Essentials of Computational Chemistry

11.1 CONDENSED-PHASE EFFECTS ON STRUCTURE AND REACTIVITY 389
measured. This point is made insofar as we will discuss below, for example, theoretical
predictions for the electrostatic component of the free energy of solvation. However, insofar
as this quantity is not an experimental observable, absolute judgments of quality comparing
one level of theory to another are necessarily model-dependent.
11.1.2 Solvation as It Affects Potential Energy Surfaces
In order to visualize the effects of solvation on structure and reactivity, it is helpful to
consider the potential energy surface created by adding the free energy of solvation point
by point to the gas-phase PES, as illustrated in Figure 11.1. (To be rigorous, one really
should use a gas-phase free-energy surface so as not to be haphazardly mixing potential and
free energies, but for qualitative purposes, we may ignore this technical point.) Processes
in solution may be regarded as occurring on the lower surface, and all of the phase-space
dimensions associated with solvent molecules have been averaged over in computing its
energies.
Figure 11.1 illustrates several critical concepts associated with solvation. First, note that
the reaction process depicted on the gas-phase surface joins two minima of roughly equal
energy, while that on the lower surface is quite exergonic in the left-to-right direction.
This derives from the minimum-energy structure at the larger x coordinate having a more
negative free energy of solvation. Differential solvation of two (or more) minima implies
a different equilibrium constant in solution than in the gas phase. Many examples of this
E
gas-phase
surface
solvated
surface
(x,y)
∆G o S(x,y)
Figure 11.1 A two-dimensional gas-phase PES and the corresponding PES derived from adding the
free energy of solvation to every point. This process is illustrated for point (x,y). Thick lines on the two
surfaces indicate some chemical reaction proceeding from one minimum-energy structure to another.
Note that there is no requirement for the x and y coordinates of equivalent stationary points on the
two surfaces to be the same