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Mayer sampling: calculation of cluster integrals using free-energy perturbation methods.
Jayant K Singh1, David A Kofke
1Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260-4200, USA.
Physical Review Letters
|July 13, 2004
Summary
Free-energy simulations calculate cluster integrals for statistical mechanics using Monte Carlo methods. This approach successfully determined virial coefficients for Lennard-Jones and SPCE water models.
Area of Science:
- Statistical mechanics
- Computational chemistry
- Thermodynamics
Background:
- Diagrammatic methods are crucial for understanding many-body systems in statistical mechanics.
- Calculating cluster integrals, essential for these methods, is computationally challenging.
- Free-energy simulation techniques offer a promising avenue for accurate integral evaluation.
Purpose of the Study:
- To develop and apply free-energy simulation methods for calculating cluster integrals.
- To demonstrate the utility of this approach by computing virial coefficients.
- To validate the method for both simple and complex molecular models.
Main Methods:
- Utilized Monte Carlo sampling with molecule numbers matching the integral order.
- Weighted configurations based on the absolute value of the integrand.
- Employed umbrella sampling to reference calculated integrals against known ones.
Main Results:
- Successfully calculated cluster integrals using the described simulation approach.
- Determined virial coefficients up to the sixth order for the Lennard-Jones model.
- Computed virial coefficients up to the fifth order for the SPCE model of water.
Conclusions:
- Free-energy simulation methods provide an effective means to compute cluster integrals.
- The demonstrated accuracy for virial coefficients highlights the method's potential in statistical mechanics.
- This technique offers a robust computational tool for advancing the study of molecular systems.