CNDO/2 treatment

It is interesting to note that according to Ref.136) regardless of the model used, the CNDO/2 treatment predicts a larger ir-polarization for cyclopropenone than for tropone. This means that the electrostatic work to achieve a cyclopropenium oxide structure is considerably less than for cycloheptatrienylium oxide. From this reason, cyclopropenone seems to be a closer approximation to an aromatic system than tropone which can be described better as a polyolefin. 

A number of studies have compared the use of the multiple regression technique using semiempirical parameters such as tt and o-, and parameters calculated for the particular molecules from molecular orbital theory. Hermann, Culp, McMahon, and Marsh (23) studied the relationship between the maximum velocity of acetophenone substrates for a rabbit kidney reductase. These workers were interested in the reaction mechanism, and two types of quantum chemical calculations were made (1) extended Huckel treatment, and (2) complete neglect of differential overlap (CNDO/2). Hydride interaction energy and approaching transition-state energies were calculated from the CNDO/2 treatment. All these parameters plus ir and a values were then subjected to regression analysis. The best results are presented in Table II. 

Good linear correlations were observed between the carbon chemical shifts and the total charge densities at the a- and /3-carbons, calculated by a complete neglect of differential overlap (CNDO/2) treatment.30... 

E j analogous to Hammett a values were calculated by the extended Huckel theory, EHT, of Hoffmann and by the complete neglect of differential overlap, CNDO/2, treatment of Pople and Segal which takes into account electron repulsions ignored in EHT. The substituent constants were obtained by subtracting the electron density value for acetophenone from that for the derivative and multiplying by -1000. This permits... 

All valence electron (AVE) calculations (simultaneous treatment of tr- and ir-electrons) Three treatments (i) EHT (extended Hiickel theory) (ii) lEHT (iterative extended Huckel theory) (iii) CNDO treatment (an SCF MO type) 68MI40908 68MI40907 69MI40907... 

Oxygen Fluorides.—An open-shell CNDO treatment has been employed29 in order to interpret the electronic spectra, ionization potentials, and electron affinities of radicals containing 2, 3, and 4 atoms, including F02 and H02. Raman spectra of 02F2 in CC1F3 have been measured for the first time.30... 

The two approximate SCF methods just mentioned are advantageous because of their simphcity and rapid convergence. They have proved useful with both semiempirical and ab initio treatments (vide infra). Their approximate nature is not associated, at least in semiempirical calculations, with any drawback, inasmuch as we found in PPP-like and CNDO treatments 13.21,22) that the methods of Roothaan and of Lon-... 

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... 

More elaborated treatments have also been applied ab initio methods by Bouscasse (130) and Bernardi et al. (131) then the all-valence-electrons methods, derived from PPP. by Gelus et ai. (132) and by Phan-Tan-Luu et al. (133) and CNDO methods by Bojesen et al. (113) and by Salmona et al. (134). 

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... 

It mrned out that CNDO/1 calculations gave poor predictions of molecular equilibrium geometries, and this failing was analysed as being due to the treatment of the Uii and the penetration terms Vab-... 

The most significant treatment of excited states within the CNDO approach is that of Del Bene and Jaffe, who made three modifications to the original CNDO parameterization scheme. Two of the modifications were just minor tinkering with the integral evaluation, and need not concern us. The key point in their method was the treatment of the p parameters. Think of a pair of bonded carbon atoms in a large molecule. Some of the p-type basis functions on Ca will be aligned to those on Cb in a type interaction was reduced. They wrote... 

Pople, Beveridge and Dobosh introduced the intermediate neglect of differential overlap model (INDO) in 1967. INDO is CNDO/2 with a more realistic treatment of the one-centre two-electron integrals. In the spirit of such models, the non-zero integrals were calibrated against experiment rather than being calculated fi om first principles. The authors concluded that, although INDO was a little better than... 

CNDO/2 for predicting molecular geometries, it gave a vastly superior treatment of singlet-triplet splittings and spin densities. 

The main difference between CNDO, INDO and NDDO is the treatment of the two-electron integrals. While CNDO and INDO reduce these to just two parameters (7AA 7ab), all the one- and two-center integrals are kept in the NDDO approximation. Within an sp-basis, however, there are only 27 different types of one- and two-center integrals, while the number rises to over 500 for a basis containing s-, p- and d-functions. 

The traditional valence-only MO schemes are Extended Hiickel and CNDO with its subsequent modifications. Present-day computing facilities make it possible to move one step further, to the ab initio treatment of valence electrons through the use of pseudopotential (PP) methods. The essentials of such methods will be illustrated in the following, through a description of the NOCOR formulation3, which will then be used for extensive calculations on sulphoxide and sulphone systems. The general concepts exposed in the foregoing sections will be illustrated by many examples. 

This semiempirical treatment (CNDO = Complete Neglect of Differential Overlap), introduced by Pople et al. 9 is derived from the full Roothaan 3> LCAO SCF MO treatment by making the following approximations ) ... 

Cyclic dipeptides, especially when N-alkylated, undergo extremely fast epimerization (79JA1885). For example, cyclo(L-Pro-L-Phe) is rapidly converted to its diastereomer, cyclo(D-Pro-L-Phe) (80% conversion), by treatment with 0.5 N NaOH at 25°C for 15 min. This diastereomer is the one in which the proline residue has epimerized and not the more activated phenylalanine. CNDO/2 calculations seem to provide a rationale for this. It is not yet completely clear why such base-catalyzed epimerizations of piperazinediones are so easy the conformation of the molecule may play a role in this (79MI1). It is also worth noting that even in linear peptides, rm-amides of N-alkyl-amino acids, which consist of s-trans and s-cis rotamers of almost equal energy, are more prone to racemization than the sec-amides, which exist only in the s-trans configuration. Of course, the amide functions of piperazine-2,5-diones are obliged to assume the s-cis conformation. 

One effect of the greater flexibility inherent in the INDO scheme is that valence bond angles are predicted with much greater accuracy than is the case for CNDO. Nevertheless, overall molecular geometries predicted from INDO tend to be rather poor. However, if a good molecular geometry is available from some other source (ideally experiment) the INDO method has considerable potential for modeling the UV/Vis spectroscopy of the compound because of its better treatment of one-center electronic interactions. 

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