Potential energy curves maxima

Such diagrams make clear the difference between an intermediate and a transition state. An intermediate lies in a depression on the potential energy curve. Thus, it will have a finite lifetime. The actual lifetime will depend on the depth of the depression. A shallow depression implies a low activation energy for the subsequent step, and therefore a short lifetime. The deeper the depression, the longer is the lifetime of the intermediate. The situation at a transition state is quite different. It has only fleeting existence and represents an energy maximum on the reaction path. 

Noumerov analysis leads to more encouraging results. The energy values associated with the first 10 (v = 0-9) vibrational levels were computed. The first eight (v = 0-7) are relative to the absolute minimum of the potential energy curve employed (see Figure 5) the remaining two (v = 8-9) are relative to levels above the maximum. 

One way of doing this is to assume that the demarcation between stable and unstable colloids occurs at the value of k for which the height of the barrier is zero. Physically, this is a somewhat arbitrary choice Thermal energy is sufficient to allow particles to overcome a barrier of low but nonzero height. Mathematically, however, the assumption that the maximum in the potential energy curve occurs at zero permits us to write... 

EXAMPLE 13.3 Expression for Stability Ratio in Terms of max. By replacing r by rm, the center-to-center distance of separation at the maximum in the potential energy curve and using a truncated Taylor series about the maximum to estimate (r), show that W potential energy barrier at the maximum. Comment briefly on these and any other assumptions or approximations involved. 

This is the Arrhenius form to which the example refers. In it, the height of the maximum in a net potential energy curve plays the role of the activation energy. In the next chapter we see how this method has been used to evaluate W for systems in which the overlapping ion atmospheres of approaching colloidal particles provides the repulsion needed to give slow coagulation. 

A survey of the hydrogen-bond lengths observed by neutron diffraction in the amino acids [60], for example shows that they have distributions with minimum and maximum values which correspond to those expected from a typical bonding potential energy curve, as shown in Fig. 2.5. There is no evidence of a cut-off distance beyond which another type of cohesive force takes over. Instead, the number of H A distances steadily decreases as they exceed the most probable H A bond length. In practice, it is observed that in crystal structures the first neighbor... 

The distribution of bond lengths for a particular two-center bond in the crystal structures of a particular class of biological compounds has a well-defined maximum but is more symmetrical than might be expected from the hydrogen-bond potential energy curve (cf. Figs. 2.4 and 4.2 a, b). 

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