Curved phenine normal vectors: Geometric measures of geodesic phenine frameworks

A vector was introduced to quantitatively describe the pyramidalization of 1,3,5-trisubstituted benzene (phenine). The vector, named curved phenine normal vector (CPNV), defined the direction of pyramidalization of the trigonal phenine panel and quantified the degree of pyramidalization. The relative orientation of the two CPNVs further defined a dihedral angle, which quantified interphenine torsions. The CPNV analysis visually showed the geometric features of nanometer-sized molecules by revealing the important role of torsions. Biased electrostatic potentials were also correlated with CPNV pyramidalizations.