Accurate specific molecular state densities by phase space integration. I: Computational method

The semiclassical determination of the specific density of quantum states, ρ(E;J), at energy E with fixed total angular momentum J is discussed for small molecules. Monte Carlo integration allows the accurate numerical determination of the phase space volume of systems with J>0 and arbitrary anharmonicity. The corresponding semiclassical number of states can be corrected for the effects of zero point motion in analogy to the well-known Whitten–Rabinovitch procedure. In this paper, the procedures are tested by comparison with rigid rotor harmonic oscillator models, while a comparison with recent exact quantum calculations on H+3 and HD+2 is described in the following paper. We conclude that, if the intramolecular potential is known or assumed, this numerical semiclassical procedure is a viable and simple way to get state densities of a much improved accuracy.