Essentials of Computational Chemistry

11.1 CONDENSED-PHASE EFFECTS ON STRUCTURE AND REACTIVITY 387
than simply measuring the concentrations in the two distinct phases are typically required).
Different physical effects contribute to the overall solvation process; of these, the most
important components are electrostatic interactions, cavitation, changes in dispersion, and
changes in bulk solvent structure.
Equilibrium electrostatic interactions between a solute and a solvent are always nonpositive
– they are zero if the solute is characterized by no electrical moments (e.g., a noble
gas atom) and negative otherwise, i.e., attractive. It is easiest to visualize the electrostatic
interactions as developing in a stepwise fashion. Consider a solute A characterized by electrical
moments; for simplicity, consider only the dipole moment. When A passes from the
gas phase into a solvent, the solvent molecules, if they have permanent moments of their
own, reorient so that, averaged over thermal fluctuations, their own dipole moments oppose
that of the solute. In an isotropic liquid with solvent molecules undergoing random thermal
motion, the average electric field at any point will be zero; however, the net orientation
induced by the solute changes this, and the field induced by introduction of the solute is
sometimes called the ‘reaction field’.
Of course, the presence of an electric field means that a term accounting for the interactions
of charged particles with this field should be included in the solute Hamiltonian. When it is
included, the effect is to increase the solute polarity in a fashion proportional to the solute
polarizability and the strength of the external field. Thus, the dipole moment of A increases.
The solvent, seeing this increase, itself polarizes and moreover increases its own orientation
to oppose A’s dipole, and so on.
However, neither the orientation/polarization of the solvent nor the electronic polarization
of A is without cost. In the first instance, since solvent molecules are oriented to oppose
the dipole moment of A, they each interact in an unfavorable sense with the reaction field
they create. Moreover, to the extent they have lost some configurational freedom, there is an
associated free-energy cost. As for the cost of electronic polarization, this may be viewed as
the gas-phase cost (as computed with the gas-phase Hamiltonian) associated with distortion
of the wave function away from the gas-phase minimum. As a result of these opposing
energetics, the polarization of the solute/solvent system stops at that point where any energy
gain from additional polarization is exactly balanced by the energy cost to achieve that
polarization. Under some fairly mild assumptions from so-called linear response theory, one
can show that this occurs when the energy cost up to a certain point becomes equal to one
half of the total interaction energy between the solute and the solvent.
It cannot be overemphasized that solvation changes the solute electronic structure. As
noted above, dipole moments in solution are larger than the corresponding dipole moments
in the gas phase. Indeed, any property that depends on the electronic structure will tend
to have a different expectation value in solution than in the gas phase. How large will the
difference be? That depends on the strength of the solute–solvent interactions. Table 11.1
lists dipole moments computed in the gas phase, chloroform, and water for six nucleic
acid bases at the HF/6-31G(d) level using the SM5.42R continuum solvation model that is
described in more detail below. Note that the increases in dipole moments on going from
the gas phase to water range from about 25 to 33 percent for these molecules; a smaller but
still substantial increase is predicted in chloroform solution.