Advertisement

Quantum Contributions to Free Energy Changes in Fluids

  • Thomas L. Beck
Chapter
Part of the Springer Series in CHEMICAL PHYSICS book series (CHEMICAL, volume 86)

Keywords

Free Energy Free Energy Change Quantum Correction Quantum Effect Free Energy Calculation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Feynman, R. P.; Hibbs, A. R., Quantum Mechanics and Path Integrals, McGraw-Hill: New York, 1965Google Scholar
  2. 2.
    Feynman, R. P., Statistical Mechanics, Benjamin/Cummings: London, 1972Google Scholar
  3. 3.
    Chandler, D.; Wolynes, P. G., Exploiting the isomorphism between quantum theory and classical statistical mechanics of polyatomic fluids, J. Chem. Phys. 1981, 74, 4078-4095CrossRefGoogle Scholar
  4. 4.
    Ceperley, D. M., Path integrals in the theory of condensed helium, Rev. Mod. Phys. 1995,67,279-355CrossRefGoogle Scholar
  5. 5.
    Parrinello, M.; Rahman, A., Study of an F center in molten KCl, J. Chem. Phys. 1984, 80,860-867CrossRefGoogle Scholar
  6. 6.
    Laria, D.; Chandler, D., Comparative study of theory and simulation calculations for excess electrons in simple fluids, J. Chem. Phys. 1987, 87, 4088-4092CrossRefGoogle Scholar
  7. 7.
    Marchi, M.; Sprik, M.; Klein, M. L., Calculation of the free energy of electron solva-tion in liquid ammonia using a path integral quantum Monte Carlo simulation, J. Phys. Chem. 1988, 92, 3625-3629CrossRefGoogle Scholar
  8. 8.
    Wang, Q.; Johnson, J. K.; Broughton, J. Q., Thermodynamic properties and phase equi-librium of fluid hydrogen from path integral simulations, Mol. Phys. 1996, 89, 1105-1119Google Scholar
  9. 9.
    Wang, Q.; Johnson, J. K.; Broughton, J. Q., Path integral grand canonical Monte Carlo, J. Chem. Phys. 1997, 107, 5108-5117CrossRefGoogle Scholar
  10. 10.
    Poulsen, J. A.; Nyman, G.; Rossky, P. J., Quantum diffusion in liquid para-hydrogen: an application of the Feynman-Kleinert linearized path integral approximation, J. Phys. Chem. B 2004, 108, 19799-19808CrossRefGoogle Scholar
  11. 11.
    Sese, L. M., A quantum Monte Carlo study of liquid Lennard-Jones methane, path-integral and effective potentials, Mol. Phys. 1992, 76, 1335-1346CrossRefGoogle Scholar
  12. 12.
    Tchouar, N.; Ould-Kaddur, F.; Levesque, D., Computation of the properties of liquid neon, methane, and gas helium at low temperature by the Feynman-Hibbs approach, J. Chem. Phys. 2004, 121, 7326-7331CrossRefGoogle Scholar
  13. 13.
    Thirumalai, D.; Hall, R. W.; Berne, B. J., A path integral Monte Carlo study of liquid neon and the quantum effective pair potential, J. Chem. Phys. 1984, 81, 2523-2527CrossRefGoogle Scholar
  14. 14.
    Morales, J. J.; Singer, K., Path integral simulation of the free energy of Lennard-Jones neon, Mol. Phys. 1991, 73, 873-880CrossRefGoogle Scholar
  15. 15.
    Sese, L. M., Feynman-Hibbs quantum effective potentials for Monte Carlo simulations of liquid neon, Mol. Phys. 1993, 78, 1167-1177CrossRefGoogle Scholar
  16. 16.
    Ortiz, V.; Lopez, G. E., Fourier path integral Monte Carlo study of a two-dimensional model quantum monolayer, Mol. Phys. 2002, 100, 1003-1009CrossRefGoogle Scholar
  17. 17.
    Sese, L. M., Path integral and effective potential Monte Carlo simulations of liquid nitrogen, hard-sphere and Lennard-Jones potentials, Mol. Phys. 1991, 74, 177-189CrossRefGoogle Scholar
  18. 18.
    Miller, T. F., III; Clary, D. C., Torsional path integral Monte Carlo method for calculating the absolute quantum free energy of large molecules, J. Chem. Phys. 2003, 119, 68-76CrossRefGoogle Scholar
  19. 19.
    Srinivisan, J.; Volobuev, Y. L.; Mielke, S. L.; Truhlar, D. G., Parallel Fourier path-integral Monte Carlo calculations of absolute free energies and chemical equilibria, Comput. Phys. Commun. 2000, 128, 446-464CrossRefGoogle Scholar
  20. 20.
