Toward accurate high temperature anharmonic partition functions

Abstract

We use four different methods to calculate an anharmonic correction factor fvib to the conventional RRHO partition functions for H2O, HO2, 3CH2, H2O2, and CH4 over a temperature range up to 3000 K. The exact quantum mechanical method benchmarks the other three approximate methods that are based on classical Monte Carlo phase space integrals, on vibrational perturbation theory, and on conventional harmonic partition functions evaluated with fundamental, rather than harmonic, frequencies. The last two of these methods converge on the exact partition function below temperatures that vary from 1500 K for the least anharmonic system (H2O) to 250 K for the most anharmonic system (H2O2). For 3CH2 and H2O2, both these methods are qualitatively incorrect because they are insensitive to a low energy barrier for internal motion. The classical method qualitatively overestimates quantum mechanical results at low temperatures because of the exclusion of zero point energy. However, here anharmonic corrections are small. At high temperatures, our anharmonic corrections can be large (up to 40% for CH4 at 3000 K) and at high enough temperatures the classical and exact quantum results will converge. Comparing perturbation theory and the classical method, the classical method becomes the approximate method of choice above ∼750 K for H2O2 and CH4, ∼2100 K for 3CH2, ∼2700 K for HO2, and > 3000 K for H2O.