Solvent dynamic effect oscillators

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. 

The dynamic (nonequilibrium) response of the solvent to the external field-induced oscillation in the solute electronic density (electronic nonequilibrium) has been formulated within the PCM in ref. [9], whereas vibrational nonequilibrium effects (due to the dynamics of the solvent resulting from solute vibrational motions) have been formulated, still within the PCM, in ref. [43],... 

The COSMO solvent model has been used to simulate the influence of water on the electronic spectrum of A -methylacetamide [81], and the results was compared with the results of molecular dynamics simulations (where the electronic spectrum were calculated as an average over 90 snapshots from MD simulations). Most of the hydration effects were found to come from the first solvation shell hydrogen-bonded water molecules, and the continuum model does not properly account for these effects. The rotatory strengths were not calculated directly in ref. [81]. However, the results were used to model ECD spectra of peptides via the coupled oscillator model, with satisfactory result. 

The vacuum potential results, corresponding to the limit of zero viscosity, are shown in Fig. 41a. At zero viscosity, the dihedral angle 41 oscillates with a period of approximately 0.63 ps. When the conditions are changed to represent water at 300 K (i.e., the solvent-modified potential-of-mean-force surface is used and r) = 1.0 cP), the dominant effect is that the dihedral motion has a periodicity of about 3.7 ps (see Fig. 41b). The solvent influence observed in these simulations is consistent with an earlier molecular dynamics study of... 

Supplementing this equation with an additional set of solvent oscillators one can incorporate a solvent environment. Notice that this does not necessarily imply harmonic solvent motions. In fact the full anharmonicity of the solvent can be accounted for in the context of linear response theory [39] where the interaction is described in terms of an effective harmonic oscillator bath. This allows calculation of relaxation rates from classical molecular dynamics simulations of the force fn(x) exerted by the solvent on the relevant system. This approach has found appli-... 

Although this term arises only from dynamically uncorrelated collisions between the solute molecules and the solvent, we see that static structural correlations couple the motions of the two solute molecules. This contribution to the friction coefficient is not difficult to calculate if expressions for AAS(r r2r3) are available. The results display oscillation arising from the static structural correlations at distances greater than 2a (we assume that solute and solvent diameters are equal.) At distances less than 2o, where a solvent molecule can no longer intervene, the friction falls. This is a shadowing effect insofar as one solute molecule screens the other from collisions with the solvent. At shorter separations ( o) the friction must diverge because the solute molecules are impenetrable. A detailed discussion of these results can be found in Ref. 92. 

Decide whether entropic effects are likely to be important (for example if charged species are released to the solvent) and, if so, decide on whether a quantum chemical approach (calculating the partition function within a harmonic-oscillator approximation) may be used or whether a molecular dynamics-based approach (e.g., free-energy perturbation theory) should be used to properly sample phase space. 

When the polymer concentration (or molecular mass) is sufficiently high and viscosity of solution exceeds essentially that of solvent, the rheological effects in bubble dynamics become much more pronounced. In Figure 7.2.7, data are presented for the relative damping decrement of free oscillations of air bubble with Ro = 2.8 mm in aqueous solution of POE via concentration. The dashed line represents theoretical values of the decrement, corresponding to Newtonian liquid with 13 =T)p. The actual energy losses, characterized by experimental points, remained almost unchanged, despite the sharp rise in the Newtonian decrement, Ap, with c. This result correlates well with the above theoretical predictions and it is explained by viscoelastic properties of the solution. The same explanation has the phe-... 

The dynamical influence of a polar medium on the electron transfer process kinetics can be taken into account quantitatively only within the framework of specific models for describing the solvent. As shown in Ref. [4], to calculate transition probabihties for slow reactions, for which the distribution over vibrational states can be considered to be equilibrium, the inertial polarization of the medium can be represented as a set of effective oscillators... 

Another method for the determination of electrophoretic mobility which has emerged in recent years is that of the measurement of the electrokinetic sonic amplitude (ESA) for a particle subjected to an alternating current (8). This electroacoustic effect is a result of the oscillation of the particles near the electrodes where a sound wave is produced that can be picked up by a pressure transducer located behind the electrode. The ESA pressure signal is simultaneously proportional to the dynamic mobility of the particle, the particle volume fraction and the density difference between particle and solvent. Thus, the electroacoustic effect is appropriate for concentrated dispersions where conventional electrophoretic methods are inappropriate. However, one disadvantage of the method is that it is not appropriate to systems having low density differences between the particles and suspending liquid. 

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