Space Group Approximation of a Molecular Crystal by Classifying Molecules for Their Electric Potentials and Roughness on Their Inertial Ellipsoid Surface

In order to predict the most probable space group where a molecule crystallizes, it is assumed that molecular shape and electric potential distribution on the molecular surface are the main factors or predictors. However, to compare and classify molecules by these two factors seems to be very difficult for in general such different objects. Thus, in order to compare molecules, they are reduced to their inertial ellipsoid in which surface 26 equally spaced points were chosen where a roughness factor and an electric potential due to all atomic charges of the whole molecule are calculated. By this procedure, different molecules encoded by these two predictor vectors can be compared and classified, showing that molecules that crystallize in the same space group have more similar predictor vectors. This result opens the possibility to predict the more probable spatial group associated with a molecule. 1. Introduction The first hypothesis considered for crystal packing prediction CPP of organic molecules is that the isolated molecule contains the information of its future crystal [1]. So it is for the so-called “blind tests,” the last published in 2011 [2], where several laboratories compete to find the crystal structure of a molecule by diverse calculations, where it is assumed that 95% of the molecules present no polymorph and prefer a cell with a given space group SG. Some approaches were previously done to get molecular crystal structure information by data mining [3, 4]. In the present study it is further assumed that the molecular crystal space group is mainly predetermined by the molecular form or roughness and by the electric potential distribution on the molecular surface, both factors being the best predictors for crystal packing, including the formation of hydrogen bonds. In fact electrostatic forces determine molecular reactions as can be observed by X-ray in the electron density distributions of crystalline molecules [5, 6], were interactions by electrostatic forces (including H-bonds) between equal molecules in a crystal, would determine its crystal packing. The purpose of this work is to classify the molecules into groups by similarity of the above predictors and to check if these assumed types of packing are correlated with their space group SG, or conversely, to verify that molecules crystallizing in the same SG have similar aggregation predictors. However, comparing these two predictors between usually dissimilar molecules does not seem so simple, unless the molecules could first be reduced to more comparable objects. In a previous work [7],