Solvent Effects in Quantum Chemistry

  • Gerald Monard
  • Jean-Louis Rivail
Reference work entry


The properties of a molecule may change quite substantially when passing from the isolated state to a solution, and computational chemistry requires the possibility of taking into account the effects of a solvent on molecular properties. These changes are mainly due to long range interactions, and electrostatics involving a large number of solvent molecules play the major role in the phenomenon and free energy changes have to be evaluated. Statistical calculations by means of usual Monte Carlo or molecular dynamics coupled with a full quantum chemical description of a sample representative of the solution is still out of reach for standard molecular modeling computations nowadays. Nevertheless, several simplified approaches are available to evaluate the free energy changes which appear when an isolated molecule, as described by standard quantum computations, undergoes the influence of a solvent and to predict the changes in the molecular properties which are the consequences of solvation. In this chapter, we develop the principles of the most usual methods that a computational chemist can find in standard codes or can implement more or less easily to approach the solvent effects in quantum chemistry investigations.


Dielectric Permittivity Solvent Molecule Pair Correlation Function Multipole Expansion Electrostatic Contribution 
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  1. Assfeld, X. (1994). PhD Dissertation, Université Henri Poincaré, Nancy.Google Scholar
  2. Bakó, I., Hutter, J., & Pálinkás, G. (2006). Car-Parrinello molecular dynamics simulation of liquid formic acid. Journal of Physical Chemistry A, 110, 2188.CrossRefGoogle Scholar
  3. Barone, V., & Cossi, M. (1998). Quantum calculation of molecular energies and energy gradients in solution by a conductor solvent model. Journal of Physical Chemistry A, 102, 1995.CrossRefGoogle Scholar
  4. Bernal-Uruchurtu, M. I., & Ruiz-López, M. F. (2000). Basic ideas for the correction of semiempirical methods describing H-bonded systems. Chemical Physics Letters, 330, 118.CrossRefGoogle Scholar
  5. Bernal-Uruchurtu, M. I., Martins-Costa, M. T. C., Millot, C., & Ruiz-López, M. F. (2000). Improving description of hydrogen bonds at the semiempirical level: Water-water interactions as test case. Journal of Computational Chemistry, 21, 572.CrossRefGoogle Scholar
  6. Bondi, A. (1964). van der Waals volumes and radii. Journal of Physical Chemistry, 68, 441.CrossRefGoogle Scholar
  7. Born, M. (1920). Volumen und hydratationswärme der Ionen. Zeitschrift fur Physik, 1, 45.CrossRefGoogle Scholar
  8. Buckingham, A. (1967). Permanent and induced molecular moments and long-range intermolecular forces. Advances in Chemical Physics, 12, 107.Google Scholar
  9. Buckingham, A. (1978). Basic theory of intermolecular forces: Applications to small molecules. In B. Pullman (Ed.), Intemolecular interactions, from Diatomics to Biopolymers (Vol. 1, p. 1). New York: Wiley.Google Scholar
  10. Cancès, E., Menucci, B., & Tomasi, J. (1997). A new integral equation formalism for the polarizable continuum model: Theoretical background and applications to isotropic and anisotropic dielectrics. Journal of Chemical Physics, 107, 3032.CrossRefGoogle Scholar
  11. Catak, S., Monard, G., Aviyente, V., & Ruiz-López, M. F. (2009). Deamidation of asparagine residues: Direct hydrolysis versus succinimide-mediated deamidation mechanisms. Journal of Physical Chemistry A, 113, 1111.CrossRefGoogle Scholar
  12. Car, R., & Parrinello, M. (1985). Unified approach for molecular dynamics and density-functional theory. Physical Review Letters, 55, 2471.CrossRefGoogle Scholar