    Doll, J. D.; Beck, T. L.; Freeman, D. L., Equilibrium and dynamical Fourier path integral methods, Adv. Chem. Phys. 1990, 78, 61-127CrossRefGoogle Scholar
  21. 21.
    Runge, K. J.; Chester, G. V., Solid-fluid phase transition of quantum hard spheres at finite temperature, Phys. Rev. B 1988, 38, 135-162CrossRefGoogle Scholar
  22. 22.
    Barrat, J.-L.; Loubeyre, P.; Klein, M. L., Isotopic shift in the melting curve of helium: a path integral Monte Carlo study, J. Chem. Phys. 1989, 90, 5644-5650CrossRefGoogle Scholar
  23. 23.
    Li, D.; Voth, G. A., A path integral Einstein model for characterizing the equilibrium states of low temperature solids, J. Chem. Phys. 1992, 96, 5340-5353CrossRefGoogle Scholar
  24. 24.
    Liu, A.; Beck, T. L., Determination of excess Gibbs free energy of quantum mixtures by MC path integral simulations, Mol. Phys. 1995, 86, 225-233CrossRefGoogle Scholar
  25. 25.
    Guillot, B.; Guissani, Y., Quantum effects in simulated water by the Feynman-Hibbs approach, J. Chem. Phys. 1998, 108, 10162-10174CrossRefGoogle Scholar
  26. 26.
    Ben-Naim, A.; Marcus, Y., Solvation thermodynamics of nonionic solutes, J. Chem. Phys. 1984, 81, 2016-2027CrossRefGoogle Scholar
  27. 27.
    Gripon, C.; Legrand, L.; Rosenman, I.; Vidal, O.; Robert, M. C.; Boue, F., Lysozyme solubility in H2 O and D2 O solutions: a simple relationship, J. Cryst. Growth 1997, 177, 238-247CrossRefGoogle Scholar
  28. 28.
    Bonnete, F.; Madern, D.; Zaccai, G., Stability against denaturation mechanisms in halophilic malate dehydrogenase “adapt” to solvent connditions, J. Mol. Biol. 1994, 244,436-447CrossRefGoogle Scholar
  29. 29.
    Beck, T. L.; Paulaitis, M. E.; Pratt, L. R., The Potential Distribution Theorem and Models of Molecular Solutions, Cambridge University Press: New York, 2006Google Scholar
  30. 30.
    Lobaugh, J.; Voth, G. A., The quantum dynamics of an excess proton in water, J. Chem. Phys. 1996, 104, 2056-2069CrossRefGoogle Scholar
  31. 31.
    Hwang, J.-K.; Warshel, A., How important are quantum mechanical nuclear motions in enzyme catalysis, J. Am. Chem. Soc. 1996, 118, 11745-11751CrossRefGoogle Scholar
  32. 32.
    Gao, J.; Truhlar, D. G., Quantum mechanical methods for enzyme kinetics, Ann. Rev. Phys. Chem. 2002, 53, 467-505CrossRefGoogle Scholar
  33. 33.
    Friesner, R. A.; Guallar, V., Ab initio quantum chemical and mixed quantum mechan-ics/molecular mechanics (QM/MM) methods for studying enzymatic catalysis, Ann. Rev. Phys. Chem. 2005, 56, 389-427CrossRefGoogle Scholar
  34. 34.
    Mahoney, M. W.; Jorgensen, W. L., Quantum, intramolecular flexibility, and polariz-ability effects on the reproduction of the density anomaly of liquid water by simple potential functions, J. Chem. Phys. 2001, 115, 10758-10768CrossRefGoogle Scholar
  35. 35.
    Chen, B.; Ivanov, I.; Klein, M. L.; Parrinello, M., Hydrogen bonding in water, Phys. Rev. Lett. 2003, 91, 215503Google Scholar
  36. 36.
    Asthagiri, D.; Pratt, L. R.; Kress, J. D., Free energy of liquid water on the basis of quasichemical theory and ab initio molecular dynamics, Phys. Rev. E 2003, 68, 041505Google Scholar
  37. 37.
    . Fernandez-Serra, M. V.; Ferlat, G.; Artacho, E., Two exchange-correlation func-tionals compared for first-principles liquid water, Los Alamos Eprint archive: cond-mat/0407724, 2004Google Scholar
  38. 38.
    Kuo, I.-F. W.; Mundy, C. J.; McGrath, M. J.; Siepmann, J. I.; VandeVondele, J.; Sprik, M.; Hutter, J.; Chen, B.; Klein, M. L.; Mohamed, F.; Krack, M.; Parrinello, M., Liquid water from first principles: investigation of different sampling approaches, J. Phys. Chem. B 2004, 108, 12990-12998CrossRefGoogle Scholar
  39. 39.
