Free energy calculations by the expanded ensemble method

The expanded ensemble method is a new effective method for free energy (F=U-TS) calculations, which was suggested by us in 1992. The partition function of the expanded ensemble is a sum of canonical partition functions with preweighting factors. A Monte Carlo random walk in the expanded ensemble allows us to evaluate the ratio of partition functions and, hence, the free energy differences.

Original papers:

• A.P.Lyubartsev, A.A.Martsinovskii, S.V.Shevkunov, P.N.Vorontsov-Velyaminov. "New approach to Monte Carlo calculation of the free energy: Method of expanded ensembles". J.Chem.Phys., v.96, pp.1776-1783 (1992). pdf text
• A.P.Lyubartsev, A.A.Martsinovskii, P.N.Vorontsov-Velyaminov, T.V.Kuznetsova. "A new approach to the Monte Carlo Calculations of free energy with the use of expanded ensembles" Rus.J.Phys.Chem.,v.67,pp.230-235 (1993)

Molecular dynamics implementation

• A.P.Lyubartsev, A. Laaksonen.,P.N.Vorontsov-Velyaminov. "Free Energy Calculations for Lennard-Jones Systems and Water Using the Expanded Ensemble Method. A Monte Carlo and Molecular Dynamics Simulation Study". Molecular Physics, v.82, pp.455-471 (1994) Abstract

Application for computation of osmotic pressure and effective forces in ordered polyelectrolytes

• A.P.Lyubartsev, L. Nordenskiold. "A Monte Carlo Simulation Study of Ion Distribution and Osmotic Pressure in Hexagonally Oriented DNA." J.Phys.Chem., v.99,pp.10373-82 (1995). Abstract
• A. P. Lyubartsev, J. X. Tang, P. A. Janmey, and L. Nordenskiöld "Electrostatically induced polyelectrolyte association of rodlike virus particles". Phys. Rev. Lett., v.81, p.5465-5468 (1998) Abstract and text
• J. X.Tang, P.A.Janmey, A.P.Lyubartsev and L.Nordenskiöld, "Metal ion induced lateral aggregation of filamentous viruses fd and M13" Biophys. J. ,v. 83: pp. 566-581 (2002) Abstract and full text from the Biophys.J. Web site

  Polymer entropy

• P.N. Vorontsov-Velyaminov, A.V.Broukhno, T.V.Kuznetsova and A.P.Lyubartsev. "Free Energy Calculations by Expanded Ensemble Method for Lattice and Continuous Polymers". J.Phys.Chem.,v.100(4),pp.1153-1158 (1996) Abstract ; Paper: PostScript file .
• N. A. Volkov, A.A.Yurchenko, A.P.Lyubartsev and P.N.Vorontsov-Velyaminov "Entropic Sampling of Free and Ring Polymer Chains" Macromol. Theory and Simulations, v. 14(8), pp.491-504  Abstract and text

Ionic Liquid Confined in Nanotube

• K. Dong, G. Zhou, X. Liu, X. Yao, S. Zhang and A.Lyubartsev "Structural Evidence for the Ordered Crystallites of Ionic Liquid in Confin\ ed Carbon Nanotubes" J. Phys. Chem. C, v. 113(23). p. 10013-10020 Abstract and Text

Chemical potential and solvation free energies

• A.P.Lyubartsev, A. Laaksonen.,P.N.Vorontsov-Velyaminov. "Determination of Free Energy from Chemical Potential. Application of the Expanded Ensemble Method". Molecular Simulations, v.18(1),pp.43-58 (1996). Abstract ; Paper (PostScript file)
• A. P. Lyubartsev, O. Førrisdahl, A. Laaksonen " Solvation Free Energies of Methane and Alkali Halide Ion Pairs. An Expanded Ensemble Molecular Dynamics Simulation Study". J.Chem.Phys., v.108(1), pp. 227-233 (1998). Abstract ; Paper (Gzipped PostScript file)
• A.P.Lyubartsev, S.P.Jacobsson, G. Sundholm and A. Laaksonen "Solubility of Organic Compounds in Water/Octanol System. An Expanded Ensemble Molecular Dynamics Simulation Study of log P parameters" J. Phys. Chem. B, v. 105, pp. 7775-7782 (2001) Abstract and full text from the JPC Web site
• D.L.Bergman, A.P.Lyubartsev, and A.Laaksonen, "Topological and spatial aspects of the hydration of solutes of extreme solvation entropy", Phys. Rev. E, v. 60, pp. 4482-4495 (1999)
 
Abstract and full text from the APS Web site
• K. M. Åberg, A.P.Lyubartsev, S.P.Jacobsson and A.Laaksonen, "Determination of solvation free energies by adaptive expanded ensemble molecular dynamics" J. Chem. Phys., v. 120, pp. 3770-3776 (2004) Abstract and full text from JCP

Review

• P. N. Vorontsov-Velyaminov and A. P. Lyubartsev Generalized ensemble methods in chemical physics Recent Research Developments in Chemical Physics, v. 4, pp. 63-78 (2003)

