The Area Law of Molecular Entropy: Moving beyond Harmonic Approximation
Abstract
:1. Introduction
1.1. Computational Techniques to Calculate the Entropy of a Single Molecule
1.2. Area Law—An Alternate Way of Calculating Entropy
1.3. Thermal Entropy of a Single Molecule and Area Law
1.4. Estimating Molecular Entropy Using the Area Law
- 1.
- Surface deformations, curvature with an value other than 1, add to the MI of the system’s microstates. Note that value 1 indicates a perfectly spherical surface.
- 2.
- Positive (0 ≤ < 1) and negative (−1 ≤ < 0) deformations change the MI of the system independently.
2. Materials and Methods
2.1. Data Curation
2.2. Molecular Structure Calculation
2.3. Theoretical Entropy Calculation
2.4. Molecular Surface Calculation
2.5. Surface Curvature
2.6. Shape Index Probabilities
- Calculate the shape index (see Equation (11)) at the center of each triangle as the mean of shape index values at the vertices. Divide the data into positive and negative groups (<0).
- Calculate the normalized histogram counts for shape index distributions with respect to a predefined number of bins. The probabilities for each bin are given by , where is the number of triangles (i.e., shape index values) allotted to the ith bin.
2.7. Data Fitting
3. Results and Discussion
3.1. Gas-Phase Entropy Varies Linearly with Shape Entropy
3.2. The Impact of Positive and Negative Curvature on the Entropy
3.3. The Coefficient of Ultraviolet Cutoff—Connecting , , and
3.4. Comparison with Entropies Calculated Using RRHO Approximation
3.5. Prediction of Relative Entropies
4. Conclusions
Supplementary Materials
Author Contributions
Funding
Institutional Review Board Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
CPU | Central Processing Unit |
DCOR | Distance Correlation |
GA | Genetic Algorithm |
LIGO | Laser Interferometer Gravitational-wave Observatory |
MAPE | Mean Average Percentage Error |
MI | Missing Information |
NMA | Normal Mode Analysis |
OPFF | Open Force Field Toolkit |
RMSD | Root Mean Square Deviation |
RMSE | Root Mean Square Error |
RRHO | Rigid Rotor Harmonic Oscillators |
SHM | Simple Harmonic Oscillators |
UFF | Universal Force Field |
VDW | van der Waal |
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SRRHO-G4 | SRRHO-NMA | ||
---|---|---|---|
∩ SRRHO-G4 ∩ SRRHO-NMA (1326) | 20.91 | 23.38 | 26.21 |
∩ SRRHO-NMA (1665) | 20.93 | – | 45.44 |
∩ SRRHO-G4 (1529) | 21.47 | 24.76 | – |
Method | = (J/mol·K) | RMSE (J/mol·K) | MAPE % | |
---|---|---|---|---|
Area | 5.42 | |||
Area + deformation | 3.94 | |||
G4 NMA | 4.09 5.41 |
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Roy, A.; Ali, T.; Venkatraman, V. The Area Law of Molecular Entropy: Moving beyond Harmonic Approximation. Entropy 2024, 26, 688. https://doi.org/10.3390/e26080688
Roy A, Ali T, Venkatraman V. The Area Law of Molecular Entropy: Moving beyond Harmonic Approximation. Entropy. 2024; 26(8):688. https://doi.org/10.3390/e26080688
Chicago/Turabian StyleRoy, Amitava, Tibra Ali, and Vishwesh Venkatraman. 2024. "The Area Law of Molecular Entropy: Moving beyond Harmonic Approximation" Entropy 26, no. 8: 688. https://doi.org/10.3390/e26080688