Reorganization energy definition

Fig. 1. Definition of the contribution to the reorganization energy. The figure represents the variations of the potential energy when only is varied, the other coordinates being kept constant at their equilibrium values...

From the definition, the reorganization energy is the energy of the product system when its solvent coordinate is still the same as that of the reactant state, i.e., where q = 0. Thus, putting q = 0 in Eq. (9.28), one gets... 

The quantity Ga( x>)- G° (the second term in Equation (3.77) is seen to have the form of a reorganization energy, A( Ax >), but with Axif > in Aif (Equation (3.80)) replaced by the arbitrary coordinate fluctuation Ax > (see definition following Equation (3.77)). Letting state a be the initial state i, we note that along the reaction coordinate, A( Ax >)... 

The use of the energy-gap reaction coordinate allows us to calculate solvent reorganization energies in a way analogous to that in the Marcus theory for electron transfer reactions.19 The major difference here is that the diabatic states for electron transfer reactions are well-defined, whereas for chemical reactions, the definition of the effective diabatic states is not straightforward. The Marcus theory predicts that... 

It is important to remember that the reorganization energy is a composite parameter rather than a fundamental physical quantity. Refinements to the semiclassical theory usually arise from quantum mechanical treatments of vibrational motions. The increased rigor associated with these models, however, is rarely accompanied by the extra data required to cope with the influx of new parameters. The approximations involved in its definition, and the errors associated with its measurement dictate that k should never be expressed with great precision. 

In the Sumi-Marcus (SM) model 13a], the perspective is changed, with a TST rate constant based on a low-frequency molecular mode (m) as the reaction coordinate, and with G dependent on a diffusive solvent coordinate X. For ease of comparison with other models, we transform X (relative to its definition in [13a]) so as to correspond to a continuous charging parameter (X = 0 for the bottom of the reactant well, and X = 1 for the bottom of the product well for the case of parabolic free energy profiles the transformation is linear the more general situation is dealt with in [98]). Also, 7.ci = A + z , and /.d = a, , where 7, , is the reorganization energy associated with the low-frequency mode m. These definitions lead to the following equation ... 

Figure 6. Di batic free energy functions for the states 3 and 3 in water (upper curve) and in the enzyme (lower curve) as a function of the energy gap between the two states. The reorganization energies (see text for definition) upon transfer from the reactant to the product state and vice versa for this (the second) reaction step are indicated. The reduction of reorganization energy in the protein is reflected by the energy gaps being significantly smaller than in the uncatalyzed reaction.

The reaction coordinate at the transition state can be identified as AE = —AFrmel, Since F (AF ) = F (AF ) at the transition state by definition. The solvent reorganization energy A, which is the difference... 

The coordinate pertaining to solvent reorganization, z, is the same fictitious charge number as already considered in the Hush-Marcus model of outer-sphere electron transfer (Section 1.4.2), and so is the definition of 2q [equation (1.27)] and the difference between the Hush and Marcus estimation of this parameter. The coordinated describing the cleavage of the bond is the bond length, y, referred to its equilibrium value in the reactant, yRX. Db is the bond dissociation energy and the shape factor ft is defined as... 

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