Seminar #5 - Monte Carlo

2024 Winter Molecular Simulation Seminar
Room 302, the 2nd experimental building at POSTECH
Presenter: Seunghyun Kang

Monte Carlo (MC) methods utilizes the random number generator to derive certain statistical quantities for given system. Along with the MD simulation to sample the statistical ensembles, various MC algorithms have been developed as a tool for molecular simulation. For example, MC simulation can cover the chemical phenomena that Molecular Dynamics (MD) cannot implement. Moreover, combined MC algorithms with MD enhanced the functionality, accuracy, and efficiency of MD simulations. Unlike MD simulation works, MC adapt random movement of atoms and molecules with particular acceptance criteria. Therefore, we can derive initial molecular model system to the given thermodynamic equilibrium state by controlling the induced random movement and acceptance criteria. With these two characteristics, movement and acceptance criteria, gives distinct technical profits that MD cannot. To apply these utility and applicability of MC in molecular simulation researches, understanding of theoretical foundations and physical insights of MC is necessary.

In this seminar, basic concepts of MC and its benefits in perspective of induced random movement will be the target of this talk. At first, I’ll explain fundamental principles of MC (ensemble average, metropolis algorithm, acceptance, etc..)[1]. Then the sampling methods in NVE, NVT, NPT ensembles^[1] and MonteCarloBarostat in OpenMM[2,3] will be introduced. The main ensembles that will be discussed in this seminar is Grand Canonical Monte Carlo (GCMC) and MC in Gibbs ensemble. In GCMC, the basic principle for molecule inserting called Widom particle insertion method^[4,5] and will be introduced. Particle insertion in molecule system can bring the advantages or applications in MC, but it also takes some technical issues to implement MC. These applications^[6-10], technical issues^[11], and its solution^[11-13] will be illustrated. The last topic of this talk is MC in Gibbs ensemble. Its theoretical foundation^[14,15] and its application in various field^[16-19] will be treated.

References

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[11] Soroush Barhaghi, M., Torabi, K., Nejahi, Y., Schwiebert, L., & Potoff, J. J. Molecular exchange Monte Carlo: A generalized method for identity exchanges in grand canonical Monte Carlo simulations. J. Chem. Phys., 2018, 149(7).
[12] Ferrenberg, A. M., & Swendsen, R. H. Optimized monte carlo data analysis. Phys. Rev. Lett., 1989, 63(12), 1195.
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[14] Lopes, J. C., & Tildesley, D. J. Multiphase equilibria using the Gibbs ensemble Monte Carlo method. Mol. Phys., 1997, 92(2), 187-196.
[15] Panagiotopoulos, A. Z., Quirke, N., Stapleton, M., & Tildesley, D. J. Phase equilibria by simulation in the Gibbs ensemble: alternative derivation, generalization and application to mixture and membrane equilibria. Mol. Phys., 1988, 63(4), 527-545.
[16] Barhaghi, M. S., & Potoff, J. J. Prediction of phase equilibria and Gibbs free energies of transfer using molecular exchange Monte Carlo in the Gibbs ensemble. Fluid Phase Equilib., 2019, 486, 106-118.
[17] Chen, B., Siepmann, J. I., & Klein, M. L. Direct Gibbs ensemble Monte Carlo simulations for solid− vapor phase equilibria: applications to Lennard−Jonesium and carbon dioxide. J. Phys. Chem. B., 2001, 105(40), 9840-9848.
[18] Punnathanam, S. N. A Gibbs-ensemble based technique for Monte Carlo simulation of electric double layer capacitors (EDLC) at constant voltage. J. Chem. Phys., 2014, 140(17).
[19] Puibasset, J. Phase coexistence in heterogeneous porous media: A new extension to Gibbs ensemble Monte Carlo simulation method. J. Chem. Phys., 2005, 122(13).