Potential Distribution Methods and Free Energy Models of Molecular Solutions

  • Lawrence R. Pratt
  • Dilip Asthagiri
Part of the Springer Series in CHEMICAL PHYSICS book series (CHEMICAL, volume 86)


Free Energy Partition Function Hydrophobic Effect Boltzmann Factor Hydration Free Energy 
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  1. 1.
    Pratt, L. R., Molecular theory of hydrophobic effects: “She is too mean to have her name repeated.”, Annu. Rev. Phys. Chem. 2002, 53, 409-436CrossRefGoogle Scholar
  2. 2.
    Pohorille, A.; Pratt, L. R., Cavities in molecular liquids and the theory of hydrophobic solubilities, J. Am. Chem. Annu. 1990, 112, 5066-5074CrossRefGoogle Scholar
  3. 3.
    Pratt, L. R.; Pohorille, A., Theory of hydrophobicity: transient cavities in molecular liquids, Proc. Natl Acad. Sci. USA 1992, 89, 2995-2999CrossRefGoogle Scholar
  4. 4.
    Hummer, G.; Garde, S.; García, A. E.; Pohorille, A.; Pratt, L. R., An information theory model of hydrophobic interactions, Proc. Natl Acad. Sci. USA 1996, 93, 8951-8955CrossRefGoogle Scholar
  5. 5.
    Gomez, M. A.; Pratt, L. R.; Hummer, G.; Garde, S., Molecular realism in default models for information theories of hydrophobic effects, J. Phys. Chem. B 1999, 103, 3520-3523CrossRefGoogle Scholar
  6. 6.
    Garde, S.; Hummer, G.; García, A. E.; Paulaitis, M. E.; Pratt, L. R., Origin of entropy convergence in hydrophobic hydration and protein folding, Phys. Rev. Lett. 1996, 77, 4966-4968CrossRefGoogle Scholar
  7. 7.
    Pratt, L. R.; Pohorille, A., Hydrophobic effects and modeling of biophysical aqueous solution interfaces, Chem. Rev. 2002, 102, 2671-2691CrossRefGoogle Scholar
  8. 8.
    Ashbaugh, H. S.; Asthagiri, D.; Pratt, L. R.; Rempe, S. B., Hydration of krypton and consideration of clathrate models of hydrophobic effects from the perspective of quasi-chemical theory, Biophys. Chem. 2003, 105, 323-338CrossRefGoogle Scholar
  9. 9.
    Ashbaugh, H. S.; Pratt, L. R., Colloquium: Scaled particle theory and the length scales of hydrophobicity, Rev. Mod. Phys. 2006, 78, 159-178CrossRefGoogle Scholar
  10. 10.
    Beck, T. L.; Paulaitis, M. E.; Pratt, L. R., The Potential Distribution Theorem and Models of Molecular Solutions, Cambridge University Press: Cambridge, 2006Google Scholar
  11. 11.
    Hammersley, J. M.; Handscomb, D. C., Monte Carlo Methods, Chapman and Hall: London, 1964Google Scholar
  12. 12.
    Asthagiri, D.; Pratt, L. R.; Paulaitis, M. E.; Rempe, S. B., Hydration structure and free energy of biomolecularly specific aqueous dications, including Zn2+ and first transition row metals, J. Am. Chem. Soc. 2004, 126, 1285-1289CrossRefGoogle Scholar
  13. 13.
    Kirkwood, J. G.; Poirier, J. C., The statistical mechanical basis of the Debye-H ückel theory of strong electrolytes, J. Phys. Chem. 1954, 86, 591-596CrossRefGoogle Scholar
  14. 14.
    Widom, B., Some topics in the theory of fluids, J. Chem. Phys. 1963, 39, 2808-2812CrossRefGoogle Scholar
  15. 15.
    Jackson, J. L.; Klein, L. S., Potential distribution method in equilibrium statistical mechanics, Phys. Fluids 1964, 7, 228-231CrossRefGoogle Scholar
  16. 16.
    Widom, B., Potential-distribution theory and the statistical mechanics of fluids, J. Phys. Chem. 1982, 86, 869-872CrossRefGoogle Scholar
  17. 17.
