Essentials of Computational Chemistry

H
H
H
H
C
5.4 INDO FORMALISM 139
gCC
no distinction in two-electron repulsions
H
N
H
:
:
gNN
Figure 5.1 The CNDO formalism for estimating repulsive two-electron interactions fails to distinguish
in one-center cases between different orbitals (top example for the case of methylene) and in
two-center cases either between different orbitals or different orbital orientations (bottom example for
the case of hydrazine)
on each nitrogen. However, we see from Eq. (5.8) that this repulsion, γNN, depends only on
the distance separating the two nitrogen atoms, not on the orientation of the lone pair orbitals.
5.4 INDO Formalism
5.4.1 INDO and INDO/S
Of the two deficiencies specifically noted above for CNDO, the methylene problem is
atomic in nature – it involves electronic interactions on a single center – while the hydrazine
problem is molecular insofar as it involves two centers. Many ultraviolet/visible (UV/Vis)
spectroscopic transitions in molecules are reasonably highly localized to a single center,
e.g., transitions in mononuclear inorganic complexes. Pople, Beveridge, and Dobosh (1967)
suggested modifications to the CNDO formalism to permit a more flexible handling of
electron–electron interactions on the same center in order to model such spectroscopic
transitions, and referred to this new formalism as ‘intermediate neglect of differential
overlap’ (INDO). The key change is simply to use different values for the unique onecenter
two-electron integrals. When the atom is limited to a basis set of s and p orbitals,
there are five such unique integrals
H
(ss|ss) = Gss
(ss|pp) = Gsp
(pp|pp) = Gpp
(pp|p′p′) = Gpp′
(sp|sp) = Lsp
:
H
H
H
N
H
C
H
:
gCC
gNN
(5.11)