Finite-temperature vibrational full configuration interaction

Abstract

Thermodynamic functions of an ideal molecular gas due to its anharmonic vibrations are evaluated in a wide range of temperature (T) by the vibrational full-configuration-interaction (FCI) method using a quartic force field and a finite number (N) of harmonic-oscillator basis functions along each normal mode. The thermodynamic functions considered are the grand potential (Ω), internal energy (U), and entropy (S). They are compared with those obtained from the Bose–Einstein theory with or without truncation of the harmonic-oscillator basis functions after quantum number N−1. The comparison reveals that the finite-basis-set errors in Ω and U are, respectively, $k_{\mathrm{B}}T\ln (k_{\mathrm{B}}T/N\hslash \omega )$ and $k_{\mathrm{B}}T$ per mode in the high-T limit, obscuring anharmonic effects when $k_{\mathrm{B}}T>\hslash \omega$, where ω is the lowest mode frequency. The benchmark data for several low-order perturbation corrections to Ω, U, and S are also obtained as the numerical derivatives of their FCI values with respect to dimensionless perturbation strength, and the domain of T and N in which these data are reliable (for the $N\to \mathrm{\infty }$ limits) is discussed.

GRAPHICAL ABSTRACT

Keywords:

• Thermodynamics
• perturbation theory
• molecular vibration
• anharmonicity
• full configuration interaction

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Correction

Acknowledgments

We thank Dr. Kiyoshi Yagi of RIKEN for allowing the use of his VCI code sindo and giving us insightful advice.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Correction Statement

This article was originally published with errors, which have now been corrected in the online version. Please see Correction (http://dx.doi.org/10.1080/00268976.2023.2286411)

Additional information

Funding

This work was supported by the Center for Scalable, Predictive methods for Excitation and Correlated phenomena (SPEC), which is funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Chemical Sciences, Geosciences, and Biosciences Division, as a part of the Computational Chemical Sciences Program and also by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Grant No. DE-SC0006028.