Ground solvation

According to Eq. (19), t, is the time scale for excited state solvation for a Debye solvent. In fact, it is the time scale for both excited state and ground solvation of dipolar solutes and ionic solutes, t, also plays a role in a broad range of reactive (Section III) and nonreactive charge transfer processes in solution. It is clearly worthwhile to establish a physical picture for this important variable. 

The electrostatic solvait effects discussed in the preceding paragraphs are not the only possible modes of interaction of solvent with reactants and transition states. Specific structural effects may cause either the reactants or the transition state to be particularly stroi ly solvated. Figure 4.12 shows how such solvation can affect the relative energies of the ground state and transition state and cause rate variations from solvent to solvent. 

Fig. 4.12. Potential energy liagrams showing effect of preferential solvation of transition state (a) and ground state (b) on the activation energy.

Solvatochromic shifts are rationalized with the aid of the Franck-Condon principle, which states that during the electronic transition the nuclei are essentially immobile because of their relatively great masses. The solvation shell about the solute molecule minimizes the total energy of the ground state by means of dipole-dipole, dipole-induced dipole, and dispersion forces. Upon transition to the excited state, the solute has a different electronic configuration, yet it is still surrounded by a solvation shell optimized for the ground state. There are two possibilities to consider ... 

Let (Xgr and jXex be the dipole moments of the ground and excited states. Then if iXgr > the less polar excited state is surrounded by a solvation shell... 

A solvated anion (reduced nucleophilicity due to enhanced ground-state stability)... 

It should be emphasized again that both the SN1 and the 5 2 reaction show solvent effects but that they do so for different reasons. SN2 reactions are disfavored in protic solvents because the ground-state energy oi the nucleophile is lowered by solvation. S l reactions are favored in protic solvents because the transition-state energy leading to carbocation intermediate is lowered by solvation. 

Here (in contrast to the approach taken in Chapter 2) we do not assume that the energy of each valence bond structure is correlated with its solvation-free energy. Instead we use the actual ground-state potential surface to calculate the ground-state free energy. To see how this is actually done let s consider as a test case an SN2 type reaction which can be written as... 

Thus it is concluded that while destabilization of the ground-state charges may be used in enzymes to reduce Ag, it is not used in enzymes that optimize kzJKM. Furthermore, we argue that the feasibility of any proposed desolvation mechanism can be easily analyzed (and in most cases disproved) by the reader once the relevant thermodynamic cycle is defined and the solvation energies of the reacting fragments are estimated. 

It is also difficult to determine exactly the relative stabilities of vinyl cations and the analogous saturated carbonium ions. The relative rates of solvolysis of vinyl substrates and their analogous saturated derivatives have been estimated to be 10 to 10 (131, 134, 140, 154) in favor of the saturated substrates. These rate differences, however, do not accurately reflect the inherent differences in stability between vinyl cations and the analogous carbonium ions, for they include effects that result from the differences in ground states between reactants, as well as possible differences between the intermediate ions resulting from differences in solvation, counter-ion effects, etc. The same difficulties apply in the attempt to estimate relative ion stabilities from relative rates of electrophilic additions to acetylenes and olefins, (218), or from relative rates of homopropargylic and homoallylic solvolysis. 

The effect of solvation on uracil and thymine photophysics has been studied by Gustavvson and coworkers, who have studied uracil with four explicit water molecules and PCM to study distorted geometries [92,93,149], The conical intersection connecting Si to the ground state that was found in the gas phase is also present in solution. The barrier connecting the Si minimum to the conical intersection is lower in solution, however, causing much shorter lifetimes. So the nanosecond lifetime which is observed in the gas phase is not observed in solution but a picosecond lifetime is observed. 

The procedure for calculating the energy of the solvated electron is to assume a particular form for t// containing one or more adjustable parameters and then calculate/, V, and E self-consistently through Eqs. (6.11)—(6.13). When a finite cavity is considered, the potentials/and Vare taken constant inside the cavity with continuity at the surface. Then, E is varied with respect to the adjustable parameter(s) until a minimum is obtained. For the ground state of e, one uses a Is wavefunction... 

Experimental mobility values, 1.2 X 10-2 cm2/v.s. for eam and 1.9 x 10-3 cm2/v.s. for eh, indicate a localized electron with a low-density first solvation layer. This, together with the temperature coefficient, is consistent with the semicontinuum models. Considering an effective radius given by the ground state wave-function, the absolute mobility calculated in a brownian motion model comes close to the experimental value. The activation energy for mobility, attributed to that of viscosity in this model, also is in fair agreement with experiment, although a little lower. 

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