Handbook of Solvents - George Wypych - ChemTech - Ventech!

4.3 Polar solvation dynamics 133
trasts the results obtained from such simulations with those obtained from linear response
continuum models. In particular we focus on the following issues:
• How well can the solvation process be described by linear response theory?
• To what extent can the dynamics of the solvation process be described by continuum
dielectric theory?
• What are the signatures of the solute and solvent structures in the deviation of the
observed dynamics from that predicted by continuum dielectric theory?
• What are the relative roles played by different degrees of freedom of the solvent
motion, in particular, rotation and translation, in the solvation process?
• How do inertial (as opposed to diffusive) solvent motions manifest themselves in
the solvation process?
This chapter is not an exhaustive review of theoretical treatments of solvation dynamics.
Rather, it provides, within a simple model, an exposition of the numerical approach to
this problem. It should be mentioned that a substantial effort has been recently directed towards
developing a theoretical understanding of this phenomenon. The starting point for
such analytical efforts is linear response theory. Different approaches include the dynamical
mean spherical approximation (MSA), 3,4 generalized transport equations, 5-8 and ad hoc
models for the frequency and wavevector dependence of the dielectric response function
ε(k, ω).
9 These linear response theories are very valuable in providing fundamental under-
standing. However, they cannot explore the limits of validity of the underlying linear response
models. Numerical simulations can probe non-linear effects, but are very useful also
for the direct visualization and examination of the interplay between solvent and solute
properties and the different relaxation times associated with the solvation process. A substantial
number of such simulations have been carried out in recent years. 10,11 The present
account describes the methodology of this approach and the information it yields.
4.3.2 CONTINUUM DIELECTRIC THEORY OF SOLVATION DYNAMICS
The Born theory of solvation applies continuum dielectric theory to the calculation of the
solvation energy of an ion of charge q and radius a in a solvent characterized by a static dielectric
constant, εs. The well known result for the solvation free energy, i.e., the reversible
work needed to transfer an ion from the interior of a dielectric solvent to vacuum, is
W q
2 ⎛ 1 ⎞
= ⎜ −
a
⎜ 1⎟
2
⎟
⎝εs⎠
[4.3.1]
Eq. [4.3.1] corresponds only to the electrostatic contribution to the solvation energy.
In experiments where the charge distribution on a solute molecule is suddenly changed (e.g.
during photoionization of the solute) this is the most important contribution because short
range solute-solvent interactions (i.e., solute size) are essentially unchanged in such processes.
The origin of W is the induced polarization in the solvent under the solute electrostatic
field.
The time evolution of this polarization can be computed from the dynamic dielectric
properties of the solvent expressed by the dielectric response function εω ( ). 12 Within the
usual linear response assumption, the electrostatic displacement and field are related to each
other by