Shallow local energy minima

Calculations of the potential energy function of a large number of different globular proteins demonstrate that these proteins all have a very large number of shallow local energy minima (26). This analysis is consistent with the physical properties of ion channel proteins suggested by the fractal properties of the channel data and inconsistent with the few deep minima predicted by the Markov model. 

Figure 12.4 A contour plot of a general two fold symmetric potential energy surface. The chart should be viewed like a topographical map, except that the contours reflect potential energy instead of altitude. The symmetry can be seen by recognizing that the left-hand and right-hand halves of the diagram are mirror images of each other. The intermediate I sits in a shallow local minimum that is bisected by the vertical mirror plane.

One of the most unexpected results obtained was for Pg, where the much-studied cubic (0 ) form corresponds to a shallow local minimum in the energy surface. Simulated annealing led, however, to the Czv structure (Fig. 4b), which is much (ca. 1.7 eV) more stable. This wedge structure, which may be viewed as a (distorted) cube with one bond rotated through 90°, is a structural unit in violet (monoclinic, Hittorf) phosphorus [48]. A second isomer of Pg ( >21, Fig. 4a) is also much more stable than the cubic form. There is a striking analogy between the structures of the Pg-isomers and those of the valence isoelectronic hydrocarbons (CH)g. The cubic form of the latter (cubane) has been prepared by Eaton and Cole [49], and can be converted catalytically to the wedge-shaped form (cuneane) [50]. 

Fig. 2. Effective interface potential (left) and corresponding disjoining pressure (right) vs film thickness as predicted by DLVO theory for an aqueous soap film containing 1 mM of 1 1 electrolyte. The local minimum in H(f), marked by °, gives the equiHbrium film thickness in the absence of appHed pressure as 130 nm the disjoining pressure 11 = —(dV/di vanishes at this minimum. The minimum is extremely shallow compared with the stabilizing energy barrier.

Again related to total energies, and particularly relevant to the hydrogen-shallow-defect pairs that we will discuss, are the phenomena of metastability and bistability (Watkins, 1989). A metastable configuration is one in which the total energy is a local minimum but not a global minimum. The lifetime of the metastable state depends, of course, on the barrier that separates it from the stable configuration. 

Fig. 10 The three-dimensional potential energy surface describing the motion of protons between N6(A) and 04(T) and between N3(T) and N1(A) shows two critical points in the ground state. The deeper minimum corresponds to the amine/keto structure of AT and a shallow one to the imine/enol structure (A T ). Upon absorption of a UV photon the initaly delocalized excitonic states (1) undergo a rapid localization on f 10 ps timescale for single bases and 100 ps timescale for stacked base pairs to form a charge transfer (CT) states. The subsequent CT states passing through a conical intersection are carried back to the ground state.

The basic operator of our algorithm is a short MD simulation as in standard minima hopping. How short should the simulation be How many MD steps should be taken before continuing with a geometry relaxation Three options were considered (1) stop after a fixed number of steps, (2) stop at the first energy local minimum which is not too shallow, and (3) stop after a certain number of energy minima. Goedecker s... 

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