    Schwegler, E.; Grossman, J. C.; Gygi, F.; Galli, G., Towards an assessment of the ac-curacy of density functional theory for first principles simulations of water II, J. Chem. Phys. 2004, 121, 5400-5409CrossRefGoogle Scholar
  40. 40.
    Allesch, M.; Schwegler, E.; Gygi, F.; Galli, G., A first principles simuation of rigid water, J. Chem. Phys. 2004, 120, 5192CrossRefGoogle Scholar
  41. 41.
    Widom, B., Some topics in the theory of fluids, J. Chem. Phys. 1963, 39, 2808-2812CrossRefGoogle Scholar
  42. 42.
    Widom, B., Potential-distribution theory and the statistical mechanics of fluids, J. Phys. Chem. 1982, 86, 869-872CrossRefGoogle Scholar
  43. 43.
    . Landau, L. D.; Lifshitz, E. M., Statistical Physics, (3rd edition, part 1), 1980Google Scholar
  44. 44.
    Stratt, R. M., Semiclassical statistical mechanics of fluids: nonperturbative incorporation of quantum effects in classical many body models, J. Chem. Phys. 1979, 70, 3630-3638CrossRefGoogle Scholar
  45. 45.
    Kleinert, H., Path Integrals in Quantum Mechanics, Statistics, and Polymer Physics, World Scientific: Singapore, 1995Google Scholar
  46. 46.
    Coalson, R. D., On the connection between Fourier coefficient and discretized Cartesian path integration, J. Chem. Phys. 1986, 85, 926CrossRefGoogle Scholar
  47. 47.
    Pratt, L. R., A statistical method for identifying transition states in high dimensional problems, J. Chem. Phys. 1986, 85, 5045-5048CrossRefGoogle Scholar
  48. 48.
    Beck, T. L., Quantum path integral extension of Widom’s test particle method for chem-ical potentials with application to isotope effects on hydrogen solubilities in model solids, J. Chem. Phys. 1992, 96, 7175-7177CrossRefGoogle Scholar
  49. 49.
    Beck, T. L.; Marchioro, T. L., The quantum potential distribution theorem, in Path Integrals from meV to MeV: Tutzing 1992, Grabert, H.; Inomata, A.; Schulman, L.; Weiss, U., Eds., World Scientific: Singapore, 1993, pp. 238-243Google Scholar
  50. 50.
    van Kampen, N. G., Stochastic Processes in Physics and Chemistry, Elsevier: New York, 1992Google Scholar
  51. 51.
    Jarzynski, C., Nonequilibrum equality for free energy differences, Phys. Rev. Lett. 1997, 78,2690-2693CrossRefGoogle Scholar
  52. 52.
    Roepstorff, G., Path Integral Approach to Quantum Physics, Springer: Berlin, Heidelberg, New York, 1994Google Scholar
  53. 53.
    Predescu, C., The partial averaging method, J. Math. Phys. 2003, 44, 1226-1239CrossRefGoogle Scholar
  54. 54.
    Lobaugh, J.; Voth, G. A., A quantum model for water: equilibrium and dynamical properties, J. Chem. Phys. 1997, 106, 2400-2410CrossRefGoogle Scholar
  55. 55.
    de la Pena, L. Hernandez; Kusalik, P. G., Quantum effects in light and heavy water: a rigid-body centroid molecular dynamics study, J. Chem. Phys. 2004, 121, 5992-6002Google Scholar
  56. 56.
    Stern, H. A.; Berne, B. J., Quantum effects in liquid water: path-integral simulations of a flexible and polarizable ab initio model, J. Chem. Phys. 2001, 115, 7622CrossRefGoogle Scholar
  57. 57.
    Gray, C. G.; Gubbins, K. E., Thoery of Molecular Fluids. Volume 1: Fundamentals, Oxford University Press: Oxford, 1984Google Scholar
  58. 58.
    Predescu, C.; Doll, J. D., Optimal series representations for numerical path integral simulations, J. Chem. Phys. 2003, 117, 7448-7463CrossRefGoogle Scholar
  59. 59.
    Mielke, S. L.; Truhlar, D. G., A new Fourier path integral method, a more gen-eral scheme for extrapolation, and comparison of eight path integral methods for the quantum mechanical calculation of free energies, J. Chem. Phys. 2001, 114, 621-630CrossRefGoogle Scholar
  60. 60.
    Kuharski, R. A.; Rossky, P. J., A quantum mechanical study of structure in liquid H2 O and D2 O, J. Chem. Phys. 1985, 82, 5164-5177CrossRefGoogle Scholar
  61. 61.
    Wallqvist, A.; Berne, B. J., Path-integral simulation of pure water, Chem. Phys. Lett. 1985,117,214CrossRefGoogle Scholar
  62. 62.
