Neglect of diatomic overlap integral

All overlap integrals arising from the overlap of two different atomic orbitals are neglected. This reduces the overlap matrix to a unit matrix. The secular equation thus reduces to:

ci|F-εiS|ci = 0.

In semiempirical theory the Coulson density matrix is used, e.g.:

Pλσα  = Σiocc(cλ iαcσiα)


where the sum is over all occupied spin molecular orbitals. In RHF calculations, only the total density matrix is calculated:

Pλσ  = 2Σiocc(cλ icσi)


where the sum is over all occupied molecular orbitals.

When a system has more than half the available M.O.s, N, filled, it is computationally  faster to calculate the positron electron equivalent:

Pλσα  = 1 - ΣNi=occ+1(cλ iαcσiα)


Pλσα  = 2 - ΣNi=occ+1(cλ icσi)


An important exception to this rule is the calculation of the one-electron two-center integral Hμν, which is approximated by:

 Hμν  = Sμν(Uμμ + Uνν)/2.


where Sμν is the overlap integral between atomic orbital ψμ on an atom, and ψν on another atom, and the U values are atomic orbital constants, supplied as data.