Computational Chemistry

mol"^1 being a current standard of “chemical accuracy” [ 50 ]. High-accuracy multi-
step methods (Section 5.5.2.2b) other than the computationally very demanding
CBS-APNO gave reasonable pKavalues; when more than one conformation (albeit
in the gas phase) was significant, conformationally averaged energies were used. The
choice of solvation method, and even the version of a particular method, is important.
Using HF/6-31+G* and another version of the CPCM method, we obtained solvation
free energies for CH 3 COOH and CH 3 COO– of"32.9 and"316.1 kJ mol"^1 respec-
tively (cf."32.3 and"324.6 kJ mol"^1 in [ 46 ]). These values yieldDGdiss,s¼
35.8 kJ mol"^1 and pKa¼6.3. With SM8 we got"21.16 and"325.5 kJ mol"^1 ,
givingDGdiss,s¼14.7 kJ mol"^1 and pKa¼2.6. This shows that even with the choice
of a generally good solvation method, one should check out the procedure with some
compounds of known pKa.
An accurategas-phasedissociation energy is important too. The very accurate
CBS-APNO method can seldom be used, being limited to about five heavy atoms
(atoms other than H or He;Table 5.10) and being unable to handle other than C,
H, N, O, F. The much less size-challenged CBS-4M is insufficiently accurate for
meaningful pKacalculations, but CBS-QB3 and G3(MP2)are useful for up to about
9–13 heavy atoms (Table 5.10and [ 46 ]). For large molecules isodesmic-type
reactions (Section 5.5.2.2) may be useful. Consider Fig.8.5; here is an example,
where RCOOH is CFH 2 COOH. Since this has only five heavy atoms we can use a
direct calculation ofDGhigh,1with CBS-APNO as a check on the accuracy of the
roundabout isodesmic method. CH 2 FCOOH has two conformations of very similar
(gas-phase) energy. The “low-level” method chosen for the isodesmic reaction was
the DFT (Chapter 7) B3PW91/6-31G(d,f), because in related work a number of
perflurorinated acids, with up to 31 heavy atoms, had been studied at this level. The
relevant quantities (cf. Fig.8.5) are:
Term (1) is the gas-phase isodesmically calculated deprotonation free energy of
the “big” acid CH 2 FCOOH; it is to be calculated from terms (2) and (3).

∆Ghigh, 2

reaction 3

RCOOH + CH 3 COO–

RCOO– + H+ + CH 3 COO–

RCOO– + CH 3 COOH

Wanted

∆Ghigh, 1

reaction 1

reaction 2

∆Giso

Fig. 8.5 The principle behind using isodesmic reactions for calculating an accurate deprotonation
free energy for an acid too big to yield directly to a high-accuracy calculation. Note that reaction 1
is really only for deprotonation of RCOOH and reaction 3 is only for deprotonation of CH 3 COOH;
the anion on the starting side of those reactions was added only for logical consistency, and
cancels. (1)DGhigh,1is the wanted quantity, the free energy of deprotonation of the large acid
RCOOH, but cannot be calculated directly. (2)DGisois the free energy of the isodesmic reaction
and can be calculated fairly accurately. (3)DGhigh,2is the free energy of deprotonation of
CH 3 COOH and can be calculated accurately directly (any appropriate reference acid could be
used here, and an experimental free energy could be used if available). For conservation of energy:
DGhigh,1¼DGisoþDGhigh,2

8.1 Solvation 533