  13. Chandler, D., & Andersen, H. C. (1972). Optimized cluster expansions for classical fluids. II. Theory of molecular liquids. Journal of Chemical Physics, 57, 1930.CrossRefGoogle Scholar
  14. Cramer, C. J., & Truhlar, D. G. (1991). Molecular orbital theory calculations of aqueous solvation effects on chemical equilibria. Journal of the American Chemical Society, 113, 8552.CrossRefGoogle Scholar
  15. Cramer, C. J., & Truhlar, D. G. (2008). A universal approach to solvation modeling. Accounts of Chemical Research, 41, 760.CrossRefGoogle Scholar
  16. Cummins, P. L., & Gready, J. E. (1997). Coupled semiempirical molecular orbital and molecular mechanics model (QM/MM) for organic molecules in aqueous solution. Journal of Computational Chemistry, 18, 1496.CrossRefGoogle Scholar
  17. Dixon, S. L., & Merz, K. M., Jr. (1996). Semiempirical molecular orbital calculations with linear system size scaling. Journal of Chemical Physics, 104, 6643.CrossRefGoogle Scholar
  18. Dixon, S. L., & Merz, K. M., Jr. (1997). Fast, accurate semiempirical molecular orbital calculations for macromolecules. Journal of Chemical Physics, 107, 879.CrossRefGoogle Scholar
  19. Florián, J., & Warshel, A. (1997). Langevin dipoles model for ab initio calculations of chemical processes in solution: Parametrization and application to hydration free energies of neutral and ionic solutes and conformational analysis in aqueous solution. Journal of Physical Chemistry B, 101, 5583.CrossRefGoogle Scholar
  20. Florián, J., & Warshel, A. (1999). Calculations of hydration entropies of hydrophobic, polar, and ionic solutes in the framework of the langevin dipoles solvation model. Journal of Physical Chemistry B, 103, 10282.CrossRefGoogle Scholar
  21. Freindorf, M., & Gao, J. (1996). Optimization of the Lennard-Jones parameters for a combined ab initio quantum mechanical and molecular mechanical potential using the 3-21G basis set. Journal of Computational Chemistry, 17, 386.CrossRefGoogle Scholar
  22. Freindorf, M., Shao, Y., Furlani, T. R., & Kong, J. (2005). Lennard-Jones parameters for the combined QM/MM method using the B3LYP/6-31G*/AMBER potential. Journal of Computational Chemistry, 26, 1270.CrossRefGoogle Scholar
  23. Gao, D., Svoronos, P., Wong, P. K., Maddalena, D., Hwang, J., & Walker, H. (2005). pKa of acetate in water: A computational study. Journal of Physical Chemistry A, 109, 10776.CrossRefGoogle Scholar
  24. Geerke, D. P., Thiel, S., Thiel, W., & van Gusteren, W. F. (2008). QM–MM interactions in simulations of liquid water using combined semi-empirical/classical Hamiltonians. Physical Chemistry Chemical Physics, 10, 297.CrossRefGoogle Scholar
  25. Giese, T. J., & York, D. M. (2007). Charge-dependent model for many-body polarization, exchange, and dispersion interactions in hybrid quantum mechanical/molecular mechanical calculations. Journal of Chemical Physics, 127, 194101.CrossRefGoogle Scholar
  26. Hansen, J. P., & McDonald, I. R. (1976). Theory of simple liquids. London: Academic Press.Google Scholar
  27. Harb, W., Bernal-Uruchurtu, M., & Ruiz-López, M. (2004). An improved semiempirical method for hydrated systems. Theoretical Chemistry Accounts, 112, 204.CrossRefGoogle Scholar
  28. Hirata, F. (2003). Molecular theory of solvation. Dordrecht: Kluwer.Google Scholar
  29. Hirata, F., & Rossky, P. J. (1982). Application of an extended RISM equation to dipolar and quadrupolar fluids. Journal of Chemical Physics, 77, 509.CrossRefGoogle Scholar
  30. Hu, H., & Yang, W. (2009). Development and application of ab initio QM/MM methods for mechanistic simulation of reactions in solution and in enzymes. Journal of Molecular Structure THEOCHEM, 898, 17.CrossRefGoogle Scholar
