A minimum asymmetry index for measuring asymmetry of the electron density distribution

Abstract

An asymmetry index (AI) is introduced to measure deviation of the electron density distribution in a molecule from any given symmetry. This AI is calculated by summing all point-wise differences between electron density distributions before and after symmetry operation. A minimum asymmetry index (MAI) rule is also introduced to evaluate uniquely the extent of asymmetry of a molecule with respect to any reference symmetry operation. This MAI rule prescribes where to locate the reference element of symmetry. The overall MAI for a given molecule with respect to a certain symmetry point group is calculated by averaging over AIs of all symmetry elements appearing in its character table. The proposed AI and the MAI rule are used to measure electron density asymmetry of the NX3, NX2Y/NXY2 and NXYZ (X, Y, Z = H, F, Cl, Br) series of molecules referenced to the C3V symmetry.