Other references on the expanded ensemble method and related approaches

• T.V.Kuznetsova, P.N.Vorontsov-Velyaminov. Free energy calculations for a quantum Heizenberg ferromagnet model. J.Phys.: Condens.Matter., v.5,p.717 (1993).
• N.B.Wilding, M.Muller Accurate measurements of the chemical potential of polymeric systems by Monte Carlo simulation J.Chem.Phys., v.101,p.4324 (1994).
• F.A.Escobedo, J.J.de Pablo Monte Carlo simulation of the chemical potential of polymers in an expanded ensemble J.Chem.Phys.,v.103,p.2703 (1995).
• G.R.Smith, A.D.Bruce A study of the multi-canonical Monte Carlo method J.Phys.A.,v.28,p.6623 (1995).
• F.A.Escobedo, J.J.de Pablo Expanded grand canonical and Gibbs ensemble Monte Carlo simulation of polymers J.Chem.Phys.,v.105,p.4391 (1996).
• G.R.Smith and A.D.Bruce Multicanonical Monte-Carlo study of solid-state phase coexistence in a model colloid Phys.Rev.E, v.53(6), p.6530 (1996).
• U.H.E.Hansmann and Y.Okamoto Monte Carlo simulations in generalized ensemble: Multicanonical algorithm versus simulated tempering Phys.Rev.E, v.54(5), p.5863 (1996).
• Kofke DA, Cummings PT Quantitative comparison and optimization of methods for evaluating the chemical potential by molecular simulation MOLECULAR PHYSICS 92 (6): 973-996 DEC 20 1997
• U.H.E.Hansmann and Y.Okamoto Numerical comparison of three recently proposed algorithms in the protein folding problem J.Comp.Chem., v.18, p.920 (1997).
• G.C.Lunch and B.M.Pettitt Grand canonical ensemble molecular dynamics simulation: Reformulation of extended system dynamics approaches J.Chem.Phys., v107(29), p.8594 (1997)
• U.H.E.Hansmann Effective way for determination of multicanonical weights Phys.Rev.E, v.56 (5B), p.6200 (1997)
• C.Bartels and M.Karplus Probability distribution for complex systems: Adaptive umbrella sampling of th epotential energy J.Phys.Chem.B, v.102, p.865-880 (1998)
• A.A.Khare and G.C.Rutledge Chenical potential of model benzene fluids using expanded ensemble Monte Carlo simulations J.Chem.Phys., v.110(6), p. 3063 (1999)
• Vorontsov-Velyaminov PN, Ivanov DA, Ivanov SD, et al. Expanded ensemble Monte Carlo calculations of free energy for closed, stretched and confined lattice polymers COLLOIDS AND SURFACES A-PHYSICOCHEMICAL AND ENGINEERING ASPECTS 148 (1-2): 171-177 MAR 1 1999
• Errington JR, Panagiotopoulos AZ New intermolecular potential models for benzene and cyclohexane JOURNAL OF CHEMICAL PHYSICS 111 (21): 9731-9738 DEC 1 1999
• Khare AA, Rutledge GC Chemical potential of aromatic compounds in pure n-alkanes using expanded ensemble Monte Carlo simulations JOURNAL OF PHYSICAL CHEMISTRY B 104 (15): 3639-3644 APR 20 2000
• Boulougouris GC, Errington JR, Economou IG, et al. Molecular simulation of phase equilibria for water-n-butane and water-n-hexane mixtures JOURNAL OF PHYSICAL CHEMISTRY B 104 (20): 4958-4963 MAY 25 2000
• Economou IG Monte Carlo simulation of phase equilibria of aqueous systems FLUID PHASE EQUILIBRIA 183: 259-269 Sp. Iss. SI JUL 1 2001
• Iba Y Extended ensemble Monte Carlo INTERNATIONAL JOURNAL OF MODERN PHYSICS C 12 (5): 623-656 JUN 2001
• Escobedo FA Simulation of bulk, confined, and polydisperse systems. II. Application to chain systems JOURNAL OF CHEMICAL PHYSICS 115 (12): 5653-5661 SEP 22 2001
• Tej MK, Meredith JC Simulation of nanocolloid chemical potentials in a hard-sphere polymer solution: Expanded ensemble Monte Carlo JOURNAL OF CHEMICAL PHYSICS 117 (11): 5443-5451 SEP 15 2002
• Vlugt TJH Measurement of chemical potentials of systems with strong excluded volume interactions by computing the density of states MOLECULAR PHYSICS 100 (17): 2763-2771 SEP 2002
• Chang J, Sandler SI Determination of liquid-solid transition using histogram reweighting method and expanded ensemble simulations JOURNAL OF CHEMICAL PHYSICS 118 (18): 8390-8395 MAY 8 2003
• Sheng ZM, Luo JW The computation of free energy of TIP4P water using expanded ensemble method ACTA PHYSICA SINICA 52 (9): 2342-2346 SEP 2003
• Fenwick MK, Escobedo FA Expanded ensemble and replica exchange methods for simulation of protein-like systems JOURNAL OF CHEMICAL PHYSICS 119 (22): 11998-12010 DEC 8 2003
• Chang J, Lenhoff AM, Sandler SI Determination of fluid-solid transitions in model protein solutions using the histogram reweighting method and expanded ensemble simulations JOURNAL OF CHEMICAL PHYSICS 120 (6): 3003-3014 FEB 8 2004