiltonians used in fits of experimental spectra of H2O, CHClF2, and acetylene, with attention to reduced dimension motion, assignability of spectra, and statistical analysis of chaotic spectra. The approximate constants may be of interest as bottlenecks to vibrational energy flow in polyatomics. They may also be useful in reducing the size of basis sets in quantum-mechanical calculations of rotation–vibration spectra.