Wave functions, INDO

A UHF wave function may also be a necessary description when the effects of spin polarization are required. As discussed in Differences Between INDO and UNDO, a Restricted Hartree-Fock description will not properly describe a situation such as the methyl radical. The unpaired electron in this molecule occupies a p-orbital with a node in the plane of the molecule. When an RHF description is used (all the s orbitals have paired electrons), then no spin density exists anywhere in the s system. With a UHF description, however, the spin-up electron in the p-orbital interacts differently with spin-up and spin-down electrons in the s system and the s-orbitals become spatially separate for spin-up and spin-down electrons with resultant spin density in the s system. 

An ab initio HF calculation with a minimum basis set is rarely able to give more than a qualitative picture of the MOs, it is of very limited value for predicting quantitative features. Introduction of the ZDO approximation decreases the quality of the (already poor) wave function, i.e. a direct employment of the above NDDO/INDO/CNDO schemes is not useful. To repair the deficiencies due to the approximations, parameters are introduced in place of some or all of the integrals. 

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. 

Schulman and Venanzi (20) have evaluated a=s (0) n(0) and b=(r 3)c(r 3)N. For other than triple bonds they find that a is 13 79 a.u. and b is l -7 a.u., while for triple bonds a is 13 10 a.u. and b is 20 85 a.u. In the opinion of the reviewer the large difference calculated for b in these two cases is not reasonable. Furthermore, if one assumes a value of 2 5 a.u. or 2 88 a.u. for (r 3)c, as obtained earlier by Schulman and Newton (42) and by Blizzard and Santry (16, 17) from their studies of C-C coupling constants, then one obtains (r 3)N <0 71 a.u. when the N atom is singly bonded to carbon. The conclusion that (r 3)N is less than one-half (r 3)c also seems unreasonable (see Table I). One must ask how much agreement should be expected between observed /(C-X) values and those obtained from semi-empirical MO calculations at the INDO level of approximation, and to what extent the disagreement between theory and experiment is due to inadequacy of the wave functions. 

Today we know that the HF method gives a very precise description of the electronic structure for most closed-shell molecules in their ground electronic state. The molecular structure and physical properties can be computed with only small errors. The electron density is well described. The HF wave function is also used as a reference in treatments of electron correlation, such as perturbation theory (MP2), configuration interaction (Cl), coupled-cluster (CC) theory, etc. Many semi-empirical procedures, such as CNDO, INDO, the Pariser-Parr-Pople method for rr-eleetron systems, ete. are based on the HF method. Density functional theory (DFT) can be considered as HF theory that includes a semiempirical estimate of the correlation error. The HF theory is the basie building block in modern quantum chemistry, and the basic entity in HF theory is the moleeular orbital. 

The choice of factors for converting the unpaired a.o. spin densities so obtained to hyperfine interactions is a subject of some contention. Empirical conversion factors have been suggested for use with INDO - derived spin densities (28). Alternatively, one may employ atomic coupling constants derived ab initio from a particular set of atomic wave functions. This is the approach which we favour, and, if only for the sake of consistency, we have used the atomic constants derived fromFroese s (29) wave function (Table H). 

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