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Journal of Statistical Physics

, Volume 175, Issue 3–4, pp 743–763 | Cite as

The Influence of Distant Boundaries on the Solvation of Charged Particles

  • Richard C. Remsing
  • John D. WeeksEmail author
Article

Abstract

The long-ranged nature of the Coulomb potential requires a proper accounting for the influence of even distant electrostatic boundaries in the determination of the solvation free energy of a charged solute. We introduce an exact rewriting of the free energy change upon charging a solute that explicitly isolates the contribution from these boundaries and quantifies the impact of the different boundaries on the free energy. We demonstrate the importance and advantages of appropriately referencing the electrostatic potential to that of the vacuum through the study of several simple model charge distributions, for which we can isolate an analytic contribution from the boundaries that can be readily evaluated in computer simulations of molecular systems. Finally, we highlight that the constant potential of the bulk dielectric phase—the Bethe potential—cannot contribute to the solvation thermodynamics of a single charged solute when the charge distributions of the solvent and solute do not overlap in relevant configurations. But when the charge distribution of a single solute can overlap with the intramolecular charge distribution of solvent molecules, as is the case in electron holography, for example, the Bethe potential is needed when comparing to experiment. Our work may also provide insight into the validity of “extra thermodynamic assumptions” traditionally made during the experimental determination of single ion solvation free energies.

Keywords

Ion solvation Water interfaces Free energy calculations Solvation thermodynamics 

Notes

Acknowledgements

This research was supported in part by NSF CHE-1300993. We thank Chris Mundy, Greg Schenter, and Marcel Baer (Pacific Northwest National Laboratory), Tim Duignan (University of Queensland), Ang Gao (Massachusetts Institute of Technology), and Teddy Baker (University of Maryland) for stimulating discussions.

