Essentials of Computational Chemistry

390 11 IMPLICIT MODELS FOR CONDENSED PHASES
O
N
H
Figure 11.2 4-Pyridone is considerably more polar than its hydroxypyridine tautomer, and its
extended π system also renders it highly polarizable. As a result, polar solvents shift the equilibrium
between the two strongly to the right in comparison to the gas phase
phenomenon are known; one of the most striking is for the tautomeric equilibrium between
4-hydroxypyridine and 4-pyridone, where aqueous solvation changes the 298 K equilibrium
constant by some six orders of magnitude (Figure 11.2; see Beak 1977).
Figure 11.1 also indicates that the free energy of activation for the left-to-right reaction
is lower on the solvated surface than on the gas-phase surface, so that the rate will be
increased in solution compared to the gas phase. Thus, differential solvation of minima and
connected TS structures can affect relative rates. Again, many examples are known. One
of the most carefully studied is the effect of solvation on the SN2 reaction of chloride ion
with chloromethane: While the gas-phase activation free energy is around 3 kcal mol −1 ,
the diffuse negative charge associated with the SN2 transition state structure compared to a
chloride ion makes the TS structure much less well solvated than the reactants, and aqueous
solvation decreases the 298 K rate by more than 15 orders of magnitude (Chandresekhar,
Smith, and Jorgensen 1985).
Given our picture of the free energy surface in solution deriving from addition of solvation
free energy to the gas-phase PES, and noting that equilibria and kinetics can be well estimated
based only on knowledge of the relative energies of appropriate stationary points, we may
represent a protocol for computing these relative energies from the thermodynamic cycle
in Figure 11.3. In order to compute the lower horizontal leg of the cycle, corresponding to
∆G
A (gas) + B (gas) + ...
W (gas) + X(gas) + ...
o (gas)
∆G o S(A)
∆G o S(B)
∆G o S(...)
A (sol) + B (sol) + ...
W (sol) + X (sol) + ...
∆Go (sol)
O
N
H
∆G o S(W)
∆G o S (X)
∆G o S(...)
Figure 11.3 Cycle for computation of a free-energy change in solution