Converged vibrational energy levels and quantum mechanical vibrational partition function of ethane

Abstract

The vibrational partition function of ethane is calculated in the temperature range of 200-600 K using well-converged energy levels that were calculated by vibrational configuration interaction, and the results are compared to the harmonic oscillator partition function. This provides the first test of the harmonic oscillator approximation for a molecule with more than five atoms. The absolute free energies computed by the harmonic oscillator approximation are in error by 0.59-0.62 kcal/mol over the 200-600 K temperature range.

Role of conformational structures and torsional anharmonicity in controlling chemical reaction rates and relative yields: butanal + HO2reactions

“…The approach of scaling the frequency by an empirical constant is an approximation and it introduces some uncertainty, which is discussed elsewhere. 48,49 Although methods for calculating anharmonic energy levels for polyatomic molecules from anharmonic potential energy functions are improving, [50][51][52] as are path integral methods for calculating conformational-vibrational-rotation partition functions without calculating converged energy levels, 53,54 actual calculations of converged vibrational partition functions for molecules with more than four atoms [55][56][57] are still rare. Therefore, the procedures used here must be used without full tests of their accuracy for complex systems.…”

Anharmonic Rovibrational Partition Functions at High Temperatures: Tests of Reduced-Dimensional Models for Systems with up to Three Fluxional Modes

“…A variety of theoretical methods have been advanced for characterizing rovibrational anharmonicity, including diffusion Monte Carlo, , variational approaches, − path integrals, − direct product diagonalization, − empirical methods, , perturbation theories, − specialized methods for torsions, − and other separable approaches. − Many of these methods are designed for spectroscopic applications and are most reliably applied to predict high-accuracy zero point energies and fundamental transition energies. There has been relatively less work done to characterize anharmonicity at high temperatures and energies.…”

Anharmonic Rovibrational Partition Functions for Fluxional Species at High Temperatures via Monte Carlo Phase Space Integrals

“…A variety of methods for computing rovibrational molecular properties have been developed. Exact quantum mechanical approaches include the vibrational self-consistent field, configuration interaction, and coupled cluster theories; − path integral sampling; − and direct product diagonalization. − Significant (and typically prohibitive) challenges remain in the application of these approaches to systems with more than a few degrees of freedom, nonzero rotation, and high internal energies. Exact methods are often developed for use in spectroscopic studies of low-energy transitions, and they are not frequently applied in the computation of high-temperature rovibrational partition functions.…”