Promoting mode

Here for simplicity we assume that there is only one promoting mode Qi. Equation (3.73) can be written as... 

For simplicity, we shall assume that the promoting mode is neither distorted nor displaced in this case we find... 

In this case we can see that the promoting mode can accept at least one vibrational quantum (due to the term 0)/, + ( t). This is usually called the propensity rule. 

Here for simplicity it is assumed that there is only one promoting mode. Equation (3.85) should be compared with Eq. (3.73). In Eq. (3.85) both vibronic and spin-orbit coupling are involved in W-,. /. Due to the rapid progress in ab initio calculations, it has now become possible to evaluate Wi >/ by using potential energy surfaces information obtained from ab initio calculations. 

In 1989, Borgis and Hynes proposed a theory for nonadiabatic proton transfer that includes all the parameters contained with the DKL model. In addition, they addressed the important issue of low-frequency vibrations serving as promoting modes in proton tunneling [11]. For nonadiabatic proton transfer, the distance dependence of the tunneling coupling, C(Q), has the analytical form [13]... 

On the basis of a Landau-Zener curve crossing formalism, Borgis and Hynes derived the nonadiabatic rate constant k, which is similar to that expressed by the DKL model but where the tunneling term Cnm found in Eq. (4) is significantly modified due to the influence of the low-frequency promoting mode Q, with a frequency 0)q, on the tunneling rate. The dependence of Cnm on Q is given by [13]... 

As evidenced by the correlation of the BH model with the experimental data, Figure 2.4, the model is only in qualitative accord with the experiment. Clearly, the BH model cannot account for the breadth in the correlation of the rate constants for porton transfer with driving force. The origin of the discrepancy may lie in the single-mode nature of the BH model, which allows only for vibrational excitation in the low-frequency promoting mode. Excitation in the reactant and product modes of the vibration associated with the transferring proton is not taken into account in the BH model. Therefore, the discrepancy between experiment... 

The fit of the LH model to the remaining kinetic data for the nitrile solvents employed only two fitting parameters, the low-frequency promoting mode, ooq, and the solvent reorganization energy, Es. A factor determining the magnitude of... 

Promotion type Promotion mode Activity Selectivity Stability promotion effect... 

The next important aspect to be considered is the electron-phonon interaction (lattice relaxation). Here, the effect of momentum conserving phonons, or promoting modes, can in principle be included in the electronic cross section this is discussed, for instance, by Monemar and Samuelson (1976) and Stoneham (1977). However, the configuration coordinate (CC) phonons (or accepting modes) are treated separately. The effect of these CC modes is usually expressed by the Franck-Condon factor dF c, where this factor is the same as the defined in our Fig. 16. Thus assuming a single mode,... 

The second line of Eq. (17) represents the Stokes term when transitional promotion is due to excitation of a promoting mode in the ground state (g), the third line is the anti-Stokes term originating from a promotion mode in the excited state (e). 

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