Basic NDDO Formalism

A modified INDO model that is not entirely obsolete is the symmetric orthogonal-ized INDO (SINDOl) model of Jug and co-workers, first described in 1980 (Nanda and Jug 1980). The various conventions employed by SINDOl represent slightly different modifications to INDO theory than those adopted in the MINDO/3 model, but the more fundamental difference is the inclusion of d functions for atoms of the second row in the periodic table. Inclusion of such functions in the atomic valence basis set proves critical for handling hyper-valent molecules containing these atoms, and thus SINDO1 performs considerably better for phosphorus-containing compounds, for instance, than do otlier semiempirical models that lack d functions (Jug and Schulz 1988). 

The INDO model extends the CNDO model by adding flexibility to tlie description of the one-center two-electron integrals. In INDO, however, there continues to be only a single two-center two-electron integral, which takes on the value /ab irrespective of which orbitals on atoms A and B are considered. As already noted, this can play havoc witli the accurate representation of lone pair interactions. 

Although these numbers seem large, this is still a considerable improvement over evaluating every possible integral, as would be undertaken in ab initio HF theory. Most modem semiempirical models are NDDO models. After examining the differences in their formulation, we will examine their performance characteristics in some detail in Section 5.6. 

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