    Goldman, N.; Leforestier, C.; Saykally, R. J., A ‘first principles’ potential energy surface for liquid water from VRT spectroscopy of water clusters, Philos. Trans. R. Soc. A 2005, 1-16. doi:10.1098/rsta.2004.1504Google Scholar
  63. 63.
    . Sit, P.; Marzari, N., Static and dynamical properties of heavy water at ambient conditions from first-principles molecular dynamics, Los Alamos Eprint Server 2005. cond-mat/0504146Google Scholar
  64. 64.
    de la Pena, L. Hernandez; Kusalik, P. G., Temperature dependence of quantum effects in liquid water, J. Am. Chem. Soc. 2005, 127, 5246-5251CrossRefGoogle Scholar
  65. 65.
    Grossman, J. C.; Schwegler, E.; Draeger, E. W.; Gygi, F.; Galli, G., Towards an assessment of the accuracy of density functional theory for first principles simulations of water, J. Chem. Phys. 2004, 120, 300-311CrossRefGoogle Scholar
  66. 66.
    Saam, J.; Tajkhorshid, E.; Hayashi, S.; Schulten, K., Molecular dynamics investigation of primary photoinduced events in the activation of rhodopsin, Biophys. J. 2002, 83, 3097-3112CrossRefGoogle Scholar
  67. 67.
    Brewer, M. L.; Schmitt, U. W.; Voth, G. A., The formation and dynamics of proton wires in channel environments, Biophys. J. 2001, 80, 1691-1702CrossRefGoogle Scholar
  68. 68.
    Wu, Y.; Voth, G. A., A computer simulation study of the hydrated proton in a synthetic proton shannel, Biophys. J. 2003, 85, 864-875CrossRefGoogle Scholar
  69. 69.
    Chakrabarti, N.; Roux, B.; Pomes, R., Structural determinants of proton blockage in aquaporins, J. Mol. Biol. 2004, 343, 493-510CrossRefGoogle Scholar
  70. 70.
    Yin, J.; Kuang, Z.; Mahankali, U.; Beck, T. L., Ion transit pathways and gating in ClC chloride channels, Proteins: Struct. Funct. Bioinform. 2004, 57, 414-421CrossRefGoogle Scholar
  71. 71.
    Asthagiri, D.; Pratt, L. R.; Kress, J. D., Ab initio molecular dynamics and quasichemical study of H+ (aq), Proc. Natl Acad. Sci. 2005, 102, 6704-6708CrossRefGoogle Scholar
  72. 72.
    Burykin, A.; Warshel, A., What really prevents proton transport through aquaporin? Charge self-energy versus proton wire proposals, Biophys. J. 2003, 85, 3696-3706CrossRefGoogle Scholar
  73. 73.
    Bliznyuk, A. A.; Rendell, A. P., Electronic effects in biomolecular simulations: investi-gations of the KcsA potassium ion channel, J. Phys. Chem. B 2004, 108, 13866-13873CrossRefGoogle Scholar
  74. 74.
    Jensen, M. O.; Rothlisberger, U.; Rovira, C., Hydroxide and proton migration in aqua-porins, Biophys. J. 2005, 89, 1744-1759CrossRefGoogle Scholar
  75. 75.
    Laio, A.; VandeVondele, J.; Rothlisberger, U., A Hamiltonian electrostatic coupling scheme for hybrid Car-Parrinello molecular dynamics simulations, J. Chem. Phys. 2002,116,6941-6947CrossRefGoogle Scholar
  76. 76.
    Pomes, R.; Roux, B., Theoretical study of H+ translocation along a model proton wire, J. Phys. Chem. 1996, 100, 2519-2527CrossRefGoogle Scholar
  77. 77.
    Pomes, R.; Roux, B., Free energy profiles for H+ conduction along hydrogen-bonded chains of water molecules, Biophys. J. 1998, 75, 33-40CrossRefGoogle Scholar
  78. 78.
    Zahn, D.; Brickmann, J., Quantum-classical simulation of proton transport via a phos-pholipid bilayer, Phys. Chem. Chem. Phys. 2001, 3, 848-852CrossRefGoogle Scholar
  79. 79.
    deGroot, B. L.; Frigato, T.; Helms, V.; Grubmuller, J., The mechanism of proton exclusion in the aquaporin-1 water channel, J. Mol. Biol. 2003, 333, 279-293CrossRefGoogle Scholar
  80. 80.
    Pomes, R.; Roux, B., Molecular mechanism of H+ conduction in the single-file water chain of the gramicidin channel, Biophys. J. 2002, 82, 2304-2316CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Thomas L. Beck
    • 1
  1. 1.Departments of Chemistry and PhysicsUniversity of CincinnatiCincinnati

Personalised recommendations