Binned geometrical distances, spheres and trie. The upper left figure shows the spheres of the binned geometrical distances of 1.0, 2.0, and 3.0 Å for the centered carbon atom. The sphere of the binned geometrical distance of 0.0 Å (distances in the range [0.0;1.0)) is not visualized as individual sphere because it contains no atoms. The upper right figure illustrates the resulting local atom pair environment of binned geometrical distances. For simplicity, only the distances to non-carbon atoms are displayed. The lower figure visualizes the corresponding trie of geometric atomic distances of the annotated atom in the upper figures. The root and leaves are labeled with the corresponding atom type. The leaves contain additionally the total number of occurrences in the local atom pair environment.