Gibbs free-energy estimates from direct path-sampling computations.

We have implemented a path-sampling scheme enabling a direct estimation of Gibbs free energy. This scheme consists of a Monte Carlo sampling of constant-pressure Langevin paths, followed by an ensemble averaging carried out over the Markov chain of paths. In practice, we sample an umbrella path ensemble, which requires to rigorously define a statistical weight for the paths, equivalent of the Boltzmann weight. This statistical weight is a function of an effective work related to the path. The umbrella ensemble is chosen so that its work histogram overlaps with the histograms corresponding to the ensembles of forward and backward paths. We have finally investigated the relations between numerical efficiency and overlapping properties of the various work histograms. This analysis yields a built-in criterion for diagnosing the convergence during a single-run simulation.

[1]  A. W. Rosenbluth,et al.  MONTE CARLO CALCULATION OF THE AVERAGE EXTENSION OF MOLECULAR CHAINS , 1955 .

[2]  G. Crooks.  Path-ensemble averages in systems driven far from equilibrium , 1999, cond-mat/9908420.

[3]  R. Zwanzig.  High‐Temperature Equation of State by a Perturbation Method. I. Nonpolar Gases , 1954 .

[4]  D. Frenkel.  Speed-up of Monte Carlo simulations by sampling of rejected states. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[5]  D. Kofke,et al.  Rosenbluth-sampled nonequilibrium work method for calculation of free energies in molecular simulation. , 2005, The Journal of chemical physics.

[6]  Berend Smit,et al.  Understanding Molecular Simulation , 2001 .

[7]  C. Dellago,et al.  Transition path sampling and the calculation of rate constants , 1998 .

[8]  Charles H. Bennett,et al.  Efficient estimation of free energy differences from Monte Carlo data , 1976 .

[9]  H. Forbert,et al.  Fourth-order algorithms for solving the multivariable Langevin equation and the Kramers equation. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  G. Crooks,et al.  Efficient transition path sampling for nonequilibrium stochastic dynamics. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  H. C. Andersen.  Molecular dynamics simulations at constant pressure and/or temperature , 1980 .

[12]  A. Kolb,et al.  Optimized Constant Pressure Stochastic Dynamics , 1999 .

[13]  C. Jarzynski,et al.  A “fast growth” method of computing free energy differences , 2001 .

[14]  D. Zuckerman,et al.  Single-ensemble nonequilibrium path-sampling estimates of free energy differences. , 2004, The Journal of chemical physics.

[15]  David A. Kofke,et al.  Appropriate methods to combine forward and reverse free-energy perturbation averages , 2003 .

[16]  G. Hummer.  Fast-growth thermodynamic integration: Error and efficiency analysis , 2001 .

[17]  D. Zuckerman,et al.  Erratum: “Single-ensemble nonequilibrium path-sampling estimates of free energy differences” [J. Chem. Phys. 120, 10876 (2004)] , 2004 .

[18]  Michael R. Shirts,et al.  Equilibrium free energies from nonequilibrium measurements using maximum-likelihood methods. , 2003, Physical review letters.

[19]  C. Dellago,et al.  Biased sampling of nonequilibrium trajectories: can fast switching simulations outperform conventional free energy calculation methods? , 2005, The journal of physical chemistry. B.

[20]  M Athènes.  Parallel Monte Carlo simulations using a residence weight algorithm. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  Daniel M. Zuckerman,et al.  Overcoming finite-sampling errors in fast-switching free-energy estimates: extrapolative analysis of a molecular system , 2002 .

[22]  G. Crooks.  Nonequilibrium Measurements of Free Energy Differences for Microscopically Reversible Markovian Systems , 1998 .

[23]  C. Jarzynski.  Nonequilibrium Equality for Free Energy Differences , 1996, cond-mat/9610209.

[24]  D. Zuckerman,et al.  Efficient use of nonequilibrium measurement to estimate free energy differences for molecular systems , 2004, Journal of computational chemistry.

[25]  Watanabe,et al.  Direct dynamical calculation of entropy and free energy by adiabatic switching. , 1990, Physical review letters.

[26]  Sean X. Sun.  Equilibrium free energies from path sampling of nonequilibrium trajectories , 2003 .

[27]  C. Jarzynski.  Equilibrium free-energy differences from nonequilibrium measurements: A master-equation approach , 1997, cond-mat/9707325.

[28]  M. Athènes.  A path-sampling scheme for computing thermodynamic properties of a many-body system in a generalized ensemble , 2004 .

[29]  M. Athènes.  Computation of a chemical potential using a residence weight algorithm. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[30]  Y. Kuzovlev,et al.  Nonlinear fluctuation-dissipation relations and stochastic models in nonequilibrium thermodynamics: II. Kinetic potential and variational principles for nonlinear irreversible processes , 1981 .

[31]  William H. Press,et al.  Numerical Recipes: FORTRAN , 1988 .