Differential overlap

The second philosophy holds that one should seek agreement with experiment. Therefore the parameters in this case implicitly include some correlation effects. Examples of this approach are MINDO/3 (Bingham et al., 1975) and MNDO (Dewar and Thiel, 1977). [In all of these techniques, C stands for complete, I for intermediate, N for neglect, and DO for differential (diatomic differential in MNDO) overlap differential overlap is the overlap between different orbitals on the same or different atoms.]... 

Let us come back to Figure 32 and concentrate our attention on the destabilizing interactions g, h, i, and j present in 121. It seems reasonable to suspect that interactions in xz and xy planes are overlap differentiated. Orbitals tt, and Uy (Figure 27) are rigorously degenerate. Since the barrier to internal rotation in the CHjCHj cation is sixfold and very small (249), one may conclude that there should not be any essential difference between overlap integral for the interaction occurring in the xz plane and... 

G. Tumes, A. Cladera, E. Gomez, J.M. Estela, V. Cerda, Resolution of highly overlapped differential pulse polarographic (DPP) and anodic stripping voltammetric (ASV) peaks by multicomponent analysis, J. Electroanal. Chem. Interfacial Electrochem. 338 (1992) 49—60. 

A. Cladera, J. Alpizar, J.M. Estela, V. Cerda, M. Catasus, E. Lastres, L. Garcia, Resolution of highly overlapping differential pulse anodic stripping voltammetric signals using multicomponent analysis and neural networks. Anal. Chim. Acta 350 (1997) 163—169. 

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showed systematic weaknesses that were directly attributable to the approximations outlined above, so that it was superseded by the intermediate m lect of diatomic differential overlap (INDO) method, introduced by Pople, Beveridge, and Dobosh in 1967 [13].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 order to overcome these weaknesses, Pople and co-workers reverted to a more complete approach that they first proposed in 1965 [14], neglect of diatomic differential overlap (NDDO). In NDDO, all four-center integrals (pv are considered in which p and v are on one center, as are 2 and cr (but not necessarily on the same one as and v). Furthermore, integrals for which the two atomic centers are diEFer-ent are treated in an analogous way to the one-center integrals in INDO, resulting... 

PM3 is a reparam eteri/ation of AM I, wdi ich is based on the n eglect of diatomic differential overlap (NDDO) approximation. XDDO... 

ZINDO/I is based on a modified version of the intermediate neglect of differential overlap (INOOh which was developed by Michael /ern cr of the Quan turn Th cory Project at th e Lin iversity oIFIorida. Zerner s original IXDO/1 used the Slater orbital exponents with a distance dependence for the first rorv transition metals only. (See Thvorel. Chirn. Ada (Bed.) 53, 21-54 (1979).) However, in HyperChem con stan I orbital expon en ts are used for all the available elements, as recommended by. Anderson, Kdwards, and /.erner, /norg. Chern. 25, 2728-2732,1986,... 

I le u. . erlap between the 2pK and 2p orbitals in this new coordinate system is j(2p — 2p ). If tile zei o differential overlap approximation were applied, then different results would be oliLiined for the two coordinate systems unless the overlap in the new, transformed svntem was also ignored. 

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. 

I lie next level of approximation is the neglect of diatomic differential overlap model (NDDO [Pople et al. 1965]) this theory only neglects differential overlap between atomic orbitals on... 

Highest occupied molecular orbital Intermediate neglect of differential overlap Linear combination of atomic orbitals Local density approximation Local spin density functional theory Lowest unoccupied molecular orbital Many-body perturbation theory Modified INDO version 3 Modified neglect of diatomic overlap Molecular orbital Moller-Plesset... 

Neglect of diatomic differential overlap Parametrisation 3 of MNDO... 

Correlation functional due to Wilk, Vosko and Nusair Zero differential overlap... 

V. Intermediate Neglect of Differential Overlap. Journal of Chemical Physics 47 2026-2033. pie J A, D P Santry and G A Segal 1965. Approximate Self-Consistent Molecular Orbital Theory. I. 

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. 

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