Some Comments on Descriptors of Relative Shape

The foregoing example uses geometry and connectivity to derive an equivalence between configurations. The same notion can be used for any other type of shape descriptor An equivalence between structures found along reaction paths has been derived in terms of surface descriptors.The result can be viewed as a form of the Hammond postulate expressed in terms of molecular shape, rather than differences of potential energy. 

Other methods can be used to quantify shape fluctuations and flexibility. The alternatives listed briefly here employ absolute shape descriptors  

Averages of local descriptors are useful for recognizing changes in accessible conformations. The moments of the distribution of dihedral angles are an example of such dynamical descriptors. These distributions will vary with the conditions of simulation, such as temperature and molecular environment. 

Conformationally averaged surface descriptors, such as solvent-accessible areas, provide a realistic descriptor of the space spanned by a flexible molecule or a weakly bound complex. Simulations indicate correlations between the stability of a diastereomeric complex and its accessible dynamic 

Flexibility indices have been developed in terms of distance matrices and related graph-theoretical descriptors. These methods are based on the number of rotatable bonds in a molecule. The actual conformers that are accessible in a given condition are not considered. Nevertheless, these indices can be useful in database searching. A number of techniques have been discussed and compared.2i4 

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