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Configurational Bias Methods for Monte Carlo Simulation

Configurational Bias Methods for Monte Carlo Simulation. Lin Chen. Advisor: Dr. David Smith. 2007 Fall PIP discussion. Metropolis Monte Carlo scheme. Insertion trial. Overlap large ΔU. Cavity, small ΔU. Acceptance Probability = Aexp(-( Δ U-μ)/k b T). μ chemical potential of substance.

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Configurational Bias Methods for Monte Carlo Simulation

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  1. Configurational Bias Methods for Monte Carlo Simulation Lin Chen Advisor: Dr. David Smith 2007 Fall PIP discussion

  2. Metropolis Monte Carlo scheme Insertion trial Overlap large ΔU Cavity, small ΔU Acceptance Probability = Aexp(-(ΔU-μ)/kbT) μchemical potential of substance

  3. Metropolis Monte Carlo scheme Delete trial Acceptance Probability = Aexp(-(μ-ΔU)/kbT) Movement trial Acceptance Probability = Aexp(-(U(n)-U(o))/kbT) U(n) and U(o) is the particle energy at new position and old position

  4. Trouble of Metropolis Monte Carlo scheme • Complex molecules(polymer) • High density systems(liquids) Example: Low insert and move effect Orientation and conformation have to be considered

  5. Configuration-Bias Monte Carlo method • Grow entire molecule segment by segment • Calculate weight w(t) for the trial • Retrace old conformation and determine retrace weight w(o) • Acceptance probability equals to x = w(t)/w(o)

  6. Insertion trial • Try Multiple configurations • Calculate w(t) from all configurations w(t) = Σexp(-Δμ/kbT) W(t) is the weight from test segment Δμ is energy change when we grow the new segment

  7. Insertion trial • Random choose a molecule in the system • Test Multiple configurations for the counterpart segment • Calculate w(o) for the configurations w(o) = Σexp(-Δμ/kbT) w(o) is the weight from the inserted molecule

  8. Insertion trial k k Acceptance Probability = Πwi(t)/Πwi(o) i=1 i=1 The whole molecule is inserted by different orientation and configuration Increase the insert effect Movement trial Similar with insertion trial

  9. Small molecule Take whole molecule as ball cheap Multi-site model accurate expensive hard to arrive equilibrium insert trouble

  10. Example: CHCl3 in water-CNT system at room temperature Binding free energy Can Configuration bias method help here

  11. Example: methane in slit_pore system ---- Do, D. D.; Do, H. D. J. Phys. Chem. 2005 1-site model 5-site model

  12. Difference in inserted number • Low P(small μ), empty • Large P(small μ), fills Number of particles vs pressure in 10 angstrom slit_pore at 113K

  13. Different temperature 273K 90.7K The difference due to: • Different models (1-site vs 5-site) • Numerical error for calculation using 5-site model?

  14. Conclusion: • Two model result in different inserted number • Sharp change shift to high pressure as temperature increase • Configurational effects are large • We would like to investigate whether CBMC methods are necessary or at least useful in such investigations

  15. Reference • Frenkel, D.; Smit, B. Molecular Simulation from Algorithms to Applications: Elsevier, 1996. • Do, D. D.; Do, H. D. J. Phys. Chem. 2005, 109, 19288-19295. • Krishna, R.; Paschek, D. Phys. Chem. Chem. Phys. 2001, 3, 453-462 • Tan, Z.; Gubbins, K. E. J. Phys. Chem.1990, 94, 6061-6069

  16. Thank you !

  17. Questions?

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