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Updated: Jul 24, 2026
11:03
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Variational formula for the free energy based on incomplete sampling in a molecular simulation
Nandou Lu1, Jhumpa Adhikari, David A Kofke
1Department of Chemical Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260-4200, USA.
Summary
Finite sampling in free-energy perturbation (FEP) calculations introduces systematic errors. However, FEP results can serve as bounds for true free energy, offering a novel approach for molecular simulation analysis.
Area of Science:
- Computational chemistry
- Statistical mechanics
- Molecular simulation
Background:
- Finite sampling in free-energy perturbation (FEP) calculations introduces systematic errors.
- The sign of these errors depends on the system governing the simulation's sampling.
Purpose of the Study:
- To establish a method for using FEP calculations as bounds on true free energy.
- To explore variational schemes based on finite-sampling inequalities.
Main Methods:
- Developing inequalities based on molecular simulation performance.
- Implementing variational schemes using known free energy reference systems.
- Calculating free energy for hard-sphere solids and fluids using perturbation methods.
Main Results:
- FEP calculation results can provide bounds on the true free energy.
- The tightness of these bounds improves with increased simulation sampling.
- Bounds correlate with the entropy difference between target and reference systems, being tightest when this difference is minimal.
Conclusions:
- Finite-sampling inequalities offer a new way to bound free energies in molecular simulations.
- This approach allows for reliable estimation of free energy, even with sampling limitations.
- The method is demonstrated for hard-sphere systems, showing its practical applicability.
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