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:

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

P_λσ^α  = Σ_i^occ(c_{λ i}^αc_σi^α)

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

P_λσ  = 2Σ_i^occ(c_{λ i}c_σi)

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:

P_λσ^α  = 1 - Σ^N_i=occ+1(c_{λ i}^αc_σi^α)

and

P_λσ^α  = 2 - Σ^N_i=occ+1(c_{λ i}c_σi)

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

 H_μν  = S_μν(U_μμ + U_νν)/2.

where S_μν is the overlap integral between atomic orbital ψ_μ on an atom, and ψ_ν on another atom, and the U values are atomic orbital constants, supplied as data.