Subject: Re: CCL:Frequency job in solvent

From: Christopher Cramer <cramer*at*pollux.chem.umn.edu>
Date: Wed, 28 Apr 2004 11:39:10 -0500 (CDT)

David,
> 
> Question for other CCL-ers: 
> Are solvent effects on vibrational frequencies primarily of electrostatic origin?  That is what the SCRF method assumes, isn't it?  But I would think that van der Waals forces (otherwise known as bumping into neighboring solvent molecules) would be the main factor. 
> 

   There are several levels of response to your question.

   Ben-Naim has first codified the intuitively reasonable relationship

delta-G(solvation) = delta-G(solute-solvent coupling) + delta-G(delta-Q)

where the first term on the right-hand-side is associated with interactions
between the solute and the solvent (and changes in interactions between
solvent molecules with each other) and the second term is associated with
changes in the solute partition function. The most obvious of these would
be, for example, if you were considering a change in standard-state volume
(e.g., using 1 mol per 24.5 L for your gas-phase standard state and 1 mol
per 1 L for your solution standard state). Such a change in standard-state
volume leads to a change in the translational partition function that
affects the translational entropy and hence affects the free energy of
transfer. Of course, there could also be a change in the rotational and
vibrational partition functions too! However, this is much trickier than
the trivial correction for the standard-state volume. A solute presumably
does not HAVE a rotational partition function -- those degrees of freedom
are converted into solute/solvent librational modes, the natures of which
are quite difficult to determine either experimentally OR theoretically.
Hence, essentially all continuum models proceed from the assumption that
there is NO delta-Q affect on the electronic, rotational, or vibrational
partition functions, and transform experimental data as appropriate to make
the standard-state volume a constant, and parameterize against the
remaining coupling free energy (thus, by parameterization, any error in
the assumption of zero delta-Q gets buried in the fit).

   Second, as for the coupling free energy itself, it is divided up into
electrostatic and non-electrostatic components. The electrostatic part is
nearly always determined either from solution of the Poisson or generalized
Born equations (using a self-consistent reaction field formalism if the
solute is being treated at a QM level) and the non-electrostatic part is
typically (but not always) added at the end in a more or less parametric
fashion. To the extent that "bumping into other molecules" is associated
with a cavitation term that becomes more positive with increasing
solvent-accessible surface area along a vibrational mode (as one example of
how such a term is often calculated), this affect will appear in a
continuum model, as will the electrostatics.

   However, let us say that you really ARE interested in how solvation
affects the vibrational frequencies. It is not necessarily formally correct
to recompute the harmonic-oscillator force constants with the dielectric
continuum turned on, because the time scale of the vibration may be
considerably faster than the bulk dielectric response time of the solvent.
That is, vibration is subject to a certain degree of non-equilibrium
solvation, but continuum solvent models are equilibrium in nature unless a
frequency-dependent dielectric constant is employed. A nice article
addressing the precise issue of IR in solution is Rivail, J.-L.;
Rinaldi, D.; Dillet, V., "Solvation Effects on Infrared Spectroscopy:  A
Computational Approach" Mol. Phys. 1996, 89, 1521-1529.

   A more general discussion of many of the above issues that is, I hope,
still very useful, is the review that Don Truhlar and I wrote 5 years ago
Cramer, C. J.; Truhlar, D. G., "Implicit Solvation Models:
Equilibria, Structure, Spectra, and Dynamics" Chem. Rev. 1999, 99,
2161-2200.

Best regards,

Chris 
-- 

Christopher J. Cramer
University of Minnesota
Department of Chemistry
207 Pleasant St. SE
Minneapolis, MN 55455-0431
--------------------------
Phone:  (612) 624-0859 || FAX:  (612) 626-2006
Mobile: (612) 597-5275
cramer*at*pollux.chem.umn.edu
http://pollux.chem.umn.edu/~cramer
(website includes information about the textbook "Essentials
    of Computational Chemistry:  Theories and Models")