Defining the Temperature of an Isolated Molecule

03 March 2022, Version 2
This content is a preprint and has not undergone peer review at the time of posting.


The microcanonical temperature of an isolated molecule is derived in terms of Boltzmann and Gibbs volume entropies within the quantum harmonic vibrational approximation. The effects of the entropy functional choice and various approximations are examined. The difference between Boltzmann and Gibbs volume temperatures is negligible for molecules as small as 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. The microcanonical temperature is discussed and exemplified with polycyclic aromatic hydrocarbon molecules and other molecules of astrophysical interest.


Microcanonical temperature
Statistical physics
Statistical thermodynamics
Isolated system


Comments are not moderated before they are posted, but they can be removed by the site moderators if they are found to be in contravention of our Commenting Policy [opens in a new tab] - please read this policy before you post. Comments should be used for scholarly discussion of the content in question. You can find more information about how to use the commenting feature here [opens in a new tab] .
This site is protected by reCAPTCHA and the Google Privacy Policy [opens in a new tab] and Terms of Service [opens in a new tab] apply.