References

  1. 1.
    Allen, M.P., Tildesley, D.J.: Computer Simulation of Liquids. Oxford, New York (1987)zbMATHGoogle Scholar
  2. 2.
    Ashbaugh, H.S.: Convergence of molecular and macroscopic continuum descriptions of ion hydration. J. Phys. Chem. B 104, 7235–7238 (2000)CrossRefGoogle Scholar
  3. 3.
    Baer, M.D., Stern, A.C., Levin, Y., Tobias, D.J., Mundy, C.J.: Electrochemical surface potential due to classical point charge models drives anion adsorption to the air-water interface. J. Phys. Chem. Lett. 3, 1565–1570 (2012)CrossRefGoogle Scholar
  4. 4.
    Bardhan, J.P., Jungwirth, P., Makowski, L.: Affine-response model of molecular solvation of ions: accurate predictions of asymmetric charging free energies. J. Chem. Phys. 137, 124101 (2012)ADSCrossRefGoogle Scholar
  5. 5.
    Beck, T.L.: The influence of water interfacial potentials on ion hydration in bulk water and near interfaces. Chem. Phys. Lett. 561–562, 1–13 (2013)CrossRefGoogle Scholar
  6. 6.
    Berendsen, H.J.C., Grigera, J.R., Straatsma, T.P.: The missing term in effective pair potentials. J. Phys. Chem. 91, 6269–6271 (1987)CrossRefGoogle Scholar
  7. 7.
    Berne, B.J., Thirumalai, D.: On the simulation of quantum systems: path integral methods. Annu. Rev. Phys. Chem. 37, 401–424 (1986)ADSCrossRefGoogle Scholar
  8. 8.
    Bethe, H.: Theorie der beugung von elektronen an kristallen. Ann. Phys. F4(87), 55–129 (1928)ADSCrossRefGoogle Scholar
  9. 9.
    Bischak, C.G., Hetherington, C.L., Wu, H., Aloni, S., Ogletree, D.F., Limmer, D.T., Ginsberg, N.S.: Origin of reversible photoinduced phase separation in hybrid perovskites. Nano Lett. 17, 1028–1033 (2017)ADSCrossRefGoogle Scholar
  10. 10.
    Canchi, D.R., García, A.E.: Cosolvent effects on protein stability. Annu. Rev. Phys. Chem. 64, 273–93 (2013)ADSCrossRefGoogle Scholar
  11. 11.
    Chandler, D., Leung, K.: Excess electrons in liquids: geometrical perspectives. Annu. Rev. Phys. Chem. 45, 557–591 (1994)ADSCrossRefGoogle Scholar
  12. 12.
    Chang, T.M., Dang, L.X.: Recent advances in molecular simulations of ion solvation at liquid interfaces. Chem. Rev. 106, 1305–1322 (2006)CrossRefGoogle Scholar
  13. 13.
    Chaudhari, M.I., Pratt, L.R., Rempe, S.B.: Utility of chemical computations in predicting solution free energies of metal ions. Mol. Simul. 44, 110–116 (2018)CrossRefGoogle Scholar
  14. 14.
    Chaudhari, M.I., Rempe, S.B., Pratt, L.R.: Quasi-chemical theory of F(aq): The “no split occupancies rule” revisited. J. Chem. Phys. 147, 161728 (2017)ADSCrossRefGoogle Scholar
  15. 15.
    Chen, M., Ko, H.H., Remsing, R.C., Andrade, M.F.C., Santra, B., Sun, Z., Selloni, A., Car, R., Klein, M.L., Perdew, J.P., Wu, X.: Ab initio theory and modeling of water. Proc. Natl. Acad. Sci. USA 114(41), 10846–10851 (2017).  https://doi.org/10.1073/pnas.1712499114 CrossRefGoogle Scholar
  16. 16.
    Collins, K.D.: Why continuum electrostatics theories cannot explain biological structure, polyelectrolytes or ionic strength effects in ion-protein interactions. Biophys. Chem. 167, 43–59 (2012)CrossRefGoogle Scholar
  17. 17.
    Cox, S.J., Geissler, P.L.: Interfacial ion solvation: obtaining the thermodynamic limit from molecular simulations. J. Chem. Phys. 148, 222823 (2018)ADSCrossRefGoogle Scholar
  18. 18.
    Duignan, T., Schenter, G.K., Galib, M., Baer, M.D., Wilhelm, J., Hutter, J., Ben, M.D., Zhao, X.S., Mundy, C.J.: Hydration structure of sodium and potassium ions with DFT-MD (2018).  https://doi.org/10.26434/chemrxiv.7466426.v1
  19. 19.
    Duignan, T.T., Baer, M.D., Mundy, C.J.: Understanding the scale of the single ion free energy: a critical test of the tetra-phenyl arsonium and tetra-phenyl borate assumption. J. Chem. Phys. 148, 222819 (2018)ADSCrossRefGoogle Scholar
  20. 20.
    Duignan, T.T., Baer, M.D., Schenter, G.K., Mundy, C.J.: Electrostatic solvation free energies of charged hard spheres using molecular dynamics with density functional theory interactions. J. Chem. Phys. 147, 161716 (2017)ADSCrossRefGoogle Scholar
  21. 21.
