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Calculating liquid-phase entropy using a real gas model within the QM/PCM framework
Yu-Ichiro Izato1, Mitsuo Koshi2
1Faculty of Environment and Information Sciences, Yokohama National University, 79-7 Tokiwadai, Hodogaya-ku, Yokohama, Japan. izato-yuichiro-tk@ynu.ac.jp.
Physical Chemistry Chemical Physics : PCCP
|March 2, 2026
Summary
This study introduces a real gas model (RGM) to accurately calculate liquid-phase molecular entropies, improving thermodynamic predictions. The RGM enhances accuracy by using free volume, offering better results than traditional ideal gas models.
Area of Science:
- Computational chemistry
- Thermodynamics
- Physical chemistry
Background:
- Conventional quantum mechanical/polarizable continuum model (QM/PCM) methods often use the ideal gas model for liquid-phase entropy calculations, leading to inaccuracies.
- This overestimation stems from neglecting molecular packing and interactions in the liquid state.
Purpose of the Study:
- To develop and validate a real gas model (RGM) for more accurate calculation of liquid-phase entropies.
- To assess the impact of improved entropy calculations on Gibbs free energy and boiling point predictions.
Main Methods:
- The RGM utilizes free volume, defined as the accessible space for a molecule's center of mass, to calculate translational entropy.
- Free volume was determined using liquid molar volume, molecular volume, and packing assumptions for pure liquids, and by considering solvent excluded volume for solutes.
- Calculations were performed using QM/PCM at the ωB97X-D/6-311++G(d,p)/IEF-PCM level, followed by RGM corrections.
Main Results:
- The RGM produced physically realistic liquid-phase entropies, with calculated values closely matching experimental data (within chemical accuracy).
- The RGM-derived pressure equation aligns with the van der Waals equation of state, suggesting liquid behavior resembles high-pressure real gas.
- Application to methanol and ethanol demonstrated improved Gibbs free energy calculations and accurate boiling point predictions.
Conclusions:
- The developed real gas model significantly enhances the accuracy of liquid-phase entropy calculations compared to ideal gas models.
- This improved entropy calculation method leads to more reliable predictions of thermodynamic properties like Gibbs free energy and boiling points.
- The RGM offers a computationally efficient approach, comparable to the ideal gas model, for accurate thermodynamic predictions in condensed phases.
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