CNDO methods

However, the CNDO method showed systematic weaknesses that were directly attributable to the approximations outlined above, so that it was superseded by the intermediate m lect of diatomic differential overlap (INDO) method, introduced by Pople, Beveridge, and Dobosh in 1967 [13]. The approximation outlined in Eq. (50) proved to be too severe and was replaced by individual values for the possible different types of interaction between two AOs. These individual values, often designated Cgg, Ggp, Gpp and in the literature, can be adjusted to give better agreement with experiment than was possible for CNDO. However, in INDO the two-center terms remain of the same type as those given in Eqs. (51) and (52) (again, there are many variations). This approximation leads to systematic weaknesses, for instance in treating interactions between lone pairs. 

In the CNDO/2 approach as originally implemented, ab initio (orbital-level) calculated values of the energies mentioned below are used in determining the requisite parameters. In the later CNDO/S method, experimental values of these energies are employed. Briefly, in any CNDO method ... 

The complete neglect of differential overlap (CNDO) method is the simplest of the neglect of differential overlap (NDO) methods. This method models valence orbitals only using a minimal basis set of Slater type orbitals. The CNDO method has proven useful for some hydrocarbon results but little else. CNDO is still sometimes used to generate the initial guess for ah initio calculations on hydrocarbons. 

More elaborated treatments have also been applied ab initio methods by Bouscasse (130) and Bernardi et al. (131) then the all-valence-electrons methods, derived from PPP. by Gelus et ai. (132) and by Phan-Tan-Luu et al. (133) and CNDO methods by Bojesen et al. (113) and by Salmona et al. (134). 

The CNDO method has been modified by substitution of semiempirical Coulomb integrals similar to those used in the Pariser-Parr-Pople method, and by the introduction of a new empirical parameter to differentiate resonance integrals between a orbitals and tt orbitals. The CNDO method with this change in parameterization is extended to the calculation of electronic spectra and applied to the isoelectronic compounds benzene, pyridine, pyri-dazine, pyrimidine and pyrazine. The results obtained were refined by a limited Cl calculation, and compared with the best available experimental data. It was found that the agreement was quite satisfactory for both the n TT and n tt singlet transitions. The relative energies of the tt and the lone pair orbitals in pyridine and the diazines are compared and an explanation proposed for the observed orders. Also, the nature of the lone pairs in these compounds is discussed. 

The INDO method is intermediate between the NDDO and CNDO methods in tenns of approximations. 

A consistently anomalous (with respect to electrochemical evidence) position of Au has been found by two different groups. According to Kuznetsov etal.,437 the complete neglect of differential overlap (CNDO) method predicts for any given metal a weaker interaction on the more dense surface. Thus the predicted sequence is (111) < (100) < (110) for fee metals such as Cu, Ag, and Au and (0001) < (1100) for hep metals such as Zn and Cd. However, for the most compact surfaces, the calculated sequence is Hg < Ag(l 11) < Cu(l 11) =Zn(0001) < Au(l 11) < Cd(0001). 

The description of configuration interaction given for rr-electron methods is also valid for all-valence-electron methods. Recently, two papers were published in which the half-electron method was combined with a modified CNDO method (69) and the MINDO/2 method was combined with the Roothaan method (70). Appropriate semiempirical parameters and applications of all-valence-electron methods are most probably the same as those reviewed for closed-shell systems (71). 

Such a peculiarity has also been observed in many other compounds with metal-carbon bonds, especially cobalt-carbon. As part of a study (using the above-mentioned extended CNDO method) of the AM(CO)3 isoelectronic series (AM from 772-C2H4Ni to rj6-C6H6Cr) it was shown that, in the t 3-C3HsCo derivative, the allyl group was linked to cobalt by means of the two C(H2) carbons and not predominantly by the C(H) carbon atom, despite the fact that Co—C(H2) = 2.10 A as compared with Co—C(H) = 1.98 A (55). 

VIII. The Use of CNDO Methods to Optimize Molecular Geometries... 

The CNDO method appears to be from this point of view a new spectroscopy for the study of molecular conformations, provided that the molecules in question belong to the class of electronically localized systems. 

At a first glance we are confronted with a striking contradiction Differential overlap is neglected in the CNDO method due to the ZDO approximation (16). Therefore there is no exchange contribution to the energy of interaction in CNDO or related calculations, z1 ex=0. 

Comparison of Empirical Charge Densities with those Calculated by the HMO and CNDO Methods for Triphenylcarbonium Ion (twist angle = 30 ) ... 

JHC735>. The polarizability and hyperpolarizability of 1,2,3-triazole have been computed by the Hartree-Fock perturbation theory on an extended basis CNDO method <90JPC1755>. 

Pople-Pariser-Parr PPP (CNDO) method. MO s from LCAO SCF, i.e. electron correlation taken into account. Equations to derive the LCAO coefficients by the variational procedure were proposed by Roothaan... 

Returning to the SCF formalism of HF theory, one can proceed in the spirit of an effective Hamiltonian method by developing a recipe for the replacement of matrix elements in the HF secular equation, Eq. (4.53). One of the 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) method adopted the following conventions ... 

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