Neglect of three and four center integrals

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 [ DH_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 f_m and f_n are on different centers the NDDO matrix element F_mn^a reduces to

F_mn^a = H_mn +S_l^AS_s^B P_ls^a <ml|ns>.

Equivalent expressions exist for F_mn^b and P_mn^b. Thus no Coulombic terms are present in the two-center Fock matrix elements.

If f_m and f_n are different but on the same center, then, since a minimal basis set is being used, all integrals of the type <mn|ls> are zero by the orthogonality of the atomic orbitals unless m = n and l = s, or m = l and m = s. The off-diagonal one-center NDDO Fock matrix elements become:

F_mn^a = H_mn + 2P_mn^a+b <mn|mn> - P_mn^a (<mn|mn> + <mm|nn>).

If f_m is the same as f_n, then, because of the symmetry of the two-electron integrals, the diagonal NDDO Fock matrix elements reduce to:

F_mm^a = H_mm + S_n^A(P_mm^a+b <mm|nn> - P_n_n^a <mn|mn>) + S_BS_l^BS_s^BP_ls^a+b<mm|ls>.