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Barbatti M. Defining the temperature of an isolated molecule. J Chem Phys 2022; 156:204304. [DOI: 10.1063/5.0090205] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The microcanonical temperature of an isolated molecule is derived in terms of Boltzmann and Gibbs volume entropies within the quantum harmonic vibrational and equivalent degenerated model approximations. The effects of the entropy functional choice and various approximations are examined. The difference between Boltzmann and Gibbs volume temperatures is negligible for molecules bigger than ten atoms. However, it is significant for smaller systems, opening a way to probe them experimentally. A simple, analytical expression of the temperature as a function of the vibrational energy is provided, allowing predictions with a ±3% margin of error compared to the exact harmonic estimate. The microcanonical temperature is discussed and exemplified with polycyclic aromatic hydrocarbon molecules and other molecules of astrophysical interest.
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Affiliation(s)
- Mario Barbatti
- Aix Marseille University, CNRS, ICR, Marseille, France and Institut Universitaire de France, 75231 Paris, France
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