The MNDO Method

As a result, even though the number of interelectronic interaction integrals of various types increases appreciably, the overall number of the parameters for the second-period elements is reduced from 102 to 41. Using this method, the computer calculation takes 1.5 times longer than with the MINDO/3 method. As may be seen from Table 2.4 compiled from the data presented by Dewar [53,62] for over 200 compounds, the MNDO method achieves a better agreement with experiment than the MINDO/3 method. 

Method Heat of formation kcal/mol Bond length A Valence angle Vibration frequency 

However, even though thanks to parametrization the MNDO method partially takes account of the electron correlation energy, the common drawback of a one-determinant approximation, namely, its inability to correctly evaluate the bond-breaking reactions, is not thereby removed as was pointed out, for example, in Ref. [70] using as an illustration a number of dissociation reactions. In such cases, a more complete inclusion of the correlation energy can remedy the situation. In this connection, Thiel suggested a MNDOC scheme [71] in which the correlation corrections are calculated explicitly in the second order of perturbation from the Epstein-Nesbet formula [72, 73]  

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The one-center two-electron integrals in the MNDO method are derived from experimental data on isolated atoms. Most were obtained from Oleari s work L. Oleari, L. DiSipio, and G. DeMich-ells. Mol. Phys., 10, 97( 1977)1, but a few were obtained by IDewar using fits to molecular properties. 

C oniparing ihc corc-core repulsion ol lhe above two ec nations with those in the MNDO method, it can be seen that the only dil -ference is in the last term. The extra terms in the AMI core-core repulsion deline spherical Ciaiissian Tun ctioii s — the a. h, and c are adjustable parameters. AMI has between two and I onr Gaussian full ctiori s per atom, ... 

The MNDO method has 22 unique two-center two-electron integrals for each pair of heavy (non-hydrogen) atoms in their local atomic frame. They are ... 

In the MNDO method, the one-center one-electron integral, is given by ... 

In the MNDO method the resonance integral, is proportional to the overlap integral,... 

Fig. 11. Abundance mass spectra of differently charged hot CgoLL clusters evaporating atoms calculated with a Monte-Carlo simulation (the Li and Cgg isotope distributions are included). Energies required to remove Li atoms were calculated using the MNDO method. The peaks at x = 12 and at x = 6 + n (where n is the cluster charge) observed in experiment (Fig. 9) are well reproduced.

Heats of formation, molecular geometries, ionization potentials and dipole moments are calculated by the MNDO method for a large number of molecules. The MNDO results are compared with the corresponding MINDO/3 results on a statistical basis. For the properties investigated, the mean absolute errors in MNDO are uniformly smaller than those in MINDO/3 by a factor of about 2. Major improvements of MNDO over MINDO/3 are found for the heats of formation of unsaturated systems and molecules with NN bonds, for bond angles, for higher ionization potentials, and for dipole moments of compounds with heteroatoms. 

Arguing that the MNDO method is more suitable than the AMI method for predicting the heats of formation of five-membered nitrogenated aromatic rings, Garcia and Vilarrasa (88H1803) calculated that 4-fluoroimidazole 14a (R = F, = H) is 2.5 kJ mol more stable than its tautomer 14b,... 

FMO calculations using the MNDO method and electron-density calculations were performed to establish which calculations are in agreement with the experimentally observed regioselectivity of the SnH amination of some nitronaphthyridines (see Section III,B). 

The enthalpies ofall the annular tautomers of l,3,4-oxadiazin-5-ones 117 and -2-ones 118 were calculated using the MNDO method (88CB887). The results clearly indicated that in both cases the hydrazone-type tautomers 117a and 118a are the most stable, while the formation of the tautomer 118c is the least probable. 

More recently Gorelik s group determined the structure of 1-phenylsulfonyl-2-pyrazoline-3-diazonium tetrafluoroborate by X-ray crystallography (Gorelik et al., 1989) and calculated (Glukhovtsev et al. 1990) the heats of the dediazoniation reaction of seven cyclic five-membered diazonium ions (including 2.13, R=H) relative to that of the benzenediazonium ion by the MNDO method (see Sec. 8.4). 

The MNDO method [17] coupled with the finite perturbation (FP) technique [18], as implemented in the MOPAC5 [19] program has been used throughout this work. 

Demiralp E, Cagin T, Goddard WA(1999) Morse stretch potential charge equilibrium force field for ceramics Application to the quartz-stishovite phase transition and to silica glass. Phys Rev l tt 82 1708-1711 Dewar MJS (1977) Ground states of molecules. The MNDO method. Approximations and parameters. J Am Chem Soc 99 4899-4907... 

The MNDO method has been employed " to study the acid-catalysed rearrangement of propylene 1,2-glycol. Propanaldehyde was found to be the major product with a small amount of acetone also being produced. The solid-state pinacol rearrangement of l,l,2-triphenylethane-l,2-diol has been performed over various solid... 

