CNDO Formalism

Returning to the SCE formalism of HE theory, one can proceed in the spirit of an effective Hamiltonian method by developing a recipe for the replacement of matrix elements in the HE secular equation, Eq. (4.53). One of die first efforts along these lines was described by Pople and co-workers in 1965 (Pople, Santry, and Segal 1965 Pople and Segal 1965). The complete neglect of differential overlap (CNDO) mediod adopted the following conventions  

Just as in EHT, die basis set is formed from valence STOs, one STO per valence orbital. In the original CNDO implementation, only atoms having s and p valence orbitals were addressed. 

In the secular determinant, overlap matiix elements are defined by 

All two-electron integrals are parameterized according to the following scheme. First, define 

the only integrals that are non-zero have /z and v as identical orbitals on the same atom, and A, and ct also as identical orbitals on the same atom, but the second atom might be different than the first (the decision to set to zero any integrals involving overlap of different basis functions gives rise to the model name). 

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The valence DOS has been computed for Ni and Ag clusters within the CNDO formalism. Blyholder [54] examined the Nis and M13 clusters. In both cases of s- and p-orbitals are occupied and lie well below the d-orbitals. Most of the intensity is near the middle of the d-orbitals with a fall-off in intensity as the HOMO is approached. Density of states for Agv, Agio, Agi3, and Agig clusters shows a strong d-component cc. 3.5 eV wide. The... 

As stated above, CNDO formalism was able to predict for many methyl derivatives (containing numerous hydrogen atoms) preferred conformations fully identical to those obtained by the most appropriate experimental techniques, electron diffraction and microwave spectroscopy. This was the case, for example, for each term of the (CH3)2M (14) and (CH3)3M (15) series. This quantum approach appeared likely to help experimentalists to locate accurately, and in a simpler way than usual, the light atoms - mainly hydrogen — in a molecule. 

We now describe some results obtained with the extended CNDO formalism concerning preferred conformations and related parameters within the field of mononuclear coordination derivatives. 

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)...

Let Rq, the lattice vector of the reference cell, correspond to the origin of the coordinate system. Then the core (H) and Fock (F) matrix elements have the following form within the CNDO formalism... 

We have illustrated the efficiency of the original CNDO/2 formalism for the conformational analysis of nonmetallic compounds and briefly indicated in Section III that an extension of this quantum technique, designed to be applicable to transition-... 

The purpose of this brief survey was to demonstrate that, despite the criticisms which may be made of the use of any semi-empirical quantum technique for structural and conformational studies, the CNDO/2 and Extended CNDO/2 formalisms are definitely reliable tools for theoretical conformational analyses in inorganic and coordination chemistry. Moreover, if these tools are combined with the most suitable experimental techniques (i.e. microwave spectroscopy and electron diffraction) in that field, many problems of geometry and conformation can be solved in a way that neither of these approaches could have accomplished alone. 

It has been customary to classify methods by the nature of the approximations made. In this sense CNDO, INDO (or MINDO), and NDDO (Neglect of Diatomic Differential Overlap) form a natural progression in which the neglect of differential overlap is applied less and less fully. It is now clearer that there is a deeper division between methods, related to their objectives. On the one hand are approximate methods which set out to mimic the ab initio molecular orbital results. The objective here is simply to find a more economical method. On the other hand, some workers, recognizing the defects of the MO scheme, aim to produce more accurate results by the extensive use of parameters obtained from experimental data. This latter approach appears to be theoretically unsound since the formalism of the single-determinant wavefunction and the Hartree-Fock equations is retained. It can be argued that the use of the single-determinant wavefunction prevents the consistent achievement of predictions better than those obtained by the ab initio scheme where no further... 

Nonetheless, some useful information regarding methylation has been obtained from molecular orbital calculations. One CNDO/2 study on the allyl and pentadienyl anions indicated that in all cases the methyl group would serve to withdraw net electron density from the anions196. For the allyl anion, a 1-methyl substituent would withdraw a substantial 0.102 electrons, while at the formally uncharged 2 position the effect was consider-... 

In oxonium salts (alkylated ethers), the positive charge is located formally on the oxygen atom. It has to be remembered, however, that this is only the formal notation. In fact, as follows from CNDO-2 calculations, the charge is located mainly on carbon and hydrogen atoms [22],... 

More recently, an all valence electron, semiempirical molecular orbital theory known as the Complete Neglect of Differential Overlap (CNDO) has been proposed by Pople based on self-consistent field (SCF) formalism (5). Although this method uses a more sophisticated approximation of the wavefunction, it neglects differential overlap. 

Other semiempirical Hamiltonians have also been used within the BKO model. A Complete Neglect of Differential Overlap (CNDO/2) ° study of the effect of solvation on hydrogen bonds has appeared. o The Intermediate Neglect of Differential Overlap (INDO) °2 formalism has also been employed for this purpose.2011 Finally, the INDO/S model,which is specifically parameterized to reproduce excited state spectroscopic data, has been used within the SCRF model to explain solvation effects on electronic spectra.222,310-312 jhis last approach is a bit less intuitively straightforward, insofar as the INDO/S parameters themselves include solvation by virtue of being fit to many solution ultraviolet/visible spectroscopic data.29J... 

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