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_ls^a  = S_i^occ(c_li^ac_si^a)

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

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_ls^a  = 1 - S^N_{i=occ + 1}(c_li^ac_si^a)

and

P_ls  = 2 - S^N_{i=occ + 1}(c_lic_si)

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

 H_mn  = S_mn(U_mm + U_nn )/2.

where S_mn is the overlap integral between atomic orbital f_m on an atom, and f_n on another atom, and the U values are atomic orbital constants, supplied as data.