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}^{α}*c*_{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}^{α}*c*_{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