the gas phase but not in solution reflects the fact that in the absence of solvent the
attacking anion solvates the carbon of its victim prior to covalent bonding.
2.First principles calculation of pKa. Thermodynamics seems to assure us that
the pKaof an acid is simply related to the Gibbs free energies of the hydrated
(we will limit ourselves to water here) acid, conjugate base and proton. Surpris-
ingly, in a study of 64 organic and inorganic acids (accompanied by a brief review
of theoretical methods of calculating pKa), Klamt et al. concluded that “the
experimental pKascale depends differently on the free energy of dissociation
than generally assumed” and “[passed] the problem forward to the scientific
community” [ 41 ]. Kelly et al. responded to this challenge, showing that adding
one water molecule to some anions and also using the SM6 model “significantly
improves the agreement between the calculated pKa value and experiment” [ 42 ].
However, the mixed microsolvation/continuum approach used there may not be
uniform enough to provide a satisfying ansatz for the general theoretical calculation
of pKa.
COSMO models [ 27 – 30 ] were compared with the SM approach [ 22 ] by Klamt
[ 43 ] and by Cramer and Truhlar [ 44 ]. A very recent paper by Klamt and coworkers
[ 45 ] shows that improved calculated pKa values are obtained for the limited domain
of strong to moderately weak acids by a “cluster-continuum” method in which the
acid and conjugate base are each associated with one or a few solvent molecules
and this “cluster” is then continuum-calculated with COSMO-RS. The authors
point out, however, that for the calculation of pKa“a consistent and generally
applicable method is still lacking”. This paper clarifies the problem raised in [ 41 ].
The matter is under study.^1
I cite three papers to show that standard continuum calculationscangive
satisfactory first-principles pKavalues: Shields and coworkers used a thermody-
namic cycle with gas phase and continuum calculations to obtain satisfactory
results for six simple carboxylic acids [ 46 ]. These were “absolute” calculations in
the sense that no acid was used as a reference point, although the experimental gas
phase free energy and aqueous solvation energy of the proton were resorted to. Not
quite as esthetically satisfying perhaps, were “relative” calculations in which acetic
acid was used as a reference compound [ 47 ]. Similar to the absolute acid calcula-
tions was work with phenols that was said to be “among the most accurate of any
such calculations for any group of compounds” [ 48 ].
The principles behind the absolute pKacalculations in [ 46 ] are illustrated with
the aid of Fig.8.4. The program was Gaussian 98 [ 49 ], and several ab initio levels
and solvation methods were explored; the favored ones are given here, with values
for acetic acid, CH 3 COOH:
Term (1) calculated at the HF/6-31+G* level with the CPCM continuous solva-
tion method was 32.3 kJ mol"^1 , i.e. the solvation free energy of CH 3 COOH
(^1) A. Klamt, personal communication, 2010 March 13.
8.1 Solvation 531