Subject: Re: CCL:G:SCRF and pKa

From: Christopher J Cramer <[email-masked]>
Date: Tue, 3 Sep 1996 14:37:24 -0500 (CDT)

Jeremy,

> 1) Can someone point me in the direction of a study of, or give me an opinion 
> of, the reliablity of the IPCM model vs. other (SCRF) methods for calculating 
> solvation energies of species in dilute aqueous solution. I'm particularly 
> interested in species for which hydrogen bonding is likely to be significant, 
> and the comparative treatment of hydroxy vs. oxo tautomers. My preliminary
> IPCM results consistantly indicate greater aqueous stabilisation of hydroxy 
> vs. oxo tautomers, apparently in contradiction both with published results
> from other methods (FEP, Onsage, PCM) and generally accepted wisdom if I 
> understand correctly.

   Awful (IPCM that is). The trouble is, IPCM calculates only the
electrostatic part of the solvation free energy (and doesn't necessarily do a
terribly good job of that -- the method remains unpublished and largely
untested to the best of my knowledge). However, for a neutral molecule with
hydrophilic functional groups, other components of the solvation free energy
may be quite large. Note that Onsager is even worse, since not only does it
restrict itself to the electrostatics, but it truncates the molecular
electronic multipole distribution at the dipole term. PCM is also only
electrostatics unless a correction is made a la Tomasi. FEP includes all
solvation components by virtue of the force field, but cannot account for
quantum mechanical polarization of the wave function by the medium other than
by parameterization of the two-body force field.

> 2) I'm interested in the state of the art for the ab initio calculation
> of pKa. I'd greatly appreciate comments & suggestions for methodology, 
> or pointers to recent literature. 

   Bottom line is that it is tremendously difficult. Most of the work in this
area has come out of the biological arena with a focus on the titration state
of proteins. Most of the work has been classical, not quantum mechanical.
Finite difference Poisson(-Boltzmann) methods have been studied most
carefully. Again, no accounting for non-electrostatic effects has been made
as far as I know. I don't have references handy, but names like Honig,
Gilson, Rashin, Pettit, Nicholls, Karplus, Scheraga, etc. come to mind.

   For organic molecules, the expert system SPARC, courtesy of Butch Carreira
at the Univ. of Georgia and Sam Karickhoff at EPA Athens is pretty hard to
beat -- I think they published those results somewhere recently. I believe
SPARC also has a Web site, and calculation of pKa's over the internet is
either already active or promised for the very near future (as long as you
know how to represent your molecule as a SMILES string). 

> A means of attacking pKa with SCRF I'm considering: in order to make 
> most use of cancellation of systematic error, modelling the overall 
> reaction:

>     HA + OH-  ->  A- + H2O

> Good estimates of the gas-phase deltaG of reaction should be calculable,
> using Hartree-Fock frequencies and correllated theories with diffuse
> functions for energies. An accurate estimate of deltaG in dilute aqueous 
> solution at 298K should lead to pKa. How best to go from the former to the 
> latter? 

   We've done the parent reaction many times, and it's a bit scary. The
experiment is well known. To get a good theoretical number requires at least
an augmented polarized valence quadruple zeta basis (primarily because
hydroxide is so hard to do) and correlated theory. Not cheap!

> IF (from question 1) the IPCM model (or other SCRF) gives reasonable 
> relative aqueous solvation single point energies from gas phase geometries, 
> could these be simply be used to correct the gas-phase free energies to 
> determine an aqueous phase free energy of reaction and hence pKa with any 
> degree of confidence?

   In my personal opinion, you'll never be able to hope for better than +/- 6
kcal/mol (actually, bigger than that if you don't plan to include
non-electrostatic effects.

> Alternatively, as opposed to single point calculations, optimisation and 
> frequency calculations could be performed with SCRF for aqueous solution, 
> and from these, the free energy of reaction in solution derived and hence 
> pKa. However, Gaussian94 only offers these calculations for the Onsager 
> model using uncorrelated theories, and I have my doubts as to how well 
> this would handle such systems.

   As you suspect, they'd be terrible. The problem is really not trivial.

   We published a paper a few years back discussing all of the above issues
at some length for a series of isoxazole heterocycles. It is JACS 1993, 115,
8810 (Solvation Effects on Heterocyclic Equilibria in Aqueous Solution). You
might find it of interest.

Chris

-- 

Christopher J. Cramer
University of Minnesota
Department of Chemistry
207 Pleasant St. SE
Minneapolis, MN 55455-0431
--------------------------
Phone:  (612) 624-0859 || FAX:  (612) 626-7541
[email-masked]
http://pollux.chem.umn.edu/~cramer