A scaling theory for the assignment of spectra in the irregular region. Continuation progress report

Abstract

The ultimate object of our program is to learn how to extract information about molecular rovibrational motions from experimental spectra or calculated energy levels. This goal of spectroscopy and theoretical chemistry has historically only been possible in the regular spectral region. Our project is one of several which are aimed at spectral interpretation in the chaotic or mixed chaotic plus regular regions. Our particular tools involve a scaling theory developed under our previous DOE support period. This theory uses experimentally fitted spectral Hamiltonians or Hamiltonian`s whose potentials are calculated using quantum chemistry, to obtain energy levels as a function of h{sup -1}. The scaling theory then uses this input to highlight the actions of the subset of all periodic orbits which control the dynamics at any given energy up to dissociation. The periodic orbits themselves, are the skeleton of classical phase space for the molecular motions and are found by classical non-linear dynamic techniques. The finding and following of these periodic orbits by constructing a bifurcation diagram, and in 2D, Poincare surfaces of section, is labor intensive and takes much of our available man hours. We have two projects, {open_quotes}acetylene{close_quotes} and {open_quotes}NO{sub 2}.{close_quotes} Below we first briefly sketch the results of the classical phase space study using the fitted spectral Hamiltonian that describes pure bending dynamics of in the acetylene X{sup 1}{Sigma}{sub g}{sup +} state to 15,000 cm{sup -1} of internal energy. The work on NO{sub 2} will follow. The specific purpose of this part of our work is to establish relations between experimental data and quantum mechanical results on one side and the behaviour of the dynamics given by the corresponding classical Hamiltonian function on the other side for the bend vibrations of the C{sub 2}H{sub 2} molecule. We transform it into a classical Hamiltonian function given in action and angle variables.