    Stell, G. Mayer-Montroll equations (and some variants) through history for fun and profit. in The Wonderful World of Stochastics A Tribute to Elliot W. Montroll, Shlesinger, M. F.; Weiss, G. H., Eds., vol. XII, Studies in Statistical Mechanics. Elsevier: New York, 1985, pp. 127-156Google Scholar
  18. 18.
    Lebowitz, J. L.; Percus, J. K.; Verlet, L., Ensemble dependence of fluctuations with application to machine computations, Phys. Rev. 1967, 153, 250CrossRefGoogle Scholar
  19. 19.
    Resnick, S. I., A Probability Path, Birkha üser: New York, 2001Google Scholar
  20. 20.
    Imai, T.; Hirata, F., Partial molar volume and compressibility of a molecule with internal degrees of freedom., J. Chem. Phys. 2003, 119Google Scholar
  21. 21.
    Bennett, C. H., Efficient estimation of free-energy differences from Monte Carlo data, J. Comp. Phys. 1976, 22, 245-268CrossRefGoogle Scholar
  22. 22.
    Ciccotti, G.; Frenkel, D.; McDonald, I. R., Simulation of Liquids and Solids. Mole-cular Dynamics and Monte Carlo Methods in Statistical Mechanics, North-Holland: Amsterdam, 1987Google Scholar
  23. 23.
    . Frenkel, D. Free-energy computation and first-order phase transitions. in International School of Physics ‘Enrico Fermi’, vol. XCVII. Soc. Italiana di Fisica: Bologna, 1986, pp. 151-188Google Scholar
  24. 24.
    Shing, K. S.; Chung, S. T., Computer-simulation methods for the calculation of solubil-ity in supercritical extraction systems, J. Phys. Chem. 1987, 91, 1674-1681CrossRefGoogle Scholar
  25. 25.
    Smith, P. E., Computer simulation of cosolvent effects on hydrophobic hydration, J. Phys. Chem. B 1999, 103, 525-534CrossRefGoogle Scholar
  26. 26.
    . Callen, H. B., Thermodynamics, [2nd edition]. See Chapter 5Google Scholar
  27. 27.
    Wood, R. H.; Yezdimer, E. M.; Sakane, S.; Barriocanal, J. A.; Doren, D. J., Free energies of solvation with quantum mechanical interaction energies from classical mechanical simulations, J. Chem. Phys. 1999, 110, 1329-37CrossRefGoogle Scholar
  28. 28.
    Sakane, S.; Yezdimer, E. M.; Liu, W. B.; Barriocanal, J. A.; Doren, D. J.; Wood, R. H., Exploring the ab initio/classical free energy perturbation method: the hydration free energy of water, J. Chem. Phys. 2000, 113, 2583-93CrossRefGoogle Scholar
  29. 29.
    Wood, R. H.; Liu, W. B.; Doren, D. J., Rapid calculation of the structures of solutions with ab initio interaction potentials., J. Phys. Chem. A 2002, 106, 6689-6693CrossRefGoogle Scholar
  30. 30.
    Liu, W. B.; Sakane, S.; Wood, R. H.; Doren, D. J., The hydration free energy of aqueous Na+ and Cl at high temperatures predicted by ab initio/classical free energy pertur-bation: 973 K with 0.535 g/cm3 and 573 K with 0.725 g/cm3 , J. Phys. Chem. A 2002, 106,1409-1418CrossRefGoogle Scholar
  31. 31.
    Sakane, S.; Liu, W. B.; Doren, D. J.; Shock, E. L.; Wood, R. H., Prediction of the Gibbs energies and an improved equation of state for water at extreme conditions from ab initio energies with classical simulations, Geochim. Cosmochim. Acta 2001, 65, 4067-4075CrossRefGoogle Scholar
  32. 32.
    Liu, W. B.; Wood, R. H.; Doren, D. J., Hydration free energy and potential of mean force for a model of the sodium chloride ion pair in supercritical water with ab initio solute-solvent interactions, J. Chem. Phys. 2003, 118, 2837-2844CrossRefGoogle Scholar
  33. 33.
