Overlap integral population

S12 is the overlap integral between %x and 2. The term 2c1c2Sn is the overlap population it expresses the electronic interaction between the atoms. The contributions cf and c2 can be assigned to the atoms 1 and 2, respectively. 

In a Mulliken population analysis, the electron density of the overlap terms is equally divided between the two atoms. Since the overlap integrals S(2s F)(lsH) and S(2phydrogen atom is positively charged. 

Strictly speaking, there should be no electron population between pairs of atoms in SHMO since orbitals are assumed not to overlap. However, it is conventional to set all overlap integrals to unity for the purpose of defining a bond order. The bond order, BAb, between centers A and is defined as... 

Here, Q- is the partial overlap population, namely, the electron population of the overlap region between the atomic orbitals y,- and Xj >n the MO atomic orbitals y,- and y, in the MO , and S,(, the overlap integral between atomic orbitals y,- and y . QH is the gross atomic population or the gross atomic charge on atom H and is given by the sum of the atomic orbital populations Qi. The net charge AQh is obtained from the difference between QH and the atomic number ZH, namely, the number of electrons in the neutral atom. 

It s possible to extend the idea of an overlap population to a crystal. Recall that in the integration of for a two-center orbital, 2cic25i2 was a characteristic of bonding. If the overlap integral is taken as positive (and it can always be arranged so), then this quantity scales as we expect of a bond... 

---