# A general definition of bond order in molecular orbital theory?

I stumbled upon this problem upon learning organic chemistry after learning the foundations of MO theory in physical chemistry. It seems that VBT and MOT can coexist with each other in many scenarios. One problem that especially confuses me about their compatibility is that how can we define a general notion of bond order in MOT. This question arises naturally as we assign integer values to bonds between atoms in VBT but this is definitely not true in MOT.

It's often taught in general chemistry course that bond order is 1/2 times number of bonding orbitals minus antibonding orbitals, but this definition only works for diatomics. I wonder if there's some more general definition that works for each adjacent(perhaps this is ill defined) pair of atoms, perhaps in the spirit of Mulliken population analysis that assigned partial atomic charges based on MO coefficients of AOs.

• One example for pi bonds: Coulson defined pi bond order within Huckel MO theory as $\Sigma_i n_ic_{ri}c_{si}$. See Levine, Quantum Chemistry 4th edition p. 567 – Andrew Dec 21 '19 at 13:55
• Wiberg bond indices and Mayer bond order may be starting points. – TAR86 Dec 21 '19 at 14:27