Static shape descriptors

Consequently, an accurate description of molecular shape should include a smearing effect resulting from nuclear motions and uncertainties. A number of solutions are proposed in the literature, including the use of nuclear wavefunctions, >2 o open sets of nuclear configurations,and a fuzzy set approach to molecular shape. We shall use the term dynamical shape for a description that takes into account nuclear flexibility. Such a characterization is performed with dynamic shape descriptors. The term static shape descriptors is reserved to those defined at a frozen nuclear geometry. 

It is possible to design shape descriptors that incorporate nuclear vibrations. However, the simpler approach to shape dynamics is to apply static descriptors to entire domains of nuclear configurations. We then observe the interrelation between molecular shape and molecular motions (e.g., vibrations, reaction paths).32,33 in this case, we find a range of values in static parameters. The span of such a range (e.g., the fluctuations in a static descriptor) can characterize shape dynamics.3 ... 

The next sections focus mostly on the properties of absolute shape descriptors. Special attention is devoted to those that are used to study static conformations and dynamics. Among the myriad of shape descriptors in the literature, we deal with a subset of those that are conceptually distinct and serve as examples for the construction of many others. 

Molecular shape has a fundamental influence on both the static and dynamic properties of molecules. For example, the shapes of nuclear and electronic distributions determine the molecular dipole moments as well as the likely sites of approach by a nucleophilic reagent. The evolution of concepts and models used by chemists for the description of the molecular shape closely mirrors the advances made in our understanding of molecular behavior. Whereas most of the early models focused on the nuclear arrangements, the more advanced recent approaches have placed increasingly more emphasis on the electronic distribution. The nuclear position descriptors, however, is still very important, since the nuclei in molecules are more particle-like than electrons and therefore much easier to be described. For the description of the shape of complex molecules, the concept of similarity appears to be very useful. 

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