Chiral measure of chiral polyhedrons

Abstract

To quantify chiral shape, a tensor describing the particle shape has been proposed. This tensor, named the shape tensor (S-tensor), is an analog of the hydrodynamic tensor that relates the rotational and translational motions of particles in a liquid. The determinant of the S-tensor, named chirality measure density (CMD), was calculated for chiral tetrahedrons and octahedrons. It was found that CMD is opposite in sign when the mirror images are chiral to each other and vanishes when they are achiral. Therefore, the CMD is a good measure to distinguish the mirror images. The interaction between chiral particles was discussed in terms of the CMD.