Similarity ideas in the theory of pericyclic reactivity

Distributions and averages of molecular conformations

A computational technique is proposed for the study of electron density variations within a distribution of molecular conformations. These variations are defined in terms of the deviations of individual electron densities from the average density associated with the average of conformations within a conformational range of a molecule.

Shape-similarity analysis of 20 stable conformations of neutral β-alanine

The family of 20 stable conformations of neutral β-alanine are analyzed in terms of their shape similarities using the topological Shape Group Method, a general molecular shape analysis technique as applied to the three-dimensional electronic density. Molecular electron densities are calculated using the 6-31G** basis set, followed by the determination of the shape groups of local curvature patterns for the entire chemically relevant range of electron density contour surfaces. The results of the shape group analysis are represented by two-dimensional shape maps. Discretized grids of these maps generate numerical shape codes, and comparisons of these numerical codes serve as measures of shape similarity of the various conformers of β-alanine. This technique is based on direct comparisons of the intrinsic shape features of molecules and requires no superposition of molecules for comparisons. Mathematically well-defined and unbiased similarity measures are obtained by this non-visual, computer-based method, useful for the detection, quantification, and analysis of electronic charge distribution similarities. The family of 20 stable conformers of β-alanine serves as a test case for the application of the methodology for a large number of conformers, representing a level of complexity analogous to that of typical conformational problems in computer-aided drug design and the screening of potential drug molecules for shape similarity. Key words: similarity measures, shape groups, β-alanine, conformation analysis, molecular shape, electron density.