The various tautomers and rotamers of alloxan have been examined in detail by the MNDO method and it is predicted that the keto form is most important in the gas phase, although in solution the monohydroxy forms are also thought to contribute. A mass spectral study has been used to investigate the enol-keto tautomeric equilibria of a series of substituted salicylaldehyde and 2-hydroxynaphthaldehyde Schiff bases. In neutral, ethanolic solutions, the cis- and trans-tm forms of 4,5-dimethyl-2-(2 -hydroxyphenyl)imidazoles (393) and (394) have been found to exist in equilibrium in the ground state. However, in neutral aqueous solutions, the trans-eao and keto forms (394) and (395) were the only species detected. Deuterium isotope effects on... 

All computations were carried out using the MNDO method (12) and published parameters (15). For the cyclic structures, transits of a perpendicular main-group moiety across the various rings generate structures (n=l-6) as shown below. 

Limitations of AMI. AMI is still a relatively new method. As such, only a few limitations have become apparent thus far. One of the more important of these are the continued inability to adequately represent hypervalent chemistry. Very recently, AMI parameters for phosphorus and sulfur have become available. Preliminary results indicate these are a considerable improvement over the MNDO method for predicting the AHf of hypervalent compounds. Unfortunately, the phosphorus, parameters include a barrier at 3.0A which complicates the interpretation of reaction mechanisms. For example, in the reaction PF3 + F2 = PF5. there are two spurious barriers which must be crossed before the real barrier to the reaction is encountered. 

Calculated using the MNDO method (unpublished results). 

The vapor-phase pyrolysis of 4-hydroxy-1,2,3-triazole and its iV-methyl derivative affords methan-imine and its A-methyl analog. Analysis of the reaction path by the MNDO method shows the presence of two stable or metastable isomers, (liif)-4-hydroxy-l,2,3-triazole and its ketone protomer <89NJC551>. 4-Diazo-1,2,3-triazoles (122) thermolyze or photolyze in benzene to 4//-l,2,3-tri-azolylidenes (123) which convert benzene to 4-phenyl-1,2,3-triazoles and/or isomerize to a-diazo-nitriles (124). Intermediates (124) react with benzene via a carbene to give addition, ring expansion or substitution products (Scheme 17) <82TL5115>. The similar thermolysis of diazotriazoles in substituted benzene gives complex mixtures in which all of the components are sometimes impossible to isolate and identify <90AHC(48)65>. 

Enthalpies of formation and bond lengths (SS, SN) were calculated by the MNDO method for l,6-dihetera-6aA -thia-3,4-diazapentalenes (1), (2), and (3) as the most probable pentalene structures formed in the reaction of 3-imino-l, 2,4-dithiazolidine-5-ones with isothiocyanates (see Section 4.13.6.1.4 and Tables 1 and 2) <83JCR(S)128>. The AH data show the ring strain to be maximal for a system with an N-S-N chain (3), the most favorable being the system (1). The effect of substituents R and can be seen in both Tables 1 and 2. The same authors calculated AHf for (4), (5), and (6) to obtain values —57.4, 30.5, and 127.8 kJ mol respectively. 

MNDO calculation of AH for 3-amino-1,2,4-dithiazole-5-thione indicated that, of its possible isomeric forms (7), (8), and (9) (R = H), (7) is the most favorable. This structure had been found experimentally in the crystal and in solution but the differences are small and structures (8) and (9) may also take part in reactions. In fact, methylation of (7 R = H) gives (9 R = Me) shown by MNDO calculation to possess the lowest AHf <82JCR(S)65>. The MNDO method was used to calculate the structure and energy of 3-amino-1,2,4-dithiazole-5-one, its molecular cation and also its fragmentation ions <82MI 4i3-oi>. 

The structure of the l,2,3,4-thiatriazole-5-thiolate anion (CS2N3 ) has been examined by Conti et al. using the MNDO method <86lCA7l>. The closed structure (5) was found to be more stable than the open structure (6) according to the calculated standard heat of formation (A//, ) of —5.4 kcal mol and 31.4 kcal mol respectively (Figure 1). This is in accordance with similar calculations previously carried out for the parent thiatriazole <76AHC(20)145>. 

FIGURE 7. The calculated structures of (a)-(d) four isomers of [Zn, N, C, H]+ ions and (e)-(m) nine isomers of [Zn, N, C2, H3]+ ions using the MNDO method with full optimization of geometry. Reproduced by permission of John Wiley Sons Ltd. from Reference 123... 

To complete the energy evaluation by the MNDO method, the nuclear repulsion energy is added to the SCF energy. The MNDO nuclear repulsion energy is computed as... 

The base-catalysed hydrolysis of ethylene oxide has been studied by the MNDO method.28 The structures of tire reactant, product, and transition state were optimized and a reaction mechanism was proposed. 

The MNDO method has been employed405 to study the reaction pathway and to optimize the structures of reactant, product, and transition state of the acid-catalysed rearrangement of 1,2-propylene glycol, and the unimolecular dehydration of protonated a,co-diols in the gas phase has been examined406 by tandem mass spectrometric experiments. It has been shown that the reaction of l,2-diarylcyclopropane-l,2-diols (342) with acids yields primarily the a,//-unsaturated ketones (343) in which the aryl... 

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