  31. Hu, H., Lu, Z., Elsner, M., Hermans, J., & Yang, W. (2007). Simulating water with the self-consistent-charge density functional tight binding method: From molecular clusters to the liquid state. Journal of Physical Chemistry A, 111, 5685.CrossRefGoogle Scholar
  32. Izvekov,S.,&Voth,G. A.(2002).Car-Parrinellomoleculardynamicssimulation of liquid water: New results. Journal of Chemical Physics, 116, 10372.CrossRefGoogle Scholar
  33. Kerdcharoen, T., & Morokuma, K. (2002). ONIOM-XS: An extension of the ONIOM method for molecular simulation in condensed phase. Chemical Physics Letters, 355, 257.CrossRefGoogle Scholar
  34. Kerdcharoen, T., & Morokuma, K. (2003). Combined quantum mechanics and molecular mechanics simulation of Ca2 +/ammonia solution based on the ONIOM-XS method: Octahedral coordination and implication to biology. Journal of Chemical Physics, 118, 8856.CrossRefGoogle Scholar
  35. Kirkwood, J. (1934). Theory of solutions of molecules containing widely separated charges with special application to zwitterions. Journal of Chemical Physics, 2, 351.CrossRefGoogle Scholar
  36. Klamt, A., & Schüürmann, G. (1993). COSMO – a new approach to dielectric screening in solvents with explicit expressions for the screening energy and its gradient. Journal of the Chemical Society Perkin Transactions, 2, 799.CrossRefGoogle Scholar
  37. Kongsted, J., Osted, A., & Mikkelsen, K. V. (2003). Coupled cluster/molecular mechanics method: Implementation and application to liquid water. Journal of Physical Chemistry A, 107, 2578.CrossRefGoogle Scholar
  38. Kongsted, J., Söderhjelm, P., & Ryde, U. (2009). How accurate are continuum solvation models for drug-like molecules? The Journal of Computer-Aided Molecular Design, 23, 395.CrossRefGoogle Scholar
  39. Kuo, I.-F. W., Mundy, C. J., McGrath, M. J., & Siepmann, J. I. (2006). Time-dependent properties of liquid water: A comparison of Car-Parrinello and Born-Oppenheimer molecular dynamics simulations. Journal of Chemical Theory and Computation, 2, 1274.CrossRefGoogle Scholar
  40. Laino, T., Mohamed, F., Laio, A., & Parrinello, M. (2006). An efficient linear-Scaling electrostatic coupling for treating periodic boundary conditions in QM/MM simulations. Journal of Chemical Theory and Computation, 2, 1370.CrossRefGoogle Scholar
  41. Laio, A., VandeVondele, J., & Rothlisberger, U. (2002). A Hamiltonian electrostatic coupling scheme for hybrid Car–Parrinello molecular dynamics simulations. Journal of Chemical Physics, 116, 6941.CrossRefGoogle Scholar
  42. Langevin, P. (1905). Magnétisme et Théorie des électrons. Annales de Chimie-Physique, 8, 70.Google Scholar
  43. Luque, F. J., Reuter, N., Cartier, A., & Ruiz-López, M. F. (2000). Calibration of the Quantum/Classical Hamiltonian in Semiempirical QM/MM AM1 and PM3 Methods. Journal of Physical Chemistry A, 104, 10923.CrossRefGoogle Scholar
  44. Luque, F., Curutchet, C., Muñoz-Muriedas, J., Bidon-Chanal, A., Sorietas, I., Morreale, A., Gelpi, J. L., & Orozco, M. (2003). Continuum solvation models: Dissecting the free energy of solvation. Physical Chemistry Chemical Physics, 5, 3827.CrossRefGoogle Scholar
  45. Marten, B., Kim, K., Cortis, C., Friesner, R. A., Murphy, R. B., Rignalda, M. N., Sitkoff, D., & Honig, B. (1996). New model for calculation of solvation free energies: Correction of self-consistent reaction field continuum dielectric theory for short-range hydrogen-bonding effects. Journal of Physical Chemistry, 100, 11775.CrossRefGoogle Scholar
  46. Martín, M. E., Aguilar, M. A., Chalmet, S., & Ruiz-López, M. F. (2002). An iterative procedure to determine Lennard-Jones parameters for their use in quantum mechanics/molecular mechanics liquid state simulations. Chemical Physics, 284, 607.CrossRefGoogle Scholar
