Molecular axes and planes as an Eigenvalue problem

A statistical approach is used to define the long molecular axis and the main molecular plane. While the concept of molecular axis and plane is immediately useful for simple rod-like or planar molecules, it can be easily generalized to arbitrary molecules as well as molecular subgroups. From the molecular axes and planes, the orientation of the molecule with respect to the lattice as well as intermolecular orientations can be characterized. The method is applied for a comparison of pentacene and para-quinquephenyl crystal structures.