Complete neglect differential overlap approximation

Based on the idea of orbital electronegativity introduced by Hinze-Whitehead-Jaffe, in 1981 Ponec had introduced the orbital electronegativity based on the semiempirical approximation CNDO ( complete neglecting differential overlapping , the complete neglect of the differential-orbital overlap even for the orbitals belonging to the same atom) (Ponec, 1981). 

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. 

Electronic transitions of Z-methylthiothiazole and A-4-thiazoline-2-thione were calculated using Pariser-Parr-Poplc and Complete Neglect of Differential Overlap approximations (61. 72). The major improvements afforded by the CNDO model are the calculation of the n cr transition and the interpretation of the 2.34-nm band as an n transition. 

Complete Neglect of Differential Overlap Approximation (CNDO)... 

The third approach is the complete neglect of differential overlap approximation (CNDO), in which only the one- and two-center, two-electron integrals remain. The direct application of these methods (NDDO, INDO, or CNDO) is not useful because of the approximations, so it is necessary to include parameters in place of all or some of the integrals. These parameters are based on atomic or molecular experimental data. 

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. 

The electron densities of the parent l,2,4-triazolo[4,3-c]- and [1,5-c]-pyrimidines (127 and 128) were calculated the total 77-electron density was obtained from HMO calculations and the total electron density by the complete neglect of differential overlap approximation method (CNDO-2). Whereas N6 caused C5 of both systems to be more electrophilic, N2 in the [4,3-c] system 127 decreased the 77-electron density at C5 more than N3 in the [1,5-c] system 128 at the same carbon. The calculations also indicated that the driving force for the 127-to-128 rearrangement should originate from the larger interaction between N1 and N2 in the [4,3-c] system 127 (electron densities, 5.22 and 5.09, respectively) compared to the interaction between N3 and N4 in the [1,5-c] system 128 (electron densities, 5.20 and... 

Invariant Procedures. Journal of Chemical Physics 43 S129-S135. pie J A and G A Segal 1965. Approximate Self-Consistent Molecular Orbital Theory. II. Calculations with Complete Neglect of Differential Overlap. The Journal of Chemical Physics 43 S136-S149. iple J A and G A Segal 1966. Approximate Self-Consistent Molecular Orbital Theory. III. CNDO Results for AB2 and AB3 systems. Journal of Chemical Physics 44 3289-3296. 

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). 

Pople JA, Segal GA. Approximate self-consistent molecular orbital theory. II. Calculations with complete neglect of differential overlap. J Chem Phys 1965 43 S136-49. 

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>. 

ANG AO ATA BF CB CF CNDO CPA DBA DOS FL GF HFA LDOS LMTO MO NN TBA VB VCA WSL Anderson-Newns-Grimley atomic orbital average t-matrix approximation Bessel function conduction band continued fraction complete neglect of differential overlap coherent-potential approximation disordered binary alloy density of states Fermi level Green function Flartree-Fock approximation local density of states linear muffin-tin orbital molecular orbital nearest neighbour tight-binding approximation valence band virtual crystal approximation Wannier-Stark ladder... 

This semiempirical treatment (CNDO = Complete Neglect of Differential Overlap), introduced by Pople et al. 9 is derived from the full Roothaan 3> LCAO SCF MO treatment by making the following approximations ) ... 

The CNDO procedure proposed and developed by Pople and his co-workers 5 61), as well as a number of its variants, are characterized by the assumption of vanishing overlap between basis set orbitals (CNDO = Complete Neglect of Differential Overlap), which reduces the number of non-zero two electron integrals drastically. Various other approximations and modifications had to be introduced... 

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