Multiple energy minima

Distance geometry methods tend to be faster than molecular mechanics methods and they are easier to parameterize. On the other hand, they are less accurate and the generated conformations can be rather crude because the distance matrix describes conformational properties only in a coarse manner as, for example, there is no possibility to describe multiple energy minima of torsional angles. Thus, the cyclohexane chair and boat conformations would be considered to be equally reasonable. 

One of the ways of circumventing the problem of finding multiple energy minima of complex molecules is to turn to more sophisticated techniques that are capable of sampling phase space efficiently without the need to home in on particular minimum energy conformations. The two most useful techniques are molecular dynamics (MD) and the Monte Carlo (MC) method. Both approaches make use of the same types of potential functions used in molecular mechanics, but are designed to sample conformation space such that a Boltzmann distribution of states is generated. MC and MD techniques for molecular systems have been widely reviewed [11-14], and only the basics of the two methods are described below. 

In the multiple copy MD [77] or locally enhance sampling (LES) [78] method, part of the system simulated is replicated multiple times, e.g. 20 copies of a peptide are simulated in the presence of 1 copy of the solvent. There are no interactions between the multiple copies. The unreplicated atoms feel the mean force of all the copies of the replicated atoms. The mean field generated by the multiple copy ensemble reduces the energy barriers but conserves the global energy minimum [78]. The number of degrees of freedom is reduced in the sense that one simulation with m copies of a subset of the atoms samples to a similar extent to m standard simulations (without multiple copies) in approximately l/m times the simulation time. Applications to peptides in solvent have shown improved sampling of phase space [79, 66]. 

The latter functional form contains a constant n that determines the periodicity of the potential (r is a phase factor), and allows bending energies with multiple minima, analogously to the torsional energy. It does, however, have problems of unwanted oscillations if an energy minimum with a natural angle close to 180° is desired (this requires... 

The lowest energy level is Vihv above the potential-energy minimum (zero-point vibration). Vibrators can exchange energy only in multiples of hv, so that level 0 is the lowest state. 

Intermolecular repulsion forces will define a hard-sphere diameter for the molecules allowing the calculation and/or measurement of the density fluctuation as one moves away from the surface. As shown in Figure 4.86, the result is a damped density curve (density distribution versus distance in molecular diameters from the surface). For a liquid between two surfaces at short separation distances, the two effects will overlap producing an interference pattern as illustrated in Figure 4.9. When the distance of separation is some integral multiple of the hard sphere diameter, nAhs, reinforcement occurs producing a local free energy minimum. For separations that correspond to fractional... 

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