Essentials of Computational Chemistry

11.1 CONDENSED-PHASE EFFECTS ON STRUCTURE AND REACTIVITY 391
the process in solution, one need only take appropriate sums and differences of the upper
horizontal leg and the vertical legs, viz.
G o (sol) = Go (gas) + G o S (W) + Go S (X) +··· − G o S (A) + Go S (B) +··· (11.2)
As the upper leg is a gas-phase quantity, it can be computed taking advantage of all of the
technology discussed in earlier chapters. The two vertical legs, on the other hand, consist
exclusively of free energies of solvation. Thus, the development of models to efficiently
compute molecular solvation free energies has been a high priority.
A compromise representation of our discussion thus far is to consider the effects of solvation
on a one-dimensional slice through the energy surface–what we normally call the
reaction coordinate–as illustrated in Figure 11.4. This representation is more informative
than the free-energy cycle in showing how the structures of the stationary points differ in
the gas phase and solution, in addition to their relative energies. A change in structure is
indicated by a movement of the stationary point along the coordinate axis. Particularly for
TS structures, which may be characterized by one or more soft normal modes and/or a soft
reaction coordinate, changes in structure induced by solvation may be important.
Note, however, that this one-dimensional representation can be somewhat misleading if
it is taken to be a computational protocol. The trouble is that the one-dimensional slice of
E
∆G S o (R)
R ‡
∆G S o (‡)
Arbitrary coordinate
P
∆G S o (P)
∆G o,‡
gas
∆G o,‡
sol
∆G o,rxn
gas
∆G o,rxn
sol
Figure 11.4 Gas-phase (upper) and solution (lower) reaction coordinates, and the thermodynamic
cycles that connect them via free energies of solvation of the various stationary points (vertical lines).
Note the significant left to right movement of all stationary points, and particularly the TS structure,
on going from the gas phase to solution