Molecular method: CNDO

By the early 1970s, molecular mechanics computer programs such as MMI and MM2 were available, running on the IBM 360. For proteins, ECEPP was developed by Harold A. Scheraga. - Countering the molecular mechanics approach, Michael J. S. Dewar modified John A. Pople s (complete) neglect-of-differential-overlap semiempirical quantum mechanical method (CNDO/2) to calculate quantities such as conformational stability and heats of formation. Such programs (MNDO) were necessarily slower than the empirical force field methods such as MM2 and ECEPP but still had fewer parameters and could account for the effects of polarization in aromatic systems. 

Nitrogen-14 nuclear quadrupole coupling constants in oxazole have been calculated by using the complete neglect of differential overlap method (CNDO/2) including all the valence electrons,232 and from ab initio molecular-orbital wave functions using Gaussian basis sets.234... 

Fiirst Sandor utca 5 H-1136 Budapest, Hungary Tel. 36-1-112-4874, fax 36-1-132-2574 Prediction of metabolic products based on a library of known transformations. HARZARDEXPERT for prediction of toxicity. MOLIDEA for molecular modeling, molecular mechanics CNDO/2 and CNDO/S calculations. DRUGIDEA for QSAR. LABSWARE for general computations and statistics. PRO-LOGP for lipophilicity calculation using R. F. Rekker method. PC. 

Although now largely supplanted for general use by more sophisticated semiempirical methods, CNDO/2 calculations have been shown to provide adequate descriptions of both molecular geometries and dipole moments. 

Practically all CNDO calculations are actually performed using the CNDO/ 2 method, which is an improved parameterization over the original CNDO/1 method. There is a CNDO/S method that is parameterized to reproduce electronic spectra. The CNDO/S method does yield improved prediction of excitation energies, but at the expense of the poorer prediction of molecular geometry. There have also been extensions of the CNDO/2 method to include elements with occupied d orbitals. These techniques have not seen widespread use due to the limited accuracy of results. 

However, these alternative methods can be only applied to certain elements. For example, the projected CNDO/INDO may be used only for molecular systemswith atomic numbers less than orequal to 18 (Ar). Elements beyond 18 are not available in the projected CNDO/INDO initial guess. 

In order to conserve the total energy in molecular dynamics calculations using semi-empirical methods, the gradient needs to be very accurate. Although the gradient is calculated analytically, it is a function of wavefunction, so its accuracy depends on that of the wavefunction. Tests for CH4 show that the convergence limit needs to be at most le-6 for CNDO and INDO and le-7 for MINDO/3, MNDO, AMI, and PM3 for accurate energy conservation. ZINDO/S is not suitable for molecular dynamics calculations. 

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-... 

HyperChem currently supports one first-principle method ab initio theory), one independent-electron method (extended Hiickel theory), and eight semi-empirical SCFmethods (CNDO, INDO, MINDO/3, MNDO, AMI, PM3, ZINDO/1, and ZINDO/S). This section gives sufficient details on each method to serve as an introduction to approximate molecular orbital calculations. For further details, the original papers on each method should be consulted, as well as other research literature. References appear in the following sections. 

An N-atom molecular system may be described by 3N Cartesian coordinates. Six independent coordinates (five for linear molecules, three for a single atom) describe translation and rotation of the system as a whole. The remaining coordinates describe the molecular configuration and the internal structure. Whether you use molecular mechanics, quantum mechanics, or a specific computational method (AMBER, CNDO, etc.), you can ask for the energy of the system at a specified configuration. This is called a single point calculation. 

The indazole molecular structure (Figure 11) shows the tautomeric proton bonded to N-1 (1//-indazole. Section 4.04.1.5.1). A linear correlation between the bond lengths and the bond orders calculated by the CNDO/2 method was observed (74T2903). 

Table 1. Dipole moments, charge transfers, and molecular hyperpolarizabiUties for azobenzene chromophores, calculated using CNDO/S method ...

The PPP-MO method has proved extremely successful for the prediction of a wide range of colour properties, and it is currently the most extensively used method for this purpose. It does have some deficiencies. For example, the method carries out its calculations based on rc-electrons only and therefore cannot, except in a rather empirical way, account for some of the subtle effects of a-electrons on colour. Among such effects commonly encountered are hydrogen bonding and steric hindrance. As more and more powerful computing facilities become accessible, there is clear evidence that colour chemists are turning their attention towards the use for colour prediction of more sophisticated molecular orbital techniques which take into account all valence electrons, such as the CNDO and ZINDO approaches, and in due course they may well prove to be the methods of choice. However, at the present time, it has not been established with absolute certainty that these methods will routinely provide superior colour prediction properties. 

Various theoretical methods (self-consistent field molecular orbital (SCF-MO) modified neglect of diatomic overlap (MNDO), complete neglect of differential overlap (CNDO/2), intermediate neglect of differential overlap/screened approximation (INDO/S), and STO-3G ab initio) have been used to calculate the electron distribution, structural parameters, dipole moments, ionization potentials, and data relating to ultraviolet (UV), nuclear magnetic resonance (NMR), nuclear quadrupole resonance (NQR), photoelectron (PE), and microwave spectra of 1,3,4-oxadiazole and its derivatives <1984CHEC(6)427, 1996CHEC-II(4)268>. 

The molecular orbital methods which have been employed for such studies include extended Hiickel theory (EHT), CNDO, and ab initio LCAO-SCF. 

The theoretical interpretation of the results was made (334) in terms of the molecular orbital perturbation theory, in particular, of the FMO theory (CNDO-2 method), using the model of the concerted formation of both new bonds through the cyclic transition state. In this study, the authors provided an explanation for the regioselectivity of the process and obtained a series of comparative reactivities of dipolarophiles (methyl acrylate > styrene), which is in agreement with the experimental data. However, in spite of similar tendencies, the experimental series of comparative reactivities of nitronates (249) toward methyl acrylate (250a) and styrene (250b) are not consistent with the calculated series (see Chart 3.17). This is attributed to the fact that calculation methods are insufficiently correct and the... 

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