INDO/1 method

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showed systematic weaknesses that were directly attributable to the approximations outlined above, so that it was superseded by the intermediate m lect of diatomic differential overlap (INDO) method, introduced by Pople, Beveridge, and Dobosh in 1967 [13].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. 

ZINDO/S is an INDO method paramcteri/ed to reproduce LV visible spectroscopic transitions when used with the singly excited Cl method. It w as developed in the research group of Michael Zerner of the Quantum fheory Project at the University of Florida. 

The CNDO and CNDO/S methods apply the ZDO approximation to all integrals, regardless of whether the orbitals are loeated on the same atom or not. In the INDO method, whieh was designed to improve the treatment of spin densities at nuelear eenters and to handle singlet-triplet energy differenees for open-shell speeies, exehange integrals... 

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 Today, it has been superseded by more accurate methods.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 Zerner s INDO method (ZINDO) is also called spectroscopic INDO (INDO/S). This is a reparameterization of the INDO method specihcally for the purpose of reproducing electronic spectra results. This method has been found to be useful for predicting electronic spectra. ZINDO is also used for modeling transition metal systems since it is one of the few methods parameterized for metals. It predicts UV transitions well, with the exception of metals with unpaired electrons. However, its use is generally limited to the type of results for which it was parameterized. ZINDO often gives poor results when used for geometry optimization. 

The INDO method (Intermediate NDO) corrects some of the worst problems with CNDO. For example, INDO exchange integrals between electrons on the same atom need not be equal, but can depend on the orbitals involved. Though this introduces more parameters, additional computation time is negligible. INDO and MINDO/3 (Modified INDO, version 3) methods are different implementations of the same approximation. 

The NDDO (Neglect of Diatomic Differential Overlap) approximation is the basis for the MNDO, AMI, and PM3 methods. In addition to the integralsused in the INDO methods, they have an additional class of electron repulsion integrals. This class includes the overlap density between two orbitals centered on the same atom interacting with the overlap density between two orbitals also centered on a single (but possibly different) atom. This is a significant step toward calculatin g th e effects of electron -electron in teraction s on different atoms. 

MINDO/3, MNDO, and AMI were developed by the Dewar group at the University of Texas at Austin. This group chose many parameters, such as heats of formation and geometries of sample molecules, to reproduce experimental quantities. The Dewar methods yield results that are closer to experiment than the UNDO and INDO methods. 

Documentation on the reliability of the different NDO methods for various applications is scattered throughout the chemistry literature. Original papers describing the methods present relevant material. The CNDO and INDO methods are discussed in books by Pople and Beveridge and by Murrell and Harget. Compilations exist for MINDO/3 and MNDO in a book by Clark. For MNDO,... 

The advantages of INDO over CNDO involve situations where the spin state and other aspects of electron spin are particularly important. For example, in the diatomic molecule NH, the last two electrons go into a degenerate p-orbital centered solely on the Nitrogen. Two well-defined spectroscopic states, S" and D, result. Since the p-orbital is strictly one-center, CNDO results in these two states having exactly the same energy. The INDO method correctly makes the triplet state lower in energy in association with the exchange interaction included in INDO. 

The INDO method is intermediate between the NDDO and CNDO methods in tenns of approximations. 

Not much information has been added in recent years to the earlier studies of tautomeric equilibria of benzimidazoles based on basicity measurements [76AHC(S1), p. 292]. For 5(6)- and 4(7)-substituted benzimidazoles and 2-methyl-5(6)-substituted benzimidazoles values are very close to 1, which indicates near equivalence in the stability of N1(H) and N3(H) tautomers. The tautomeric equilibria of 2-substituted (H, NH2, OMe, CN) 5-nitrobenzimidazoles and 4-nitrobenzimidazoles were analyzed with the use of semiempirical MINDO/3 and INDO methods. It was predicted that electron-releasing groups in position 2 shifted the equilibria to the 6-NO2 and 4-NO2 tautomers, respectively. 

Yonezawa and collaborators (99) have reported unrestricted open-shell SCF calculations where the one-center exchange integrals were taken into account their treatment concerned allyl, vinyl, and nitrogen dioxide radicals. The one-center exchange integrals also are involved in the INDO method (85). Here, the following relationship for hyperfine splitting constants holds ... 

The results of the above cited applications [18-28,45] have clearly shown that CS INDO method is fairly successful in combining equally satisfactory predictions of electronic spectra and potential surfaces (especially along internal rotation pathways) of conjugated molecules, a goal never reached by other NDO-type procedures. CS INDO shares, at least partly, the interpretative advantages of the CIPSI-PCILO-CNDO procedure [32,33,36,37], coming from using the same hybrid AO basis sets, but improves its predictive capabilities as far as spectroscopic and photochemical properties are concerned. 

The geometry of nitronates has not been adequately studied by quantum-chemical calculations. For example, the bond lengths in nitronate Me2C=N(0)OMe were calculated by the INDO method for ideal geometry (248). 

Earlier, [3+ 2]-cycloaddition reactions of nitronates have been described in terms of the FMO theory. For example, French researchers studied reactions of olefins containing EWG groups with nitronates by the FMO—INDO method (248, 338b, 419). Recently, more modem methods have been used for calculations of FMO and the potential energy surfaces for several analogous reactions (87, 399,... 

This conclusion is further supported by an inspection of the indices of nonbonded attraction as calculated by the INDO method. 

Indices of pi and sigma nonbonded interactions in the Css and Cee conformations of the 2-propyl cation as calculated by the INDO method are shown above. As can be seen, both pi and sigma nonbonded interactions favor the Cee relative to the conformation. 

Comparison of the calculated and experimental values shows that the FPT-INDO method reproduces in a satisfactory way the coupling constants measured on rigid model compounds (2). The coefficients A,... 

Identity element, 387-388 Identity operation, 54, 395 Improper axis of symmetry, 53 Improper rotation, 396 Index of refraction, 132 INDO method, 71, 75-76 and ESR coupling constants, 380 and force constants, 245 and ionization potentials, 318 and NMR coupling constants, 360 Induced dipole moment, 187 Inertial defect, 224-225 Inertia tensor, 201... 

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