# Wiberg bond orders¶

## Theory¶

The concept of bond order has been proposed by Wiberg [Wiberg-1966] as a calculated bond property using orthonormalized atomic orbitals which are a basis set for semi-empirical molecular orbitals. Originally it was formulated for the CNDO basis set, but it might be extended to AM1 or PM3 methods. Wiberg bond order is a measure of electron population overlap between two atoms:

$$W_{AB} = \sum\limits_{\mu \in A} \sum\limits_{\nu \in B} P_{\mu\nu}^2$$

where summation is over atomic orbitals $$\mu$$ on atom A and atomic orbitals $$\nu$$ on atom B, and $$P_{\mu\nu}$$ is the corresponding density matrix element. For non-bonded pairs of atoms in a molecule, $$W_{AB}$$ is very low but always nonzero.