Complete neglect of differential overlaps CNDO

Ihc complete neglect of differential overlap (CNDO) approach of Pople, Santry and Segal u as the first method to implement the zero-differential overlap approximation in a practical fashion [Pople et al. 1965]. To overcome the problems of rotational invariance, the two-clectron integrals (/c/c AA), where fi and A are on different atoms A and B, were set equal to. 1 parameter which depends only on the nature of the atoms A and B and the ii ilcniuclear distance, and not on the type of orbital. The parameter can be considered 1.0 be the average electrostatic repulsion between an electron on atom A and an electron on atom B. When both atomic orbitals are on the same atom the parameter is written , A tiiid represents the average electron-electron repulsion between two electrons on an aiom A. 

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. 

In the Complete Neglect of Differential Overlap (CNDO) approximation only the Coulomb one-centre and two-centre two-electron integrals remain (eq. (3.78)). 

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). 

In order to obtain nonzero spin densities even on hydrogen atoms in tt radicals, one has to take the one-center exchange repulsion integrals into account in the eigenvalue problem. In other words, a less rough approximation than the complete neglect of differential overlap (CNDO) is required. This implies that in the CNDO/2 approach also, o and n radicals have to be treated separately (98). 

The simplest theory that is consistent with these requirements employs the complete neglect of differential overlap (CNDO)29. This semi-empirical approach will be discussed in some detail, albeit without extensive mathematical justification, as it illustrates the type of approximations that are made in more advanced theories. In addition to the assumptions outlined above, the remaining Coulomb-type integrals are reduced to a single value -yAB that depends only on the nature of atoms A and B with which < > and t are associated, respectively, and not on the actual type of orbitals that overlap. This is equivalent to stating ... 

Various theoretical methods (self-consistent field molecular orbital (SCF-MO) modified neglect of diatomic overlap (MNDO), complete neglect of differential overlap (CNDO/2), intermediate neglect of differential overlap/screened approximation (INDO/S), and STO-3G ab initio) have been used to calculate the electron distribution, structural parameters, dipole moments, ionization potentials, and data relating to ultraviolet (UV), nuclear magnetic resonance (NMR), nuclear quadrupole resonance (NQR), photoelectron (PE), and microwave spectra of 1,3,4-oxadiazole and its derivatives <1984CHEC(6)427, 1996CHEC-II(4)268>. 

Complete mix activated sludge (CMAS) process, 25 900, 903-904 Complete neglect of differential overlap (CNDO) technique, 16 737 Completion developer, 19 301 Completion fluids, 9 26-30 Complex III inhibitors, 14 348—349 Complexation... 

Complete Neglect of Differential Overlap (CNDO) calculations by Naray-Szabo and Surjan (80MI2), however, were interpreted to favor the lactim form 30a of MOT which is in line with the experimental UV spectra. 

A variety of more advanced, all-electron methods of this type Me available, and are generally referred to as semi-empirical calculations. The acronyms used to name the individual methods are descriptive of the manner in which atomic overlap calculations are performed. Among the more widely used semi-empirical methods are those of complete neglect of differential overlap (CNDO/2) (12), modified intermediate neglect of differential overlap (MINDO/3) (13), and modified neglect of diatomic overlap (MNDO) (14). 

A number of papers have appeared recently in which semiempirical quantum mechanical methods, such as the complete neglect of differential overlap (CNDO), incomplete neglect of differential overlap (INDO), or Hiickel methods, have been applied to electron-deficient systems in an attempt to calculate their properties (31, 49, 64, 75, 77, 78, 89, 90, 92). Although the quantitative results of these calculations must be treated with great care, they do provide an indication of some of the parameters that determine formation and stability of electron-deficient bonded systems. 

On the basis of complete neglect of differential overlap (CNDO/2) calculations which include silicon p and d orbitals in the basis set, the effect of the trimethylsilyl substituent is due to electron withdrawal by the interaction of both the silicon p and d orbitals with the aromatic ir-system (85). In as much as the silicon p orbitals are primarily involved in the cr and cr orbitals of the trimethylsilyl group, interaction of the silicon p orbitals with the ir-system amounts to a hyperconjugative, v — cr, electron withdrawl (85). 

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 ... 

The method of CHF-PT-EB CNDO has been used for several organometallic complexes. This method utilizes a coupled Hartree-Fock (CHF) scheme10 applied through the perturbation theory (PT) of McWeeny,11"13 and an extended basis (EB), complete neglect of differential overlap (CNDO/2) wavefunction. The exponents of the basis set are optimized with respect to experimental polarizabilities and second hyperpolarizabili-ties.14,15 A detailed description of the CNDO/2 method may be found in Ref. 16. 

Polarizability-Kow Relationships Molar polarizabilities can be derived from molecular orbital (MO) calculations by the complete neglect of differential overlap (CNDO) method [42]. The following correlation has been found for polar compounds that contain either hydrogen-bond-accepting or hydrogen-bond-donating groups (alkanols, alkanones, dialkyl ethers, alkanenitriles) ... 

So far, only a few papers have appeared on NMR spectra of 2-benzopyrylium salts. The H-NMR spectra of eleven l-R -3-R2-6,7-dimethoxy-benzo[c]pyrylium salts were interpreted with the use of a complete neglect of differential overlap (CNDO/2) method in standard geometry, and a fair correlation between charge densities and chemical shifts has been obtained (90MI3). The experimental 8 values for this series are presented here. 

The electronic structures of hydrochlorothiazide 146 and related substances have been determined by the complete neglect of differential overlap (CNDO/2) method (83AF688). The calculation confirms that the diuretic thiazides are electron-accepting, whereas diazoxide 147, a non-... 

Finally, semiempirical complete neglect of differential overlap (CNDO) calculations [145] again emphasize N2 binding to the trigonal cavity, but now with one nitrogen atom at the center of the cavity and the other on the outside of the cluster as shown in Figure 25. 

The Complete Neglect of Differential Overlap (CNDO) Method... 

As early as in 1972, a theoretical study of the structure of unknown 1,2,3,4-thiatriazole was carried out using the semiempirical complete neglect of differential overlap (CNDO) method <1972JCD73>. Because of the known large discrepancy for the C-S length predicted by semi-empirical calculations compared with the experimental data for l,2,3,4-thiatriazole-5-thiolate <1986ICA71>, this study has only historical interest. 

Further complete neglect of differential overlap (CNDO) methodology in the same laboratory <1996IC1313>, on the simplest possible 1,3,2,4-radical 12, shows that the concerted dimerization process, to yield compound 14a via transition state 13 (Equation 2), is a photochemically symmetry allowed rearrangement. 

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