Potential surface model, double-minimum

Most systematic studies on gas-phase SN2 reactions have been carried out with methyl halides, substrates which are free of complications due to competing elimination. Application of the Marcus rate-equilibrium formalism to the double-minimum potential energy surface led to the development of a model for intrinsic nucleophilicity in S 2 reactions233. The key quantities in this model are the central energy barriers, Eq, to degenerate reactions, like the one of equation 22, which are free of a thermodynamic driving force. 

A model of the potential surface is needed to understand why an SN2 reaction is slow. The double minimum surface shown in Figure 1 can accommodate the experimental results for this system (1-7). Although the central barrier is at a lower energy than that of the reactants, the reaction proceeds slowly because the transition state associated with the central barrier is tight and the sum of states associated with it is smaller than that associated with the loose transition state for decomposition back to reactants. The rate constant for the reaction is given by the rate constant for formation of the complex multiplied by the fraction of complexes that go on to products. This branching fraction is the ratio of the forward step over the sum of the forward and back steps and can be related to the efficiency, which is the reaction rate divided by the collision rate. 

The symmetric configuration (C2v) is one of unstable equilibrium with respect to the antisymmetric S-0 stretching coordinate gs, so that the potential surface has a shallow double-minimum section in this direction. A vibrational analysis in terms of a quadratic/quartic-cum-Gaussian model potential suggests a barrier between equivalent conformers of height 141(20) cm (0.017 eV), some 43(20) cm" (0.0053 eV) above zero-point [5]. 

The recently proposed semi empirical method for simulation of photochemical processes and calculation of quantum yields of reactions has been modified. The specific form of double minimum potential energy surfaces of the molecules involved in the conversion has been considered in a more correct manner. It has been shown that the number of molecular models parameters can be reduced by two-thirds compared with the approach used previously. The quantum yields of photochemical transformations of six dienes into their cyclic isomers have been calculated. Substantially better quantitative agreement of the calculated values with the experimental data has been achieved for all the reactions. It has been shown that the model parameters have good transferability in a series of related molecules. 

Measurement of the differential capacitance C = d /dE of the electrode/solution interface as a function of the electrode potential E results in a curve representing the influence of E on the value of C. The curves show an absolute minimum at E indicating a maximum in the effective thickness of the double layer as assumed in the simple model of a condenser [39Fru]. C is related to the electrocapillary curve and the surface tension according to C = d y/dE. Certain conditions have to be met in order to allow the measured capacity of the electrochemical double to be identified with the differential capacity (see [69Per]). In dilute electrolyte solutions this is generally the case. 

In contrast to y, the value of C can be measured not only for liquid electrodes but also for solid ones. Usually, the specific adsorption of ions increases the capacitance of the EDL, whereas the adsorption of organic molecules decreases it. In the framework of a simplified model of the double layer as a capacitor, this corresponds to varying the distance between the capacitor plates and decreasing the permittivity. In dilute solutions of a surface-inactive 1,1-electrolyte, a capacitance minimum appears in the vicinity of pzc (see curve 1 in Fig. 4). The position of this minimum is determined by the potential Eq = 0. In solutions with relatively high (>0.1 M) concentrations of surface-inactive electrolytes, this minimum of C, Fo-curve disappears, but the pzc position stiU corresponds to Fq = 0 (curve 2 in Fig. 4). Numerical integration of these C, Fo-curves... 

The description of the double layer properties by the Stem-Gouy model is a very crude one. A veiy weak point is the assumption that the dielectric contact suddenly changes from that of the solution to that of the Helmholtz double layer. The main information comes, therefore, from the minimum which indicates the potential of zero excess charge on the metal. This is, however, only correct in the absence of specific adsorption of ions. If ions are adsorbed, the counter charge for the diffuse double layer is the sum of the surface charge in the metal and of the adsorbed ions. Since the concentration of adsorbed ions also varies with the applied potential, this effect increases the apparent capacity of the Helmholtz double layer. 

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