    Duignan, T.T., Baer, M.D., Schenter, G.K., Mundy, C.J.: Real single ion solvation free energies with quantum mechanical simulation. Chem. Sci. 8, 6131–6140 (2017)CrossRefGoogle Scholar
  22. 22.
    England, J.L., Haran, G.: Role of solvation effects in protein denaturation: from thermodynamics to single molecules and back. Annu. Rev. Phys. Chem. 62, 257–277 (2011)ADSCrossRefGoogle Scholar
  23. 23.
    Euwema, R.N., Surratt, G.T.: The absolute positions of calculated energy bands. J. Phys. Chem. Solids 36, 67–71 (1975)ADSCrossRefGoogle Scholar
  24. 24.
    Figueirido, F., Buono, G.S.D., Levy, R.M.: On finite-size effects in computer simulations using the ewald potential. J. Chem. Phys. 103, 6133–6142 (1995)ADSCrossRefGoogle Scholar
  25. 25.
    Geissler, P.L.: Water interfaces, solvation, and spectroscopy. Annu. Rev. Phys. Chem. 64, 317–37 (2013)ADSCrossRefGoogle Scholar
  26. 26.
    Hansen, J.P., McDonald, I.R.: Theory of Simple Liquids. Elsevier Ltd, London (2006)zbMATHGoogle Scholar
  27. 27.
    Harder, E., Roux, B.: On the origin of the electrostatic potential difference at a liquid-vacuum interface. J. Chem. Phys. 129, 234706 (2008)ADSCrossRefGoogle Scholar
  28. 28.
    Harris, F.E.: Hartee-Fock studies of electronic structures of crystalline solids. In: Theoretical Chemistry: Advances and Perspectives, vol. 1. Academic Press, New York (1975)Google Scholar
  29. 29.
    Hofer, T.S., Hünenberger, P.H.: Absolute proton hydration free energy, surface potential of water, and redox potential of the hydrogen electrode from first principles: QM/MM MD free-energy simulations of sodium and potassium hydration. J. Chem. Phys. 148, 222814 (2018)ADSCrossRefGoogle Scholar
  30. 30.
    Horváth, L., Beu, T., Manghi, M., Palmeri, J.: The vapor-liquid interface potential of (multi)polar fluids and its influence on ion solvation. J. Chem. Phys. 138, 154702 (2013)ADSCrossRefGoogle Scholar
  31. 31.
    Hummer, G., Pratt, L.R., García, A.E.: Free energy of ionic hydration. J. Phys. Chem. 100, 1206–1215 (1996)CrossRefGoogle Scholar
  32. 32.
    Hummer, G., Pratt, L.R., García, A.E.: Ion sizes and finite-size corrections for ionic-solvation free energies. J. Chem. Phys. 107(21), 9275–9277 (1997)ADSCrossRefGoogle Scholar
  33. 33.
    Hummer, G., Pratt, L.R., García, A.E.: Molecular theories and simulation of ions and polar molecules in water. J. Phys. Chem. A 102, 7885–7895 (1998)CrossRefGoogle Scholar
  34. 34.
    Hummer, G., Pratt, L.R., García, A.E., Berne, B.J., Rick, S.W.: Electrostatic potentials and free energies of solvation of polar and charged molecules. J. Phys. Chem. B 101, 3017–3020 (1997)CrossRefGoogle Scholar
  35. 35.
    Hummer, G., Pratt, L.R., García, A.E., Garde, S., Berne, B.J., Rick, S.W.: Reply to comment on “electrostatic potentials and free energies of solvation of polar and charged molecules”. J. Phys. Chem. B 102, 3841–3843 (1998)CrossRefGoogle Scholar
  36. 36.
    Hunenberger, P., Reif, M.: Single-Ion Solvation: Experimental and Theoretical Approaches to Elusive Thermodynamic Properties, Theoretical and Computational Chemistry. RCS, London (2011)Google Scholar
  37. 37.
    Jackson, J.D.: Classical Electrodynamics. Wiley, New York (1999)zbMATHGoogle Scholar
  38. 38.
    Kang, Q., Vernisse, L., Remsing, R.C., Thenuwara, A.C., Shumlas, S.L., McKendry, I.G., Klein, M.L., Borguet, E., Zdilla, M.J., Strongin, D.R.: Effect of interlayer spacing on the activity of layered manganese oxide bilayer catalysts for the oxygen evolution reaction. J. Am. Chem. Soc. 139, 1863–1870 (2017)CrossRefGoogle Scholar
  39. 39.
    Kastenholz, M.A., Hünenberger, P.H.: Computation of methodology-independent ionic solvation free energies from molecular simulations. i. the electrostatic potential in molecular liquids. J. Chem. Phys. 124, 124106 (2006)ADSCrossRefGoogle Scholar
  40. 40.
    Kastenholz, M.A., Hünenberger, P.H.: Computation of methodology-independent ionic solvation free energies from molecular simulations. ii. the hydration free energy of the sodium cation. J. Chem. Phys. 124, 224501 (2006)ADSCrossRefGoogle Scholar
