Potential energy, local minima

Global Minimum. The lowest energy Local Minimum on a Potential Energy Surface. 

The third is the half-width at which the central potential energy is minimum, and the fourth is the half-width at which the two local minima coalesce into one. The latter... 

The combination is in this case an out-of-phase one (Section I). This biradical was calculated to be at an energy of 39.6 kcal/mol above CHDN (Table ni), and to lie in a real local minimum on the So potential energy surface. A normal mode analysis showed that all frequencies were real. (Compare with the prebenzvalene intermediate, discussed above. The computational finding that these species are bound moieties is difficult to confimi experimentally, as they are highly reactive.)... 

Characterize a potential energy surface for acertain niimberof atoms, i.e., detect all the local energy minima, the global minimum on the surface, and all the transition states between different minima. 

A potential energy diagram for nng inversion m cyclohexane is shown m Figure 3 18 In the first step the chair conformation is converted to a skew boat which then proceeds to the inverted chair m the second step The skew boat conformation is an inter mediate in the process of ring inversion Unlike a transition state an intermediate is not a potential energy maximum but is a local minimum on the potential energy profile... 

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.

A drop of water that is placed on a hillside will roll down the slope, following the surface curvature, until it ends up in the valley at the bottom of the hill. This is a natural minimization process by which the drop minimizes its potential energy until it reaches a local minimum. Minimization algorithms are the analogous computational procedures that find minima for a given function. Because these procedures are downhill methods that are unable to cross energy barriers, they end up in local minima close to the point from which the minimization process started (Fig. 3a). It is very rare that a direct minimization method... 

This particular potential energy surface seems very clean-cut, because there is a single minimum in the range of variables scanned. The chances are that this minimum is a local one, and a more careful scan of the potential surface with a wider range of variables would reveal many other potential minima. 

A minimum on a potential energy surface represents an equilibrium stracture. There will invariably be a number of such local minima, and we can imagine a number of paths on the surface that connect one particular minimum to another. If the highest-energy point on each path is considered, the transition structure can be defined as the lowest of these maxima. The reaction path is the lowest-energy route between two minima. 

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