INDEX potential energy barrier

Let us now refer back to Fig. 10(b) to set up a formal indexing system for the system of potential energy maxima and potential energy minima. Then the equations for transport across the series of potential energy barriers can be identified for individual barriers, and the relationship between the equations can be examined. It is clear that the area densities effective for forward hopping over one barrier will be the same area... 

Figure 5 shows the calculated potential energy of interaction Vt of AI2O3 particles (t/ = 0.25 pm, A = 4.5 x 10 J, and 0.01 M ionic strength) as a function of the surface-to-surface distance of separation for various conditions of potential in an aqueous suspension. Note that the height of the potential energy barrier increases quite sharply as the potential becomes larger than a certain critical value ( 30 mV in Fig. 5). Therefore, the potential is a very good index of the magnitude of the repulsive interaction between colloid particles. Because of this, measurements of potential are most commonly used to assess the stability of a given colloidal sol.

The planar form of phosphole is a first-order saddle point on the potential energy surface, 16—24 kcal/ mol above the minimum (at different levels of the theory). ° (The calculated barriers are the highest at the HF level, which underestimates aromatic stabilization of the planar saddle point, while the MP2 results are at the low end.) It has been demonstrated by calculation of the NMR properties, structural parameters, ° and geometric aromaticity indices as the Bird index ° and the BDSHRT, ° as well as the stabilization energies (with planarized phosphorus in the reference structures) ° and NIGS values ° that the planar form of phosphole has an even larger aromaticity than pyrrole or thiophene. 

It is not necessary to restrict ourselves to bonds that are described by Morse potentials. We can regard eqn. (56) as a quadratic equation in x, use any form of the potential energy V(R) with the usual shape (i.e., a minimum, a repulsive barrier at short distances, and a monotonical increase at large distances), and determine x to get another definition of the bond order. This is called the unity bond index quadratic exponential potential (UBI QEP) method by Shustor-ovich and Sellers. ... 

Owing to the exponential dependence of the rate upon energy, the rate problem reduces mainly to the determination of the lowest energy barrier that has to be surmounted. The ISM model, which was presented in the previous chapter, points, in general terms, to some structural factors that control the barriers of chemical reactions and as a consequence the rate constants. These relevant factors are (i) reaction energy, AEP, AFfi or AG° (ii) the electrophilicity index of Parr, m, a measure of the electron inflow to the reactive bonds at the ttansition state, also characterised as a transition-state bond order (iii) when the potential energy curves for reactants and products can be represented adequately by harmonic oscillators, the relevant strucmral parameters are the force constants of reactive bonds, f and/p in reactants and products, respectively and (iv) equilibrium bond-lengths of reactive bonds, and Zp in reactants and products, respectively. 

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