Continuum solvent coordinate, considered

Ovchinnikov and Benderskii also considered that the continuum solvent coordinates are changed during electron transition and used the Franck-Condon factor, 6p(JE), due to charge along solvent coordinate, and the total Franck-Condon factor was obtained using the relation... 

The Sn2 reaction in solution. We saw above the application of microsolvation to Sn2 reactions ([14, 15]). Let us now look at the chloride ion-chloromethane Sn2 reaction in water, as studied by a continuum method. Figure 8.2 shows a calculated reaction profile (potential energy surface) from a continuum solvent study of the Sn2 attack of chloride ion on chloromethane (methyl chloride) in water. Calculations were by the author using B3LYP/6-31+G (plus or diffuse functions in the basis set are considered to be very important where anions are involved Section 5.3.3) with the continuum solvent method SM8 [22] as implemented in Spartan [31] some of the data for Fig. 8.2 are given in Table 8.1. Using as the reaction coordinate r the deviation from the transition state C-Cl... 

Ail the above choices present some problems. The definition of the diabatic states is complicated, and the associated solvent coordinate is only valid if the solute wave function may be written as a linear combination of the two diabatic states. If more complex wave functions are used (Cl, for instance), a larger set of solvent coordinates must be introduced. In this case it is necessary to consider as many solvent coordinates as electronic configurations. Anyway, we cannot forget to recall that just this diabatic states description has more recently permitted a very interesting development of the continuum solvent methods with the introduction of a full quantization of the solvent electronic polarization in the work of Kim and Hynes, ... 

The Marcus treatment uses a classical statistical mechanical approach to calculate the activation energy required to surmount the barrier. It assumes a weakly adiabatic electron transfer process and non-equilibrium dielectric polarization of the solvent (continuum) as the source of activation. This model also considers the vibrational contributions of the inner solvation sphere. The Hush treatment considers ion-dipole and ligand field concepts in the treatment of inner coordination sphere contributions to the energy of activation [55, 56]. 

The next developments of the FC approach were in papers by (R. A.) Marcus,41 49 and a later series from the Soviet Union. About the same time Hush50 introduced other concepts, to be discussed below. The early work of Marcus41 considered the Inner Sphere to be invariant with frozen bonds and vibrational coordinates up to the time of electron transfer. The classical subsystem for ion activation has its ground state floating on a continuum of classical levels, i.e., vibrational-librational-hindered translational motions of solvent molecules in thermal equilibrium with the ground state of the frozen solvated ion. 

Here hence denotes the position of monomer with label i (i= 1,..., N) in the feth chain molecule (fe = 1,..., N ). For simplicity, we have specialized here to a monodisp>erse system of linear homopolymers hut the generalization to polydisperse systems or to heteropolymers or to branched architecture is straightforward, as well as to multicomponent systems (including solvent molecule coordinates, for instance). Typically, the volume in which the S3 tem is considered is a cubic LxLxL box (in d = 3 dimensions, or a square LxL box in d = 2 dimensions), and one chooses periodic boundary conditions to avoid surface effects but if the latter are of interest, the corresponding change of boundary conditions is straightforward. All of what has been said so far applies to lattice models as well as to models in the continuum. 

In fact, the strategy which is commonly followed in the QM calculation of the quantities entering the description of vibrational spectra of systems in the condensed phase is to start from the theory developed for isolated systems and to supplement that theory with solvent peculiarities. In the framework of continuum solvation methods, this imphes the development of reUable and computationally affordable algorithms for the evaluation of (free) energy first and second derivatives with respect to nuclear coordinates and/or external electric or magnetic fields (if required), no matter what specific vibrational spectroscopy is to be considered. 

LAUNAY - Not exactly. The use of 1/n in the Marcus formula comes from the theory of non equilibrium polarization of the solvent considered as a dielectric continuum. One may think that the contribution of the solvent to the activation energy is broken in two terms a term due to orientational polarization and a term due to electronic polarization. Only the first term is kept, because it is slow and the corresponding rearrangement must occur before electron transfer (cf the case of the first coordination sphere). The second term is deleted because it is fast and thus can occur during electron transfer. Since at optical frequencies, only the electronic polarization can respond, this term 1/n = op separation between the fast... 

For comparison with real reactions, it is usually necessary to strip the chemical system to its essentials to reduce the number of atoms in the reaction system and permit computational feasibility. Most reactions are run in solution whereas the computations apply to the gas phase thus, solvation needs to be considered at some level. Solvation is particularly important when ions are involved. It is less important for the reactions of neutral polar organometallics but these compounds generally have significant dipole moments and solvation is not insignificant. Nevertheless, most calculations of reaction systems have generally ignored solvation at least explicitly. In some recent cases solvation was modeled by coordination of one or more solvent molecules with the metal or by use of a continuum model for solvation (see Solvation Modeling). 

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