  47. Marx, D., & Hutter, J. (2000). Ab initio molecular dynamics: Theory and Implementation. In J. Grotendorst (Ed.), Modern methods and algorithms of quantum chemistry, (p. 301). Jülich: John von Neumann Institute for Computing, NIC series.Google Scholar
  48. Miertus, S., Scrocco, E., & Tomasi, J. (1981). Electrostatic interaction of a solute with a continuum. A direct utilizaion of ab initio molecular potentials for the prevision of solvent effects. Chemical Physics, 55, 117.CrossRefGoogle Scholar
  49. Monard, G., Bernal-Uruchurtu, M. I., van der Vaart, A., Merz, K. M., Jr., & Ruiz-López, M. F. (2005). Simulation of liquid water using semiempirical hamiltonians and the divide and conquer approach. Journal of Physical Chemistry A, 109, 3425.CrossRefGoogle Scholar
  50. Monard, G., Prat-Resina, X., González-Lafont, A., & Lluch, J. M. (2003). Determination of enzymatic reaction pathways using QM/MM methods. International Journal of Quantum Chemistry, 93, 229.CrossRefGoogle Scholar
  51. Nam, K., Gao, J., & York, D. M. (2005). An efficient linear-scaling ewald method for long-range electrostatic interactions in combined QM/MM calculations. Journal of Chemical Theory and Computation, 1, 2.CrossRefGoogle Scholar
  52. Onsager, L. (1936). Electric moments of molecules in liquids. Journal of the American Chemical Society, 58, 1486.CrossRefGoogle Scholar
  53. Pascual-Ahuir, J. L., & Silla, E. J. (1990). GEPOL: An improved description of molecular surfaces. I. Building the spherical surface set. Journal of Computational Chemistry, 11, 1047.CrossRefGoogle Scholar
  54. Reichardt, C. (1979). Solvent effects in organic chemistry. Weinheim, New York: Verlag Chemie.Google Scholar
  55. Riccardi, D., Li, G., & Cui, Q. (2004). Importance of van der Waals Interactions in QM/MM Simulations. Journal of Physical Chemistry B, 108, 6467.CrossRefGoogle Scholar
  56. Rinaldi, D., & Rivail, J. L. (1973). Polarisabilites moléculaires et effet diélectrique de milieu í l’état liquide. Étude théorique de la molécule d’eau et de ses diméres. Theoretica Chimica Acta, 32, 57.CrossRefGoogle Scholar
  57. Rinaldi, D., Ruiz-López, M. F., & Rivail, J. L. (1983). Ab initio SCF calculations on electrostatically solvated molecules using a deformable three axes ellipsoidal cavity. Journal of Chemical Physics, 78, 834.CrossRefGoogle Scholar
  58. Rinaldi, D., Bouchy, A., Rivail, J. L., & Dillet, V. (2004). A self-consistent reaction field model of solvation using distributed multipoles. I. Energy and energy derivatives. Journal of Chemical Physics, 120, 2343.CrossRefGoogle Scholar
  59. Rinaldi, D., Bouchy, A., & Rivail, J. L. (2006). A self-consistent reaction field model of solvation using distributed multipoles. II: Second energy derivatives and application to vibrational spectra. Theoretical Chemistry Accounts, 116, 664.CrossRefGoogle Scholar
  60. Rivail, J., & Rinaldi, D. (1996). Liquid-state quantum chemistry: Computational applications of the polarizable continuum models. In J. Leszczynski (Ed.), Computational chemistry, review of current trends (p. 139). Singapore: World Scientific Publishing.CrossRefGoogle Scholar
  61. Rivail, J. L., & Terryn, B. (1982). Free-energy of an electric charge distribution separated from an infinite dielectric medium by a 3 axes ellipsoidal cavity – application to the study of molecular solvation. Journal of Chemical Physics, 79, 1.Google Scholar
  62. Roca, M., Messer, B., & Warshel, A. (2007). Electrostatic contributions to protein stability and folding energy. FEBS Letters, 581, 2065.CrossRefGoogle Scholar
  63. Silla, E. J., Tuñón, I., & Pascual-Ahuir, J. L. (1991). GEPOL: An improved description of molecular surfaces II. Computing the molecular area and volume. Journal of Computational Chemistry, 12, 1077.CrossRefGoogle Scholar
