ABSTRACT
It was realized very early that the use of the Coulson bond order index dis-
cussed in Section 1.2 is restricted to the pi-electron theories because in the
general case one has more than one basis function on each atom. As a con-
sequence, neither the individual two-center D-matrix elements nor their sum
for a given pair of atoms obey the required invariance under the rotation of
the molecular system with respect of the external laboratory system of co-
ordinates. The quantity proposed for identifying chemical bonds had been
Mulliken’s overlap population qAB-see the right-hand side of Eq. (3.26) or
Eq. (4.26)—which is linear in the interatomic D-matrix elements and has the
proper invariance property. Mulliken’s overlap populations often are indeed
useful measures of the bond strengths. However, the overlap population does
not take the values of (about) one, two, or three for the classical single, dou-
ble, and triple chemical bonds, respectively. Therefore, it cannot be identified
with the classical notion of bond order (multiplicity). As will be seen, in order
to find a quantum mechanical counterpart of the latter, one needs a quantity
which is quadratic in the D-matrix elements.
