Solvent configuration

The interaction with the solvent is of similar importance as the intramolecuiar energy contributions and a correct representation of the solvent is therefore es.sential. If an explicit solvent description is chosen, averaging over many different solvent configurations is necessary in order to obtain converged statistical averages. Advantageous in this respect is describing the solvent as... 

In a few cases, where solvent effects are primarily due to the coordination of solute molecules with the solute, the lowest-energy solvent configuration is sufficient to predict the solvation effects. In general, this is a poor way to model solvation effects. 

Fig. 3. Functions in the integrand of the partition function formula Eq. (6). The lower solid curve labeled Pq AU/kT) is the probability distribution of solute-solvent interaction energies sampled from the uncoupled ensemble of solvent configurations. The dashed curve is the product of this distribution with the exponential Boltzmann factor, e AJJ/kT r the upper solid curve. See Eqs. (5) and (6).

Fig. 4. A schematic two-dimensional illustration of the idea for an information theory model of hydrophobic hydration. Direct insertion of a solute of substantial size (the larger circle) will be impractical. For smaller solutes (the smaller circles) the situation is tractable a successful insertion is found, for example, in the upper panel on the right. For either the small or the large solute, statistical information can be collected that leads to reasonable but approximate models of the hydration free energy, Eq. (7). An important issue is that the solvent configurations (here, the point sets) are supplied by simulation or X-ray or neutron scattering experiments. Therefore, solvent structural assumptions can be avoided to some degree. The point set for the upper panel is obtained by pseudo-random-number generation so the correct inference would be of a Poisson distribution of points and = kTpv where v is the van der Waals volume of the solute. Quasi-random series were used for the bottom panel so those inferences should be different. See Pratt et al. (1999).

Note that the additional factor within the average, the n j (1 — bj), would be zero for any solvent configuration in which a solvent molecule is found in the inner shell. Thus, this expression involves a potential distribution average under the constraint that no binding in the inner shell is permitted. We can formally write the full expression for the excess chemical potential as... 

As noted in the Introduction, the PDT is widely recognized with the moniker test particle method. This name reflects a view of how calculations of ((e l3AU° ))0 might be tried solute conformations are sampled, solvent configurations are sampled, and then the two systems are superposed the energy change is calculated, and... 

Ions and protons are much heavier than electrons. While electrons can easily tunnel through layers of solution 5 to 10 A thick, protons can tunnel only over short distances, up to about 0.5 A, and ions do not tunnel at all at room temperature. The transfer of an ion from the solution to a metal surface can be viewed as the breaking up of the solvation cage and subsequent deposition, the reverse process as the jumping of an ion from the surface into a preformed favorable solvent configuration (see Fig. 9.1). 

If only the solvation of the gas-phase stationary points are studied, we are working within the frame of the Conventional Transition State Theory, whose problems when used along with the solvent equilibrium hypothesis have already been explained above. Thus, the set of Monte Carlo solvent configurations generated around the gas-phase transition state structure does not probably contain the real saddle point of the whole system, this way not being a correct representation of the conventional transition state of the chemical reaction in solution. However, in spite of that this elemental treatment... 

Using the sequence of gas-phase MEP frames each dividing surface is defined by the set of solvent configurations that are generated around the frozen solute structure of each frame. Then, some kind of solute-solvent separation is assumed again. 

The second cause of broadening of electronic spectra is the fluctuations in the structure of the solvation shell surrounding the fluorophore. The distribution of solute-solvent configurations and the consequent variation in the local electric field leads to a statistical distribution of the energies of the electronic transitions. This phenomenon is called inhomogeneous broadening (for a review see Nemkovich et al., 1991). 

Figure 3. Equipotential sections through the potential energy surface for an exchange reaction, as in Figure 2. The heavy horizontal line indicates the solvent configuration appropriate to the activated complex and is the solvent configuration at which inner-sphere tunneling takes place.

For Cs+, I imagine there are many solvent configurations about the metal ion which have approximately the same energy. 

We suppress the free-energy character of these two states in order to highlight the emergence of new ftee energies whenever we average either over conformational states (e.g.. Section 3.3) or over solvent configurations (see Chapter 9). 

There are several ways of carrying out the average over all configurations of the solvent molecules. The most common one is a system at constant temperature T, pressure P, and solvent composition N. The appropriate average is carried out in the so-called T, P, N ensemble, i.e., for any function of the solvent configuration... 

Hydrogen transfer does occur during oxidation of DMS, but it is not the determining factor of the activation barrier. Hydrogen transfer can occur via multiple different pathways depending on the local solvent configuration. 

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