Energy landscape state

Figure B3.3.10. Contour plots of the free energy landscape associated with crystal niicleation for spherical particles with short-range attractions. The axes represent the number of atoms identifiable as belonging to a high-density cluster, and as being in a crystalline environment, respectively, (a) State point significantly below the metastable critical temperature. The niicleation pathway involves simple growth of a crystalline nucleus, (b) State point at the metastable critical temperature. The niicleation pathway is significantly curved, and the initial nucleus is liqiiidlike rather than crystalline. Thanks are due to D Frenkel and P R ten Wolde for this figure. For fiirther details see [189].

Solving the master equation for the minimally frustrated random energy model showed that the kinetics depend on the connectivity [23]. Eor the globally connected model it was found that the resulting kinetics vary as a function of the energy gap between the folded and unfolded states and the roughness of the energy landscape. The model... 

In the previous section we discussed how a Hopfield net can sometimes converge to a local minimum that docs not correspond to any of the desired stored patterns. The problem is that while the dynamics embodied by equation 10.7 steadily decreases the net s energy (equation 10.9), because of the general bumpiness of the energy landscape (see figure 10.5), whether or not such a steady decrease eventually lands the system at one of the desired minima depends entirely on where the system begins its descent, or on its initial state. There is certainly no general assurance that the system will evolve towards the desired minimum. 

Based on the theoretical electrochemistry method outlined above in combination with DFT calculations, the potential energy of the intermediates can be obtained at a given potential, (Fig. 3.5). Since aU steps involve exactly one proton and electron transfer, the height of the different steps scales directly with the potential. To calculate the potential energy landscape at the equilibrium potential, the levels are moved down hyn X 1.23 eV, where n is the number of the electrons at the given state (the horizontal axis in Fig. 3.5). 

Figure 2.25. Energy landscape (BP/DNP) for the Cu ZSM-5 + 2NO- Cu—0 ZSM-5 + N20 reaction, showing all associated spin and conformation isomers calculated for the M5 site. The values are given in kcal x mol-1. The letters S, D and T indicate the singlet, doublet, and triplet states, respectively (after [75]).

Fig. 6. Schematic energy landscape for protein folding (folding funnel). The approximate regions of the energy landscape that correspond to the various partly folded states of apoMb are indicated on the right.

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