Neglect of Differential Overlap

The INDO model contains all of the terms that the CNDO model contains, plus all one-center, two-electron terms. The original version of INDO/2 was similarly parameterized to reproduce model minimum basis set calculations, and the Fock matrix elements appeared much as they do in the CNDO/2 model, with equations suitably modified by the additional integrals. In applications, it was clear that the added integrals improved geometric predictions, especially bond angles. This model has also been parameterized for most elements of the periodic system. 

Additional parameters are required in INDO/S. These are the Slater-Condon integrals, Eq. [12d], and it is necessary to evaluate, for example, (sp ps) and p,py pypP) they are taken from atomic spectroscopy. Predictions from the INDO/S model are similar to those of CNDO/S for n- n excitations for molecules containing H and the first-row atoms. The INDO/S model is more successful for n 7t excitations (and is capable of distinguishing the n- n singlet and triplet states, separated at first order by terms that are zero under CNDO). The INDO model is much more successful for molecules containing heavier elements, where the Slater-Condon integrals are much larger. 

The oscillator strengths are calculated in the INDO/S model by utilizing the dipole length operator including all one-center terms. 

To date, no extensive parameterization of the INDO/S model has been performed. Very few molecules have served in the database for the fitting of the only free parameters, which are as follows  

Other parameters needed come from atomic information. 

The earliest three-dimensional semiempirical self-consistent field method was the complete neglect of differential overlap, or CNDO method. CNDO ignored most of the integrals used in the ab initio calculations and approximated, by simple expressions, those integrals that were retained. Many terms, for example, the two-electron one-center integral, were derived from experimental data. 

Let us now look at die approximations used in CNDO. Although not the forum for a detailed explanation of the theoretical background, we will focus on the differences between the various methods. For a detailed description of approximate molecular orbital theory, interested readers are referred to the excellent book by Pople and Beveridge.  

All overlap integrals involving different atomic orbitals are set to zero. This reduces the secular equation from 

All charge clouds arising from different atomic orbitals, Pp., are ignored. This eliminated most multicenter two-elearon integrals since 

All two-center two-electron integrals between a pair of atoms are set equal, i.e., 

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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,... 

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. 

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... 

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. 

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. 

There are three modihed intermediate neglect of differential overlap (MINDO) methods MINDO/1, MINDO/2, and MINDO/3. The MINDO/3 method is by far the most reliable of these. This method has yielded qualitative results for organic molecules. However its use today has been superseded by that of more accurate methods such as Austin model 1 (AMI) and parameterization method 3 (PM3). MINDO/3 is still sometimes used to obtain an initial guess for ah initio calculations. 

The intermediate neglect of differential overlap (INDO) method was at one time used for organic systems. Today, it has been superseded by more accurate methods. INDO is still sometimes used as an initial guess for ah initio calculations. 

The typed neglect of differential overlap (TNDO) method is a semiempirical method parameterized specifically to reproduce NMR chemical shifts. This... 

There is one semiempirical program, called HyperNMR, that computes NMR chemical shifts. This program goes one step further than other semiempiricals by defining different parameters for the various hybridizations, such as sp carbon vs. sp carbon. This method is called the typed neglect of differential overlap method (TNDO/1 and TNDO/2). As with any semiempirical method, the results are better for species with functional groups similar to those in the set of molecules used to parameterize the method. 

MINDO (modified intermediate neglect of differential overlap) a semiempirical method... 

NBO (natural bond order) the name of a set of population analysis techniques NDO (neglect of differential overlap) the fundamental assumption behind many semiempirical methods... 

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. 

The Extended Hiickel method neglects all electron-electron interactions. More accurate calculations are possible with HyperChem by using methods that neglect some, but not all, of the electron-electron interactions. These methods are called Neglect of Differential Overlap or NDO methods. In some parts of the calculation they neglect the effects of any overlap density between atomic orbitals. This reduces the number of electron-electron interaction integrals to calculate, which would otherwise be too time-consuming for all but the smallest molecules. 

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