Complete Neglect

A very simple — and in fact quite widely used — approximation completely neglects long range electrostatic interactions beyond a certain cut-off distance [43] of typic ally 8 — 15 A. For systems which are significantly larger... 

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. 

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. 

Breslow studied the dimerisation of cyclopentadiene and the reaction between substituted maleimides and 9-(hydroxymethyl)anthracene in alcohol-water mixtures. He successfully correlated the rate constant with the solubility of the starting materials for each Diels-Alder reaction. From these relations he estimated the change in solvent accessible surface between initial state and activated complex " . Again, Breslow completely neglects hydrogen bonding interactions, but since he only studied alcohol-water mixtures, the enforced hydrophobic interactions will dominate the behaviour. Recently, also Diels-Alder reactions in dilute salt solutions in aqueous ethanol have been studied and minor rate increases have been observed Lubineau has demonstrated that addition of sugars can induce an extra acceleration of the aqueous Diels-Alder reaction . Also the effect of surfactants on Diels-Alder reactions has been studied. This topic will be extensively reviewed in Chapter 4. 

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. 

Unlike semiempirical methods that are formulated to completely neglect the core electrons, ah initio methods must represent all the electrons in some manner. However, for heavy atoms it is desirable to reduce the amount of computation necessary. This is done by replacing the core electrons and their basis functions in the wave function by a potential term in the Hamiltonian. These are called core potentials, elfective core potentials (ECP), or relativistic effective core potentials (RECP). Core potentials must be used along with a valence basis set that was created to accompany them. As well as reducing the computation time, core potentials can include the effects of the relativistic mass defect and spin coupling terms that are significant near the nuclei of heavy atoms. This is often the method of choice for heavy atoms, Rb and up. 

Some programs, such as COLUMBUS, allow a calculation to be done with some orbitals completely neglected from the calculation. For example, in a transition metal compound, four d functions could be used so that the calculation would have no way to occupy the function that was left out. 

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. 

Note Do not use CNDO on any problem where electron-spin is critically important. Its complete neglect of atomic exchange integrals makes it incapable of dealing with these problems. 

The CNDO/INDO, MINDO/3, Z3NDO/1, and ZINDO/S methods might be expected to imply an even simpler equation for the electron density than the above. For example, a rigorous complete neglect of CNDO approximation, suggests that equations (87) and (88) should be replaced by expressions with a sum only over diagonal elements of the density matrix. This would represent a molecular charge density that is the exact sum of atomic densities. Alter-... 

The INDO (Intermediate Neglect of Differential Overlap) differs from CNDO in the treatment of one-center exchange integrals. The CNDO (Complete Neglect of Differential Overlap) treatment retains only the two-electron integrals (p.p. vv) = The Yj y are... 

In this section we study a system with purely repulsive interactions which demonstrates the importance of entropy effects on the stability of phases when the effect of the corrugation potential due to the structured surface is completely neglected. The phase diagrams are determined by finite size scaling methods, in particular the methods of Sec. IV A. 

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

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). 

The hard-core limiting forms of U(r) do not lead to physically acceptable results. We conclude that this is caused by a complete neglect of the effect of the attractive forces on the slope of the repulsive part in U(r). If the interaction energy is assumed as the sum of a Morse exponential function and the polarization energy evaluated at r = r°, the resulting transition probabilities appear useful for analyzing ion-molecule collisions. 

This by no means exhaustive discussion may serve to indicate the value of the information provided by magnetic data relative to the nature of the chemical bond. The quantum-mechanical rules for electron-pair bonds are essential to the treatment. Much further information is provided when these methods of attack are combined with crystal structure data, a topic which has been almost completely neglected in this paper. It has been found that the rules for electron-pair bonds permit the formulation of a set of structural principles for non-ionic inorganic crystals similar to that for complex ionic crystals the statement of these principles and applications illustrating their use will be the subject of an article to be published in the Zeitschrift fur Kristallographie. 

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). 

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