Continuing with the neglect of differential overlap, all two-electron integrals
involving charge clouds arising from the overlap of two atomic orbitals on
different centers are ignored. Since no rotation can convert a two center
two-electron integral into a set of integrals involving three and four center
terms, rotational invariance is not compromised by this approximation.
Rotational invariance is present if the calculated observables [
ΔH_{f},
Dipole, I.P., etc] are not dependent on the orientation of the system. The
effects of this approximation on the Roothaan equations are as follows:

In the Fock matrix, if
ψ_{μ} and
ψ_{μ}
are on different
centers the NDDO matrix element F_{μν}^{α}
reduces to

Equivalent expressions exist for
F_{μν}^{β}
and
P_{μν}^{β}.
Thus no Coulombic terms are present in the two-center
Fock matrix elements.

If ψ_{μ} and
ψ_{μ}
are different but on the same center,
then, since a minimal basis set is being used, all integrals of the type
<μν|λσ> are zero by the orthogonality of the atomic
orbitals unless μ = ν and λ = σ, or
μ = λ and ν = σ.
The off-diagonal one-center NDDO Fock matrix elements become: