Energy trough

In this section we deal with those systems where the entropy loss on adsorption is less than would be expected if all movement perpendicular to the surface was denied to the adsorbate. This will happen in cases where the potential energy trough is shallow and where translational motion perpendicular to the surface is replaced by a vibration of low frequency. 

Below a normalized bite of 1.1 there is a shallow potential energy trough that incorporates the capped trigonal prism with the bidentate ligand spanning the prism edge trans to the capping atom... 

The form of this potential energy surface is critically dependent on the effective bond length ratio J (unidentate/bidentate). As 7 (unidentate/bidentate) becomes less than unity, stereochemistry C becomes very stable, a typical potential energy surface being shown in Figure 70. Conversely, as /i(unidentate/bidentate) increases, it is the other end of the potential energy trough that deepens,... 

Figure 11.6 illustrates the energy that must be supplied by thermal activation. The curve of ab vs. A shows the force that must be applied to the dislocation (per unit length) if it were forced to surmount the Peierls barrier in the manner just described in the absence of thermal activation. The quantity A is the area swept out by the double kink as it surmounts the barrier and is a measure of the forward motion of the double kink. A = 0 corresponds to the dislocation lying along an energy trough (minimum) as in Fig. 11.5a. A2 is the area swept out when maximum force must be supplied to drive the double kink. A4 is the area swept out when the saddle point has been reached and the barrier has been effectively surmounted. The area under the curve is then the total work that must be done by the applied stress to surmount the barrier in the absence of thermal activation. When the applied stress is a a (and too small to force the barrier), the swept-out area is A, and the energy that must be supplied by thermal activation is then the shaded area shown in Fig. 11.6. The activation energy is then...

The current picture of protein folding is nicely summarized in Figure 17.1. There are a multitude of pathways from the state of unfolded protein at the top of the figure to the native protein at the bottom. Without folding intermediates, the walls of the funnel to the bottom would be smooth. If the energy trough around a nonnative protein is too deep, the misfolded protein cannot exit this local minimum. 

Afterwards, the relative activation energies of the diastereoisomeric transition structures are split into contributions able to represent the factors the organic chemist is used to invoke in the attempt to "understand" the variety of the reaction outcome, i.e. steric and electrostatic repulsions, deformation energy of reactants, incipient bond energies, trough-space delocalisations and their subsets often called secondary interactions. The an ysis of delocalisation energies rests on the use of hybrid basis sets derived from Del Re s Maximum Localisation Criterion. ... 

The ES complex would be in an energy trough, with a consequentially large activation energy to the transition state. 

Several studies have been devoted to the adiabatic JT hypersurface of the cubic T X (e -I- ta) problem [2]. The existence of a spherical equipotential energy trough in the limit of equal JT stabilization energies for the e and t2 modes, has first been established by O Brien [27]. As for the icosahedral T term a projective drawing of this trough in function space simply consists of a constant spherical potential. 

This property indicates the existence of a broad, shallow energy trough characteristic of fluid, liquidlike systems. Hence the low viscosity observed in monolayers (Shah and Shulman, 1967) and bilayers (Ladbrooke et al., 1968) would reflect the disorder of bimolecular complexes rather than the absence of complexes as postulated by Shah and Shulman (1967). 

Thermal expansion is due to the asymmetric curvature of this potential energy trough rather than the increased atomic vibrational amplitudes with rising temperature. If the potential energy curve were symmetric (Figure 19.3h), there would be no net change in interatomic separation and, consequently, no thermal expansion. 

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