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Defining the temperature of an isolated molecule
1Aix Marseille University, CNRS, ICR, Marseille, France and Institut Universitaire de France, 75231 Paris, France.
The Journal of Chemical Physics
|June 1, 2022
Summary
This study derives microcanonical temperature for isolated molecules using Boltzmann and Gibbs entropies. Results show temperature differences are significant for small molecules, enabling experimental probing.
Area of Science:
- Theoretical Chemistry
- Statistical Mechanics
- Molecular Thermodynamics
Background:
- Understanding molecular temperature is crucial for chemical reactions and material properties.
- Existing methods for calculating microcanonical temperature have limitations for small systems.
- Entropy functionals play a key role in defining thermodynamic properties.
Purpose of the Study:
- To derive and analyze the microcanonical temperature of isolated molecules.
- To investigate the impact of different entropy functionals (Boltzmann and Gibbs) on temperature calculations.
- To develop an analytical expression for predicting molecular temperature.
Main Methods:
- Utilizing quantum harmonic vibrational and equivalent degenerated model approximations.
- Comparing Boltzmann and Gibbs volume entropies for temperature derivation.
- Developing an analytical temperature-energy relationship.
Main Results:
- A negligible difference between Boltzmann and Gibbs temperatures for molecules >10 atoms.
- A significant difference for smaller molecules, suggesting experimental feasibility.
- An analytical expression for temperature with a ±3% error margin compared to exact harmonic estimates.
Conclusions:
- The choice of entropy functional significantly impacts microcanonical temperature for small molecules.
- The derived analytical expression provides accurate temperature predictions.
- This work offers new avenues for experimental characterization of small molecular systems and astrophysical molecules.
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