  41. 41.
    Kathmann, S.M., Kuo, I.F.W., Mundy, C.J., Schenter, G.K.: Understanding the surface potential of water. J. Phys. Chem. B 115, 4369–4377 (2011)CrossRefGoogle Scholar
  42. 42.
    Kholopov, E.V.: Mean potential of bethe in the classical problem of calculating bulk electrostatic potentials in crystals. Phys. Stat. Sol. (b) 243, 1165–1181 (2006)ADSCrossRefGoogle Scholar
  43. 43.
    Kleinman, L.: Comment on the average potential of a Wigner solid. Phys. Rev. B 24, 7412–7414 (1981)ADSCrossRefGoogle Scholar
  44. 44.
    Knipping, E.M., Lakin, M.J., Foster, K.L., Jungwirth, P., Tobias, D.J., Gerber, R.B., Dabdub, D., Finlayson-Pitts, B.J.: Experiments and simulations of ion-enhanced interfacial chemistry on aqueous nacl aerosols. Science 288, 301–306 (2000)ADSCrossRefGoogle Scholar
  45. 45.
    Leung, K., Marsman, M.: Energies of ions in water and nanopores within density functional theory. J. Chem. Phys. 127, 154722 (2007)ADSCrossRefGoogle Scholar
  46. 46.
    Leung, K., Rempe, S.B., von Lilienfeld, O.A.: Ab initio molecular dynamics calculations of ion hydration free energies. J. Chem. Phys. 130, 204507 (2009)ADSCrossRefGoogle Scholar
  47. 47.
    Lovett, R., Stillinger, F.H.: Ion-pair theory of concentrated electrolytes. ii. approximate dielectric response calculation. J. Chem. Phys. 48(9), 3869–3884 (1968)ADSCrossRefGoogle Scholar
  48. 48.
    Makov, G., Payne, M.C.: Periodic boundary conditions in ab initio calculations. Phys. Rev. B 51, 4014–4022 (1995)ADSCrossRefGoogle Scholar
  49. 49.
    McCartney, M.R., Smith, D.J.: Electron holography: phase imaging with nanometer resolution. Annu. Rev. Mater. Res. 37, 729–767 (2007)ADSCrossRefGoogle Scholar
  50. 50.
    Moreira, L.A., Boström, M., Ninham, B.W., Biscaia, E.C., Tavares, F.W.: Hofmeister effects: Why protein charge, ph titration and protein precipitation depend on the choice of background salt solution. Colloids and Surfaces A: Physicochem. Eng. Aspects 282–283, 457–463 (2006)Google Scholar
  51. 51.
    Mukhopadhyay, A., Fenley, A.T., Tolokh, I.S., Onufriev, A.V.: Charge hydration asymmetry: the basic prinicple and how to use it to test and improve water models. J. Phys. Chem. B 116, 9776–9783 (2012)CrossRefGoogle Scholar
  52. 52.
    Netz, R.R., Horinek, D.: Progress in modeling of ion effects at the vapor/water interface. Annu. Rev. Phys. Chem. 63, 401–18 (2012)ADSCrossRefGoogle Scholar
  53. 53.
    Pollard, T.P., Beck, T.L.: Re-examining the tetraphenyl-arsonium/tetraphenyl-borate (TATB) hypothesis for single-ion solvation free energies. J. Chem. Phys. 148, 222830 (2018)ADSCrossRefGoogle Scholar
  54. 54.
    Pratt, L.R.: Contact potentials of solution interfaces: Phase equilibrium and interfacial electric fields. J. Phys. Chem. 96, 25–33 (1992)CrossRefGoogle Scholar
  55. 55.
    Prozorov, T., Almeida, T.P., Kovács, A., Dunin-Borkowski, R.E.: Off-axis electron holography of bacterial cells and magnetic nanoparticles in liquid. J. R. Soc. Interface 14, 20170464 (2017)CrossRefGoogle Scholar
  56. 56.
    Rajamani, S., Ghosh, T., Garde, S.: Size dependent ion hydration, its asymmetry, and convergence to macroscopic behavior. J. Chem. Phys. 120, 4457–4466 (2004)ADSCrossRefGoogle Scholar
  57. 57.
    Reif, M.M., Hünenberger, P.H.: Origin of asymmetric solvation effects for ions in water and organic solvents investigated using molecular dynamics simulations: the swain acity-basity scale revisited. J. Phys. Chem. B 120, 8485–8517 (2016)CrossRefGoogle Scholar
  58. 58.
    Remsing, R.C., Baer, M.D., Schenter, G.K., Mundy, C.J., Weeks, J.D.: The role of broken symmetry in solvation of a spherical cavity in classical and quantum water models. J. Phys. Chem. Lett. 5, 2767–2774 (2014)CrossRefGoogle Scholar
  59. 59.
    Remsing, R.C., Duignan, T.T., Baer, M.D., Schenter, G.K., Mundy, C.J., Weeks, J.D.: Water lone pair delocalization in classical and quantum descriptions of the hydration of model ions. J. Phys. Chem. B 122, 3519–3527 (2018)CrossRefGoogle Scholar
