Handbook of Solvents - George Wypych - ChemTech - Ventech!

4.3 Polar solvation dynamics 141
Figure 4.3.3. The function S(t) obtained with ε ′ = 17.0
(solid line, same as in Figure 4.3.2), together with the
same function obtained with ε ′ = 1.0 (dashed line). ε′ is
the continuum dielectric constant associated with the reaction
field boundary conditions. [From Ref. 11a].
withn=1(ethyl methyl ether, full line) and
n = 2 (1,2-methoxy ethoxy ethane, dotted
line). In these solvents the main contribution
to the solvation energy of a positive ion
comes from its interaction with solvent oxygen
atoms. Because of geometric restriction
the number of such atoms in the ion’s first
solvation shell is limited, leading to a relatively
early onset of dielectric saturation.
Figure 4.3.2 shows the time evolution
of the solvation functions C(t), Eq. [4.3.25]
and S(t) (Eq. [4.3.24]). C(t) is evaluated
from an equilibrium trajectory of 220 ps for
a system consisting of the solvent and a
charged or uncharged atom. The
nonequilibrium results for S(t) are averages
over 25 different trajectories, each starting
from an initial configuration taken from an equilibrium run of an all-neutral system following
switching, at t=0,ofthecharge on the impurity atom from q=0toq=e.
These results show a large degree of similarity between the linear response (equilibrium)
and nonequilibrium results. Both consist of an initial fast relaxation mode that, at
closer inspection is found to be represented well by a Gaussian, exp[-(t/τ) 2 ], followed by a
relatively slow residual relaxation. The initial fast part is more pronounced in C(t). The latter
is also characterized by stronger oscillations in the residual part of the relaxation. The
fact that the linear response results obtained for equilibrium simulations with an uncharged
solute and with a solute of charge q are very similar give further evidence to the approximate
validity of linear response theory for this systems.
The sensitivity of these results to the choice of boundary conditions is examined in
Figure 4.3.3. We note that the use of reaction field boundary conditions as implemented
here is strictly valid only for equilibrium simulations, since the dynamic response of the di-
electric continuum at R>Rcis not taken into account. One could argue that for the
short-time phenomena considered here, ε′ should have been taken smaller than the static dielectric
constant of the system. Figure 4.3.3 shows that on the relevant time scale our dynamical
results do not change if we take ε ′ = 1 instead of ε ′ = ε= 17. (The absolute solvation
energy does depend on ε ′ , and replacing ε ′ =17by ε ′ = 1 changes it by ≅ 5%.)
In the simulations described so far the solvent parameters are given by the aforementioned
data. For these, the dimensionless parameter p ′ , Eq. [4.3.35], is 0.019. In order to
separate between the effects of the solvent translational and rotational degrees of freedom,
we can study systems characterized by other p′ values. Figure 4.3.4 shows results obtained
for p ′ = 0 (dotted line), 0.019 (solid line), 0.25 (dashed line), and ∞ (dashed-dotted line). Except
for p ′ = 0, these values were obtained by changing the moment of inertia I, keeping
M=50 amu. The value p ′ = 0 was achieved by takingM=MA=∞and I=33.54 amu Å 2 . Note
that the values p ′ = 0 and p ′ = ∞ correspond to models with frozen translations and frozen rotations,
respectively. Figures 4.3.4(a) and 4.3.4(b) show, respectively, the solvation energy
Esolv(t) and the solvation function S(t) obtained for these different systems. The following
points are noteworthy: