Term (2) is the gas-phase isodesmic free energy for proton transfer from
RCOOH to the conjugate base CH 3 COO"of our reference acid. At the B3PW91/
6-31G(d,f) level this is ["327.598929 " 228.969707] " ["328.158016 "
228.394842]¼"0.015778 hartrees¼"41.43 kJ mol"^1
Term (3) is the gas-phase free energy of deprotonation of the reference acid
CH 3 COOH; this can be calculated accurately with the high-level CBS-APNO,
giving¼["228.500394"0.010000]"["229.053416]¼0.543022 hartees¼
1425.7 kJ mol"^1.
The gas-phase isodesmically calculated deprotonation free energy of
CH 2 FCOOH follows (Fig.8.4):
DGhigh; 1 ¼DGisoþDGhigh; 2¼" 41 : 4 þ 1425 :7 kJ mol"^1 ¼ 1384 :3 kJ mol"^1 :Compare this with a direct CBS-APNO calculation on CH 2 FCOOH:
DGhigh,1(APNO)¼["327.754836"0.010000]"["328.290375]¼0.525539
hartrees¼1379.8 kJ mol"^1. The isodesmically secured energy is 4.5 kJ mol"^1
higher than the direct APNO value. The NIST website gives 1,385–1,387 kJ mol"^1
for the free energy of deprotonation, with an estimated error of 8.4 kJ mol"^1 [ 51 ].
If we take the deprotonation energy of CH 2 FCOOH to be actually in the range
1,380–1,387, the isodesmic calculation works well. But note that an error of 1 pKa
unit results from a free energy error of only 5.7 kJ mol"^1 , and an error of 0.5 pKa
units from an error of only 2.9 kJ mol"^1. We are working at the edge of fairly
accurate pKavalues.
Hybrid solvation: Implicit solvation plus Explicit solvation; microsolvation
subjected to the continuum method. Here the solute molecule is associated with
explicit solvent molecules, usually no more than a few and sometimes as few as
one, and with its bound (usually hydrogen-bonded) solvent molecule(s) is subjected
to a continuum calculation. Suchhybridcalculations have been used in attempts to
improve values of solvation free energies in connection with pKa:[ 42 ], and also
[ 45 ] and references therein. Other examples of the use of hybrid solvation are the
hydration of the environmentally important hydroxyl radical [ 52 ] and of the
ubiquitous alkali metal and halide ions [ 53 ]. Hybrid solvation has been surveyed
in a review oriented toward biomolecular applications [ 54 ].
If one is investigating a reaction with the intimate participation of solvent
molecules, then in principle they should be explicitly considered, as in the study
of the hydrolysis of CH 3 Cl with explicit water molecules (Hydrolysis of CH 3 Cl
with 13 explicit water molecules, above), for here at least one water molecule is a
reactant, not a mere enfolding medium. The implicitþcontinuum approach may be
useful if one seeks not only insight into a mechanism, as inThe effect of micro-
solvation on the E2 and SN2 reaction F"þC 2 H 5 FþnHF, above, but also wants
relative energies in solution of various species involved. An attempt to do this
would place the reactants (probably representing a stationary point), e.g. [F"/
C 2 H 5 F/explicit solvent] in a continuum cavity to obtain a free energy of solvation.
534 8 Some “Special” Topics