Solvent inertial effects

There is little experimental information on possible solvent dynamical effects for electron transfer in aqueous solution. However, water is a dynamically "fast solvent, vos being determined by "solvent inertial effects so that the usual transition-state formula [eqn. (22)] should be applicable for determining vn (Sect. 3.2.1). Consequently, solvent dynamical effects in this and other "low friction media (e.g. acetonitrile) should be controlled by the rotational frequency of individual solvent molecules and limited to reactions involving only very small inner-shell barriers (Sect. 3.3.1). 

The Raman effect can be seen, from a classical point of view, as the result of the modulation due to vibrational motions in the electric field-induced oscillating dipole moment. Such a modulation has the frequency of molecular vibrations, whereas the dipole moment oscillations have the frequency of the external electric field. Thus, the dynamic aspects of Raman scattering are to be described in terms of two time scales. One is connected to the vibrational motions of the nuclei, the other to the oscillation of the radiation electric field (which gives rise to oscillations in the solute electronic density). In the presence of a solvent medium, both the mentioned time scales give rise to nonequilibrium effects in the solvent response, being much faster than the time scale of the solvent inertial response. 

A suspension is a dispersion of particles within a solvent (usually a low-molar-mass liquid). Thermodynamics (Brownian motion and collisions) favours the clumping of small particles, and this can be increased by flow. However, particles over 1 pm tend to settle under gravity, unless stability measures have been considered (matching the density of the particle to that of the medium, increasing the Brownian/gravitational force ratio, electrostatic stabilization, steric stabilization). Other complications can occur in the dynamics of suspensions, such as particle migration across streamlines, particle inertial effects and wall slip (Larson, 1999). 

For some problems, such as the motion of heavy particles in aqueous solvent (e.g., conformational transitions of exposed amino acid sidechains, the diffusional encounter of an enzyme-substrate pair), either inertial effects are unimportant or specific details of the dynamics are not of interest e.g., the solvent damping is so large that inertial memory is lost in a very short time. The relevant approximate equation of motion that is applicable to these cases is called the Brownian equation of motion,... 

As discussed in Sect. 2.1, the solvent is treated as purely viscous (as opposed to viscoelastic) in LD and BD simulations. This approximation will be valid when solvent relaxation times are much shorter than all relevant relaxation processes of the polymer chain. In BD simulations, an additional approximation is made by ignoring inertial effects. A consequence of these approximations is that all relaxation times in a BD simulation scale linearly with the solvent viscosity r. ... 

This approximation means that the surrotmding solvent has high effective viscosity so that the motion of particles can be described in terms of a random walk since the damping effect of the solvent will overcome any inertial effects. Note that while the predicted dynamical properties depend on the friction coefficient y, the equilibrium properties do not depend on y. 

The GLE is a stochastic equation of motion for the coordinate z (see Figure 24). The left-hand side of Eq. (41) is the inertial force along z in terms of the effective polarization mass m of the solvent and the acceleration z. The term... 

While none of the calculated quantities exhibits an overall monotonic trend with increasing polarity, they all show the same nonmonotonic pattern, in which the trend of dipole shifts is inversely correlated with that for HDA, p,12, and AEn. A key feature governing this behavior is the fact that inertial solvation is equilibrated to the site with less access to solvent (i.e., AC, the site of the initial state hole) in comparison with the more accessible ABP site (where the charge resides in the final state). As a result, there is a mismatch in dipolar solvation in the vertical CSh absorption, such that within the solvent sequence (e0 = 1-8, 7.0, and 37.5), increasing the polarity actually decreases the degree of charge localization (i.e., smaller A/xn and A/zda, an effect dominated by the oxidized D site in the final state), and hence increases the D/A coupling (as reflected in HDA and also p.n). 

The first result of this calculation is that the inertial motion causes almost no dephasing. This result is a direct contrast to models like the IBC theory, which attribute all the dephasing to collisional, i.e., inertial, dynamics. The difference between these theories lies in their assumptions about correlations in the solvent motion. The IBC explicitly assumes that the collisions are independent, i.e., the solvent motion has no correlations. As a result, the collisions are an effective sink for phase memory from the vibration. On the other hand, within the VE model the solvent motions appear as sound waves. Their effect on the vibrational frequency decays as they propagate away from the vibrator, but they remain fully coherent at all times. Because they remain coherent, they cannot destroy the phase... 

Figure 3 presents a comparison of the non-equilibrium solvent response functions, Eq (1), for both the photoexcitation ("up") and non-adiabatic ("down") transitions (cf. Fig. 2). The two traces are markedly different the inertial component for the downwards transition is faster and accounts for a much larger total percentage of the total solvation response than that following photoexcitation. The solvent molecular motions underlying the upwards dynamics have been explored in detail in previous work, where it was also determined that the solvent response falls within the linear regime. Unfortunately, the relatively small amount of time the electron spends in the excited state prevents the calculation of the equilibrium excited state solvent response function due to poor statistics, leaving the matter of linear response for the downwards S(t) unresolved. Whether the radiationless transition obeys linear response or not, it is clear that the upward and downwards solvation response behave very differently, due in part to the very different equilibrium solvation structures of the ground and excited state species. Interestingly, the downwards S(t), with its much larger inertial component, resembles the aqueous solvation response computed in other simulation studies, and bears a striking similarity to that recently determined in experimental work based on a combination of depolarized Raman and optical Kerr effect data. ...

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