    Liu, W. B.; Wood, R. H.; Doren, D. J., Density and temperature dependences of hydration free energy of Na+ and Cl at supercritical conditions predicted by a ini-tio/classical free energy perturbation, J. Phys. Chem. B 2003, 107, 9505-9513CrossRefGoogle Scholar
  34. 34.
    Pettitt, B. M., A Perspective on “Volume and heat of hydration of ions” - Born M. (1920) Z Phys. 1 : 45, Theor. Chem. Acc. 2000, 103, 171-172Google Scholar
  35. 35.
    Torrie, G. M.; Valleau, J. P., Nonphysical sampling distributions in Monte Carlo free-energy estimation: umbrella sampling, J. Comput. Phys. 1977, 23, 187-199CrossRefGoogle Scholar
  36. 36.
    Hertz, J.; Krogh, A.; Palmer, R. G., Introduction to the Theory of Neural Computation, Addison-Wesley: Redwood City, CA, 1991Google Scholar
  37. 37.
    Plishke, M.; Bergerson, B., Equilibrium Statistical Physics, World Scientific: Singapore, 1994Google Scholar
  38. 38.
    Kalos, M. H.; Whitlock, P. A., Monte Carlo Methods, Volume I: Basics, Wiley-Interscience: New York, 1986CrossRefGoogle Scholar
  39. 39.
    . Press, W. H.; Teukolsky, S. A.; Vetterling, W. T.; Flannery, B. P., Numerical Recipes in Fortran 77, [2nd edition]Google Scholar
  40. 40.
    Hummer, G.; Pratt, L. R.; García, A. E., Multistate Gaussian model for electrostatic solvation free energies, J. Am. Chem. Soc. 1997, 119, 8523-8527CrossRefGoogle Scholar
  41. 41.
    Pratt, L. R.; Pohorille, A. in Proceedings of the EBSA 1992 International Workshop on Water-Biomolecule Interactions, Palma, M. U.; Palma-Vittorelli, M. B.; Parak, F., Eds. Societ á Italiana de Fisica: Bologna, 1993, pp. 261-268Google Scholar
  42. 42.
    Pohorille, A.; Wilson, M. A., Molecular structure of aqueous interfaces., Theochem 1993,284,271-98CrossRefGoogle Scholar
  43. 43.
    Pohorille, A., Transient cavities in liquids and the nature of the hydrophobic effect, Pol. J. Chem. 1998, 72, 1680-1690Google Scholar
  44. 44.
    Pratt, L. R., Hydrophobic effects Wiley: Chichester, 1998, pp. 1286-1294Google Scholar
  45. 45.
    Pohorille, A.; Wilson, M. A., Excess chemical potential of small solutes across water-membrane and water-hexane interfaces, J. Chem. Phys. 1996, 104, 3760-3773CrossRefGoogle Scholar
  46. 46.
    Pratt, L. R.; LaViolette, R. A., Quasi-chemical theories of associated liquids, Mol. Phys. 1998,94,909-915CrossRefGoogle Scholar
  47. 47.
    Pratt, L. R.; Rempe, S. B. Quasi-chemical theory and implicit solvent models for sim-ulations. in Simulation and Theory of Electrostatic Interactions in Solution. Computa-tional Chemistry, Biophysics, and Aqueous Solutions, Pratt, L. R.; Hummer, G., Eds., vol. 492, AIP Conference Proceedings. American Institute of Physics, Melville: New York, 1999, pp. 172-201Google Scholar
  48. 48.
    Paulaitis, M. E.; Pratt, L. R., Hydration theory for molecular biophysics, Adv. Prot. Chem. 2002, 62, 283-310CrossRefGoogle Scholar
  49. 49.
    Mathews, J.; Walker, R. L., Mathematical Methods of Physics, Benjamin: New York, 1964Google Scholar
  50. 50.
    Frisch, M. J. et al. Gaussian 98 (Revision A.2), 1998, Gaussian, Inc.: Pittsburgh PAGoogle Scholar
  51. 51.
    Becke, A. D., Density-functional thermochemistry. III. The role of exact exchange, J. Chem. Phys. 1993, 98, 5648CrossRefGoogle Scholar
  52. 52.
    Asthagiri, D.; Pratt, L. R.; Ashbaugh, H. S., Absolute hydration free energies of ions, ion-water clusters, and quasi-chemical theory, J. Chem. Phys. 2003, 119, 2702-2708CrossRefGoogle Scholar
  53. 53.
    Asthagiri, D.; Pratt, L. R.; Kress, J. D.; Gomez, M. A., The hydration state of HO (aq), Chem. Phys. Lett. 2003, 380, 530-535CrossRefGoogle Scholar
  54. 54.
    Asthagiri, D.; Pratt, L. R.; Kress, J. D.; Gomez, M. A., HO (aq) hydration and mobility, Proc. Natl Acad. Sci. USA 2004, 101, 7229-7233CrossRefGoogle Scholar
  55. 55.
    Asthagiri, D.; Pratt, L. R.; Kress, J. D., Ab initio molecular dynamics and quasichemical study of H+ (aq)., Proc. Natl Acad. Sci. USA 2005, 102, 6704-6708CrossRefGoogle Scholar
  56. 56.
    Pratt, L. R.; LaViolette, R. A.; Gomez, M. A.; Gentile, M. E., Quasi-chemical theory for the statistical thermodynamics of the hard-sphere fluid, J. Phys. Chem. B 2001, 105, 11662-11668CrossRefGoogle Scholar
  57. 57.
    Pratt, L. R.; Ashbaugh, H. S., Self-consistent molecular field theory for packing in classical liquids, Phys. Rev. E 2003, 68, 021505CrossRefGoogle Scholar
  58. 58.
    Allen, M .P.; Tildesley, D. J., Computer Simulation of Liquids, Oxford Science: Oxford, 1987Google Scholar
  59. 59.
    . Frenkel, D.; Smit, B., Understanding Molecular Simulation. From Algorithms to Applications, [2nd edition]Google Scholar
  60. 60.
    Gallicchio, E.; Kubo, M. M.; Levy, R. M., Enthalpy-entropy and cavity decomposition of alkane hydration free energies: numerical results and implications for theories of hydrophobic solvation, J. Phys. Chem. B 2000, 104, 6271-6285CrossRefGoogle Scholar
  61. 61.
    Grossman, J. C.; Schwegler, E.; Galli, G., Quantum and classical molecular dynamics simulations of hydrophobic hydration structure around small solutes, J. Phys. Chem. B 2004,108,15865-15872CrossRefGoogle Scholar
  62. 62.
    Raschke, T. M.; Levitt, M., Detailed hydration maps of benzene and cyclohexane reveal distinct water structures, J. Phys. Chem. B 2004, 108, 13492-13500CrossRefGoogle Scholar
  63. 63.
    Hummer, G.; Pratt, L.R.; García, A.E., Free energy of ionic hydration, J. Phys. Chem. 1996,100,1206-1215CrossRefGoogle Scholar
  64. 64.
    Lebowitz, J. L.; Waisman, E. M., Statistical-mechanics of simple fluids: beyond van der Waals, Phys. Today 1980, 33, 24-30CrossRefGoogle Scholar
  65. 65.
    Jarzynski, C., Microscopic analysis of Clausius-Duhem processes, J. Stat. Phys. 1999, 96,415-427CrossRefGoogle Scholar
  66. 66.
    Papoulis, A., Probability, Random Variables, and Stochastic Processes, McGraw-Hill: Singapore, 1991Google Scholar
  67. 67.
    Friedman, H. L.; Krishnan, C. V. Thermodynamics of ion hydration. in Water A Com-prehensive Treatise, Franks, F., Ed., vol. 3. Plenum: New York, 1973, pp. 1-118Google Scholar
  68. 68.
    Stell, G. Fluids with long-range forces. in Statistical Mechanics. Part A: Equilibrium Techniques, Berne, B. J., Ed. Plenum: New York, 1977, pp. 47-84Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Lawrence R. Pratt
    • 1
  • Dilip Asthagiri
    • 2
  1. 1.Theoretical DivisionLos Alamos National LaboratoryLos Alamos
  2. 2.Theoretical DivisionLos Alamos National LaboratoryLos Alamos

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