  60. 60.
    Remsing, R.C., Klein, M.L.: Solvation dynamics in water confined within layered manganese dioxide. Chem. Phys. Lett. 683, 478–482 (2017)ADSCrossRefGoogle Scholar
  61. 61.
    Remsing, R.C., McKendry, I.G., Strongin, D.R., Klein, M.L., Zdilla, M.J.: Frustrated solvation structures can enhance electron transfer rates. J. Phys. Chem. Lett. 6, 4804–4808 (2015)CrossRefGoogle Scholar
  62. 62.
    Remsing, R.C., Rodgers, J.M., Weeks, J.D.: Deconstructing classical water models at interfaces and in bulk. J. Stat. Phys. 145, 313–334 (2011)ADSCrossRefzbMATHGoogle Scholar
  63. 63.
    Remsing, R.C., Weeks, J.D.: Hydrophobicity scaling of aqueous interfaces by an electrostatic mapping. J. Phys. Chem. B 119, 9268–9277 (2015)CrossRefGoogle Scholar
  64. 64.
    Remsing, R.C., Weeks, J.D.: Role of local response in ion solvation: born theory and beyond. J. Phys. Chem. B 120, 6238–6249 (2016)CrossRefGoogle Scholar
  65. 65.
    Rodgers, J.M., Weeks, J.D.: Accurate thermodynamics for short-ranged truncations of coulomb interactions in site-site molecular models. J. Chem. Phys. 131, 244108 (2009)ADSCrossRefGoogle Scholar
  66. 66.
    Ross, F.M.: Opportunities and challenges in liquid cell electron microscopy. Science 350(6267), aaa9886 (2015)CrossRefGoogle Scholar
  67. 67.
    Rowlinson, J.S., Widom, B.: Molecular Theory of Capillarity. Dover Publications, Inc, New York (2002)Google Scholar
  68. 68.
    Scheu, R., Rankin, B.M., Chen, Y., Jena, K.C., Ben-Amotz, D., Roke, S.: Charge asymmetry at aqueous hydrophobic interfaces and hydration shells. Angew. Chem. Int. Ed. Engl. 53(36), 9560–3 (2014).  https://doi.org/10.1002/anie.201310266 CrossRefGoogle Scholar
  69. 69.
    Shi, Y., Beck, T.L.: Length scales and interfacial potentials in ion hydration. J. Chem. Phys. 139, 044504 (2013)ADSCrossRefGoogle Scholar
  70. 70.
    Simon, P., Lichte, H., Formanek, P., Lehmann, M., Huhle, R., Carrillo-Cabrera, W., Harscher, A., Ehrlich, H.: Electron holography of biological samples. Micron 39, 229–256 (2008)CrossRefGoogle Scholar
  71. 71.
    Sprik, M., Klein, M.L.: Application of path integral simulations to the study of electron solvation in polar fluids. Comput. Phys. Rep. 7, 147–166 (1988)ADSCrossRefGoogle Scholar
  72. 72.
    Stillinger, F.H., Lovett, R.: General restriction on the distribution of ions in electrolytes. J. Chem. Phys. 49(5), 1991–1994 (1968)ADSCrossRefGoogle Scholar
  73. 73.
    Stillinger, F.H., Lovett, R.: Ion-pair theory of concentrated electrolytes. i. basic concepts. J. Chem. Phys. 48(9), 3858–3868 (1968)ADSCrossRefGoogle Scholar
  74. 74.
    Tobias, D.J., Stern, A.C., Baer, M.D., Levin, Y., Mundy, C.J.: Simulation and theory of ions at atmospherically relevant aqueous liquid-air interfaces. Annu. Rev. Phys. Chem. 64, 339–59 (2013).  https://doi.org/10.1146/annurev-physchem-040412-110049 ADSCrossRefGoogle Scholar
  75. 75.
    Weeks, J.D., Chandler, D., Andersen, H.C.: Role of repulsive forces in determining the equilibrium structure of simple liquids. J. Chem. Phys. 54, 5237–5247 (1971)ADSCrossRefGoogle Scholar
  76. 76.
    Wilson, M.A., Pohorille, A., Pratt, L.R.: Comment on “study on the liquid-vaport interface of water. i. simulation results of thermodynamics properties and orientational structure”. J. Chem. Phys. 90, 5211–5213 (1989)ADSCrossRefGoogle Scholar
  77. 77.
    Zangwill, A.: Modern Electrodynamics. Cambridge University Press, Cambridge (2013)zbMATHGoogle Scholar
  78. 78.
    Zhang, Z., Remsing, R.C., Chakraborty, H., Gao, W., Yuan, G., Klein, M.L., Ren, S.: Light-induced dilation in nanosheets of charge-transfer complexes. Proc. Natl. Acad. Sci. USA 115, 3776–3781 (2018)CrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Department of Chemistry, Institute for Computational Molecular ScienceTemple UniversityPhiladelphiaUSA
  2. 2.Department of Chemistry and Biochemistry, Institute for Physical Science and TechnologyUniversity of MarylandCollege ParkUSA

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