Solvation Models

As we have noted several times, both the molecular mechanics calculations performed by PCModel and the MO calculations of SPARTAN and GAUSSIAN treat the molecules as alone in a vacuum: no neighboring molecules of the same kind, and no solvent.

PCModel does allow us to change the value of the dielectric constant that is used in calculations of dipolar repulsions.

We would expect that when a real molecule passes from the gas phase into solution

The energy terms associated with these polarizations are generally referred to as ENP (Electronic, Nuclear, and Polarization), and are primarily a function of the bulk dielectric.

The current methods for solvation modeling generally follow one of two approaches.

Neither of these continuum approaches as described attempts to take account of the energetic effects in the CDS terms, thus focusing on a different set of contributions to solvation than the molelcular dynamics methods.

Cramer, Truhlar, and their coworkers, have developed the SMx set of solvation models in an attempt to address these limitations.6 Their models are incorporated into SPARTAN, along with refinements developed by Hehre and coworkers at Wavefunction. The C-T models were specifically developed to be associated with the AM1 and PM3 semi-empirical Hamiltonians. (However, this group has very recently published an extension of their methods to some ab initio basis sets.)

These methods use an extended Born treatment of the ENP solvation terms.

As implemented in SPARTAN, however, these methods result in calculation of a solvation enthalpy as the difference in enthalpy of formation between the molecule in the gas phase and the molecule in solution.

In order to examine how the inclusion of solvation influences calculated structures and energies, you may wish to examine the equilibrium below:

These molecules are small enough that you can do full optimizations in both gas phase and water (use either AM1 or PM3 with the C-T model; it gives more negative, and therefore better, energies.) Interestingly, the energy of the pyridinol is strongly dependent upon the orientation of the O-H bond; syn- to N is lower than anti-. (Why?)

In principle, solvation energies calculated by the Cramer-Truhlar method are transferable from semi-empirical to ab initio structures. In this case, one should optimize the geometry with the appropriate ab initio basis set, and then do single point AM1 calculations using the ab initio geometry to evaluate the solvation energy. The result can then be applied to the ab initio energy. (This approach is now implemented automatically in Spartan ab initio calculations.)

GAUSSIAN provides a variety of SCRF (Self-Consistent Reaction Field) solvation models.

Clearly, solvation modeling is an extremely complex area, and requires considerable sophistication for proper usage.

References

The references cited are intended to be a representative selection, rather than an exhaustive compilation. You also may wish to read the paper by Still and co-workers8 on inclusion of solvation in molecular mechanics calculations. The Cramer-Truhlar treatment is based on similar assignments of solvation properties to atom types.

1. (a) Allen, M. P.; Tildesley, D. J. Computer Simulations of Liquids, Oxford University Press, London, 1987; (b) Haile, J. M. Molecular Dynamics Simulation, Wiley-Interscience, New York, 1992; (c) Warshel, A. Computer Modeling of Chemical Reactions in Enzymes and Solutions, Wiley-Interscience, New York, 1991.

2. (a) Jorgenson, W. L. Acc. Chem. Res., 1989, 22, 184; (b) Beveridge, D. L.; DiCapua, F. M. Ann. Rev. Biophys. Chem., 1989, 18, 431.

3. (a) Kollman, P. A.; Merz, K. M. Acc. Chem. Res., 1990, 23, 246; (b) Straatsma, T. P.; McCammon, J. A. J. Chem. Phys., 1991, 95, 1175.

4. (a) Onsager, L. J. Am. Chem. Soc., 1936, 58, 1486; (b) Kirkwood, J. G. J. Chem. Phys., 1939, 7, 911; (c) Tapia, O.; Goscinski, O. Mol. Physics., 1975, 29, 1653.

5. (a) Born, M. Z. Physik, 1920, 1, 45; (b) Rashin, A. A.; Honig, B. J. Phys. Chem., 1985, 89, 5588.

6. Cramer, C. J.; Truhlar, D. G., "Solvation Models for Free Energies in Aqueous Solution", Chem. Rev., 1999, 99, 2161.

7. (a) Eisenberg, D.; McLachlan, A. D. Nature, 1986, 319, 199; (b) Ooi, T.; Oobatake, M.; Nemethy, G.; Scheraga, H. A. Proc. Natl. Acad. Sci., 1987, 84, 3086.

8. Still, W. C.; Tempczak, A.; Hawley, R. C.; Hendrickson, T. J. Am. Chem. Soc., 1990, 112, 6127.

9. Onsager, L. J. Am. Chem. Soc., 1938, 58, 1486.

10. (a) Miertus, S.; Tomasi, J. Chem. Phys., 1982, 65, 239; (b) Miertus, S.; Scrocco, E.; Tomasi, J. Chem. Phys., 1981, 55, 117.

11. Foresman, J. B.; Keith, T. A.; Wiberg, K. B.; Snoonian, J.; Frisch, M. J. J. Phys. Chem., 1996, 100, 16098.

12. Keith, T. A.; Frisch, M. J. manuscript in preparation.

Useful Reviews

Bashford, D.; Case, D. A., "Generalized Born Models of Macromolecular Solvation Effects", Ann. Rev. Phys. Chem., 2000, 51, 129.

Cramer, C. J.; Truhlar, D. G., "Implicit Solvation Models: Equilibria, Structure, Spectra, and Dynamics", Chem. Rev., 1999, 99, 2160.


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