Modified Neglect of Diatomic Overlap MNDO

The core-core repulsion of the Modified Neglect of Diatomic Overlap (MNDO) modeP has the form  

In addition, MNDO uses the approximation, for some of the lighter elements. 

MNDO has been parameterized for the elements H, B, C, N, O, F, Al, Si, P, S, Cl, Zn, Ge, Br, Sn, I, Hg and Pb. The G s, Gsp, Gpp, Gp2, H p parameters are taken from atomic spectra, while the others are fitted to molecular data. Although MNDO has been succeeded by the AMI and PM3 methods, it is still used for some types of calculation where MNDO is known to give better results. 

MNDOC has the same functional form as MNDO, however, electron correlation is explicitly calculated by second-order perturbation theory. The derivation of the MNDOC parameters is done by fitting the correlated MNDOC results to experimental data. Electron correlation in MNDO is only included implicitly via the parameters, from fitting to experimental results. Since the training set only includes ground-state stable molecules, MNDO has problems treating systems where the importance of electron comelation is substantially different from normal molecules. MNDOC consequently performs significantly better for systems where this is not the case, such as transition structures and excited states. 

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The systems discussed in this chapter give some examples using different theoretical models for the interpretation of, primarily, UPS valence band data, both for pristine and doped systems as well as for the initial stages of interface formation between metals and conjugated systems. Among the various methods used in the examples are the following semiempirical Hartree-Fock methods such as the Modified Neglect of Diatomic Overlap (MNDO) [31, 32) and Austin Model 1 (AMI) [33] the non-empirical Valence Effective Hamiltonian (VEH) pseudopotential method [3, 34J and ab initio Hartree-Fock techniques. 

Modified neglect of diatomic overlap (MNDO) calculations can support the structures assigned to certain of these fused tricyclic systems, such as 401, where confirmatory X-ray crystallographic data are lacking <1983JCM128>. 

A theoretical study of degenerate Boulton-Katritzky rearrangements concerning the anions of the 3-hydroxyimi-nomethyl-l,2,5-oxadiazole has been carried out by using semi-empirical modified neglect of diatomic overlap (MNDO) and ab initio Hartree-Fock procedures. Different transition structures and reactive pathways were obtained in the two cases. Semi-empirical treatment shows asymmetrical transition states and nonconcerted processes via symmetrical intermediates. By contrast, ab initio procedures describe concerted and synchronous processes involving symmetrically located transition states <1998JMT(452)67>. 

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>. 

Values reported are averages from two levels of Hartree-Fock (HE) modified neglect of diatomic overlap (MNDO) theory in Ref 15. 

The performance of several semi-empirical (modified neglect of diatomic overlap (MNDO), AMI, PM3, and SAMI) and ab initio (Hartree-Fock (FIF) and MP2/6-31G ) methods for determining structural and electronic factors of a series of isothiazolo[5,4-b]pyridines was compared by Martinez-Merino et al. <1996T8947>. They found that most of the semi-empirical methods calculated reasonable molecular structures when compared to the actual X-ray structures (compounds 3-5) (see, for example. Table 1 for selected bond lengths of compound 3). Flowever, the dipole moments were not reproducible using these 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). 

The modified neglect of diatomic overlap (MNDO) semi-empirical SCF MO calculations were used to investigate conformational properties of five-to-eight-membered cyclic sulfur diimides <1996JMT(364)79>. 3,4,5,6-Tetrahydro-1,2,7-thiadiazepine system was found to have two main conformations, namely envelope 22 and half-chair 23, favoring conformer 22. The calculated energy barrier for interconversion of 22 to 23 was reported to be 7.5 kj mol 1 (Equation 2). 

Various parameterizations of NDDO have been proposed. Among these are modified neglect of diatomic overlap (MNDO),152 Austin Model 1 (AMI),153 and parametric method number 3 (PM3),154 all of which often perform better than those based on INDO. The parameterizations in these methods are based on atomic and molecular data. All three methods include only valence s and p functions, which are taken as Slater-type orbitals. The difference in the methods is in how the core-core repulsions are treated. These methods involve at least 12 parameters per atom, of which some are obtained from experimental data and others by fitting to experimental data. The AMI, MNDO, and PM3 methods have been focused on ground state properties such as enthalpies of formation and geometries. One of the limitations of these methods is that they can be used only with molecules that have s and p valence electrons, although MNDO has been extended to d electrons, as mentioned below. 

A detailed ab initio and modified neglect of diatomic overlap (MNDO) study of structural parameters and pyramidal phosphorus atom inversion and also enthalpy differences between the participants in the conformational equilibrium (axial and equatorial) of 1-R-phosphorinanes (R = H, CH3, C2H5) has been investigated and is in good agreement with the observed NMR and X-ray values <1999IJB660>. 

Modified neglect of diatomic overlap (MNDO) calculations have been shown to accurately predict the isomer distribution of polychlorinated dibenzo-1,4-dioxins and polychlorinated dibenzofurans in industrial combustion processes, an indication of thermodynamic control in these processes <2002MI1287>. 

Modified neglect of diatomic overlap (MNDO) calculations tend to underestimate the C-S bond due to the noninclusion of the 3d- AOs, which result in smaller sulfur atomic orbitals and hence shorter C-S bonds. Consequently, the C-S-C angles obtained from MNDO calculations are about 1° larger than experimental. 

Theoretical study using semiempirical Austin Model 1 (AMI) and modified neglect of diatomic overlap (MNDO) methods on the interconversion of the closed [6,6] and the open [5,6] isomers of CsoS revealed a stepwise pathway via a local energy minimum corresponding to the closed [5,6] isomer. The results are in good agreement with those derived from the experiments <2002JPC9284>. 

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