  64. Sumner, I., & Iyengar, S. S. (2008). Combining quantum wavepacket ab initio molecular dynamics with QM/MM and QM/QM techniques: Implementation blending ONIOM and empirical valence bond theory. Journal of Chemical Physics, 129, 054109.CrossRefGoogle Scholar
  65. Tannor, D. J., Marten, B., Friesner, R. M. R. A., Sitkoff, D., Nicholls, A., Rignalda, M., Goddard, W., & Honig, B. (1994). Accurate first principles calculation of molecular charge distributions and solvation energies from Ab Initio quantum mechanics and continuum dielectric theory. Journal of American Chemical Society, 116, 11875.CrossRefGoogle Scholar
  66. Ten-no, S., Hirata, F., & Kato, S. (1993). A hybrid approach for the solvent effect on the electronic structure of a solute based on the RISM and Hartree-Fock equations. Chemical Physics Letters, 214, 391.CrossRefGoogle Scholar
  67. Ten-no, S., Hirata, F., & Kato, S. (1994). Reference interaction site model self-consistent field study for solvation effect on carbonyl compounds in aqueous solution. Journal of Chemical Physics, 100, 7443.CrossRefGoogle Scholar
  68. Todorova, T., Seitsonen, A. P., Hutter, J., Kuo, I.-F. W., & Mundy, C. J. (2006). Molecular dynamics simulation of liquid water: Hybrid density functionals. Journal of Physical Chemistry B, 110, 3685.CrossRefGoogle Scholar
  69. Tomasi,J.(2004). Thirtyyearsofcontinuumsolvationchemistry:Areview,and prospects for the near future. Theoretical Chemistry Accounts, 112, 184.CrossRefGoogle Scholar
  70. Tomasi, J., Mennucci, B., & Cammi, R. (2005). Quantum Mechanical Continuum Solvation Models. Chemical Reviews, 105, 2999.CrossRefGoogle Scholar
  71. Tongraar, A., Liedl, K. R., & Rode, B. M. (1998). Born-Oppenheimer ab initio QM/MM dynamics simulations of Na+ and K+ in water: From structure making to structure breaking effects. Journal of Physical Chemistry A, 102, 10340.CrossRefGoogle Scholar
  72. Tongraar, A., & Rode, B. M. (2004). Dynamical properties of water molecules in the hydration shells of Na+ and K+: Ab initio QM/MM molecular dynamics simulations. Chemical Physics Letters, 385, 378.CrossRefGoogle Scholar
  73. VandeVondele, J., Krack, M., Mohamed, F., Parrinello, M., Chassaing, T., & Hutter, J. (2005). Quickstep: Fast and accurate density functional calculations using a mixed Gaussian and plane waves approach. Computer Physics Communications, 167, 103.CrossRefGoogle Scholar
  74. Warshel, A. (1991). Computer modeling of chemical reactions in enzymes and solutions. New York: Wiley.Google Scholar
  75. Warshel, A., & Russel, S. T. (1984). Calculations of electrostatic interactions in biological systems and in solutions. Quarterly Review of Biophysics, 17, 283.CrossRefGoogle Scholar
  76. Warshel, A., Sharma, P. K., Kato, M., & Parson, W. W. (2006). Modeling electrostatic effects in proteins. Biochimica et Biophysica Acta, 1764, 1647.CrossRefGoogle Scholar
  77. Woods, C. J., Manby, F. R., & Mulholland, A. J. (2008). An efficient method for the calculation of quantum mechanics/molecular mechanics free energies. Journal of Chemical Physics, 128, 014109.CrossRefGoogle Scholar
  78. Yamabe, S., Minato, T., & Inagaki, S. (1988). Ab initio structures of transition-states in electrophilic addition-reactions of molecular halogens with ethene. Journal of the Chemical Society Chemical Communications, 532, 35.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Gerald Monard
    • 1
  • Jean-Louis Rivail
    • 2
  1. 1.Theoretical Chemistry and Biochemistry Group SRSMCNancy-University CNRS Boulevard des AiguillettesVandoeuvre-les-NancyFrance
  2. 2.Theoretical Chemistry and Biochemistry Group SRSMCNancy-University CNRS Boulevard des AiguillettesVandoeuvre-les-NancyFrance

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