  Many modern semiempirical molecular orbital models are built on the neglect
of diatomic differential overlap (NDDO) approximation. An in-depth
understanding of this approximation is therefore indispensable to rationalize
the success of these semiempirical molecular orbital models and to develop
further improvements on them. The NDDO approximation provides a recipe to
approximate electron-electron repulsion integrals (ERIs) in a symmetrically
orthogonalized basis based on a far smaller number of ERIs in a locally
orthogonalized basis. We first analyze the NDDO approximation by comparing ERIs
in both bases for a selection of molecules and for a selection of basis sets.
We find that the errors in Hartree-Fock and second-order Moller-Plesset
perturbation theory energies grow roughly linearly with the number of basis
functions. We then examine different approaches to correct for the errors
caused by the NDDO approximation and propose a strategy to directly correct for
them in the two-electron matrices that enter the Fock operator.
