Orbitals in NDDO Models

To extend NDDO methods to elements having occupied valence d orbitals that participate in bonding, it is patently obvious that such orbitals need to be included in the formalism. However, to accurately model even non-metals from the third row and lower, particularly in hypervalent situations, d orbitals are tremendously helpful to the extent they increase the flexibility with which the wave function may be described. As already mentioned above, the d orbitals present in the SINDOl and INDO/S models make them extremely useful for spectroscopy. However, other approximations inherent in the INDO formalism make these models poor choices for geometry optimization, for instance. As a result, much effort over the last decade has gone into extending the NDDO fonnalism to include d orbitals. 

Thiel and Voityuk (1992, 1996) described the first NDDO model with d orbitals included, called MNDO/d. For H, He, and the first-row atoms, the original MNDO parameters are kept unchanged. For second-row and heavier elements, d orbitals are included as a part of the basis set. Examination of Eqs. (5.12) to (5.14) indicates what is required parametrically to add d orbitals. In particular, one needs and /ij parameters for the one-electron integrals, additional one-center two-electron integrals analogous to those in Eq. (5.11) (there are 

It appears, then, dial MNDO/d has high utility for thermochemical applications. In addition to the elements specified in Table 5.2, MNDO/d parameters have been determined for Na, Mg, Zn, Zr, and Cd. However, since die model is based on MNDO and indeed identical to MNDO for light elements, it still performs rather poorly with respect to intermolecular interactions, and widi respect to hydrogen bonding in particular. 

Very recent extensions of the formalism of Thiel and Voityuk to AMI have been reported by multiple groups. Voityuk and Rosch (2000) first described an AMl/d parameter set for Mo, and, using the same name for the method, Lopez and York (2003) reported a parameter set for P designed specifically to facilitate the study of nucleophilic substitutions of biological phosphates. Winget et al. (2003) described an alternative model, named AMI, that adds d orbitals to P, S, and Cl. As with MNDO/d, the primary improvement of this model is in its general ability to describe hypervalent molecules more accurately. Subtle differences in the various individual formalisms will not be further delved into here. 

A semiempirical model including d orbitals has also been reported by Dewar and coworkers (Dewar, Jie, and Yu 1993 Holder, Dennington, and lie 1994), although the full details of its functional fonn still await publication. Semi-ah initio model 1 (SAMI, or 

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