The Solvent Coordinate An Application

In this section, we give some details for a classical model of the interaction of a barrier transition coupled to a dynamical solvent coordinate. Such a model was developed in great detail for an isomerization reaction in [21], but it can easily be adapted to the vibrational part of the tautomerization reaction. 

The transition state in this picture is the point where both dipoles have the same length therefore the difference in bond length, denoted x, may be taken as the reaction coordinate, and the top of the barrier is located at x = 0. There is an intrinsic barrier frequency a , but as we tried to make clear in Section 9.6, this frequency is modified by a potential of mean force due to the solvent fluctuations. 

Although it is, in principle, possible to evaluate the reaction fields at the positions of the dipoles due to the dielectric outside, we take a somewhat simpler approach, along the lines of a theory developed in [21]. The solvent is itself represented by dipoles. These dipoles create a reaction field at the position of the reactive dipoles. Considering for a moment the reactive dipoles separately, it should be obvious that dipole 1 creates a field at its own position, but also at the position of dipole 2, and vice versa. But as we are only interested in the difference in length of the two reactive dipoles, the whole solvent ends up being represented by a single solvent dipole. 

The nonadiabatic barrier frequency co- is the intrinsic barrier frequency that governs the barrier motion when we keep the solvent frozen at the position where it is in equilibrium with the transition state of the reactive coordinate, which in this model means at x, = 0. In terms of the notation of Section 9.6, it would be -X(0) = col — The solvent is characterized by a solvent frequency and a solvent relax- 

---