Wigner functions and bond orders

The momentum-space origin of the Wigner function for electronic systems gives a convenient fingerprint of the bonding situation in a molecule. This is owing to its connection to the off-diagonal regions of the one-particle reduced density matrix which are known to map the covalent sharing of electrons in a bound system. Since the topology of this "Parity Function" follows similar patterns as the commonly employed bond orders based on population analysis, this article endeavors to correlate the values of the parity function at special points in real space with such bond orders. We also point out a relationship between the parity function and experimentally obtainable scattering cross-sections. Throughout this paper, atomic units are used, i.e. we are conventionally setting (h) over bar = m(e) = e = a(0) = E-h = 1. This also implies that the speed of light is the inverse of the fine-structure constant c = 1/alpha. The only exception is that bondlengths are sometimes given in Angstroms, 1 angstrom = 10(-10) m = 1.8897a(0).