Typed neglect of differential overlap

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. 

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. 

A method which is similar to the Pariser-Parr-Pople method for the n electron system and is applicable to common, saturated molecules has been proposed by Pople 28>. This method is called the CNDO complete neglect of differential overlap) SCF calculation. Katagiri and Sandorfy 29> and Imamura et al. °) have used hybridized orbitals as basis of the Pariser-Parr-Pople type semiempirical SCF calculation. 

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 ... 

Most present-day semiempirical methods are based on the idea of the neglect of differential overlap (NDO) of inner electrons developed by Pople and co-workers (see, for example, Pople and Beveridge, 1970 Dewar, 1975). NDO-type approximations generally result in a decrease in computational resource requirements that are 1/100 to 1/1000 of the corresponding ab initio methods. 

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). 

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