Atomic structures landscapes

Optimization problems in crystallographic structure refinement are seldom convex, that is very rarely characterized by a unimodal function/(x). Regularization of a two-atom model is an example of such a unimodal function. Fig. 11.2a. in contrast. Fig. 11.2b shows a profile of a function for modelling an amino acid side chain - the peaks correspond to the possible rotamers. In this case, the shape of the function/(x) is called multimodal. Such functions arise naturally in structural macromolecular optimization problems and possess a highly complex multiminima energy landscape that does not lend itself favourably to standard robust optimization techniques. 

Figure 8.50 A comparison of the performance of atom-atom potentials using the UNI method80 and PIXEL potentials in the description of the energy landscape for 133 naphthalene crystal structures. The experimental crystal structure is represented by a cluster of 5 points representing very similar structures with different unit cell settings. Energies are given on the abscissa in kj mol 1. The plot shows the usual way of representing the results of crystal structure calculations with the expectation that the most stable structure should be at the lowest energy and exhibit the highest density. (Reproduced with permission from The Royal Society of Chemistry).

After asserting the nanostructured nature of ionic liquids, the structural analysis of these fluids continued in two different directions. The first was to check how the built-in flexibility of the isolated ions of the model affect (or are affected by) the nanostructured nature of the ionic liquid, and how that can influence properties like viscosity, electrical conductivity, or diffusion coefficients. It must be stressed that the charges in the CLAP model are fixed to the atomic positions, which means that the most obvious way to probe the relation between the structure of the ionic liquid as a whole in terms of the structure of its individual ions is to investigate the flexibility (conformational landscape) of the latter. The second alternative direction was to probe the structure of ionic liquids not by regarding into the structure of the component ions but by instead using an external probe (for example, a neutral molecular species), solubility experiments with selected solute molecules being the most obvious experimental approach. 

In addition to these thermodynamic and structural effects, the range of the potential can be expected to influence the dynamics of a system. This section summarizes a case study for the 13-atom Morse cluster, M13, to investigate the connection between the global features of the energy landscape [159] and the dynamics [149] as a function of the range of the potential. 

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