Looking for an unambiguous geometrical definition of organic series from 3-d molecular similarity indices.

A mathematically consistent definition of series was derived by the application of Principal Component Analysis to 3-D similarity indices (ASP Software). For two data sets of aromatic molecules, a mono-dimensional numerical ordering was derived, corresponding to the consensus distance from the series lead. The series is unambiguously defined in terms of location along the mono-dimensional axis, along which shape and electrostatic features of the molecules vary in a coordinated way. Molecules along the axis are characterized by the same pattern of electrostatic potential and shape shared by the lead compound, of which they represent linearly "shifted" replicas. This approach can contribute to the exploration of the chemical spaces from a local "fine grain" perspective, thus complementing the "coarse grain" descriptions normally used in the analysis of large data sets.