MNDO theory

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

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. 

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. 

Before 1980, force field and semiempircal methods (such as CNDO, MNDO, AMI, etc.) [1] were used exclusively to study sulfur-containing compounds due to the lack of computer resources and due to inefficient quantum-chemical programs. Unfortunately, these computational methods are rather hmit-ed in their reliability. The majority of the theoretical studies under this review utilized ab initio MO methods [2]. Not only ab initio MO theory is more reliable, but also it has the desirable feature of not relying on experimental parameters. As a consequence, ab initio MO methods are apphcable to any systems of interest, particularly for novel species and transition states. 

As can be seen from Table I, the C-C bond distance as described by LDF is closer to experiment than the corresponding HF value obtained with a 6-3IG basis. Including correlation via second and third order Moller-Plesset perturbation theory and via Cl leads to very close agreement with experiment. The C-H bond length is significantly overestimated in the LDF calculations by almost 2%. The HCH bond angle is reasonably well described and lies close to all the HF and post-HF calculations. Still, all the theoretical values are too small by more than one degree compared with experiment the deviation from experiment is particularly pronounced for the semi-empirical MNDO calculation. 

These compounds have been the subject of several theoretical [7,11,13,20)] and experimental[21] studies. Ward and Elliott [20] measured the dynamic y hyperpolarizability of butadiene and hexatriene in the vapour phase by means of the dc-SHG technique. Waite and Papadopoulos[7,ll] computed static y values, using a Mac Weeny type Coupled Hartree-Fock Perturbation Theory (CHFPT) in the CNDO approximation, and an extended basis set. Kurtz [15] evaluated by means of a finite perturbation technique at the MNDO level [17] and using the AMI [22] and PM3[23] parametrizations, the mean y values of a series of polyenes containing from 2 to 11 unit cells. At the ab initio level, Hurst et al. [13] and Chopra et al. [20] studied basis sets effects on and y. It appeared that diffuse orbitals must be included in the basis set in order to describe correctly the external part of the molecules which is the most sensitive to the electrical perturbation and to ensure the obtention of accurate values of the calculated properties. 

AMI semi-empirical and B3LYP/6-31G(d)/AMl density functional theory (DFT) computational studies were performed with the purpose of determining which variously substituted 1,3,4-oxadiazoles would participate in Diels-Alder reactions as dienes and under what conditions. Also, bond orders for 1,3,4-oxadiazole and its 2,5-diacetyl, 2,5-dimethyl, 2,5-di(trifluoromethyl), and 2,5-di(methoxycarbonyl) derivatives were calculated <1998JMT153>. The AMI method was also used to evaluate the electronic properties of 2,5-bis[5-(4,5,6,7-tetrahydrobenzo[A thien-2-yl)thien-2-yl]-l,3,4-oxadiazole 8. The experimentally determined redox potentials were compared with the calculated highest occupied molecular orbital/lowest unoccupied molecular orbital (HOMO/LUMO) energies. The performance of the available parameters from AMI was verified with other semi-empirical calculations (PM3, MNDO) as well as by ab initio methods <1998CEJ2211>. 

The deviations between theory and experiment normally tend to be somewhat smaller for first-row than for second-row compounds. Among the established semiempirical methods, PM3 seems to be the best for the first-row compounds, but the OM1 and OM2 approaches with orthogo-nalization corrections [23-25] perform even better, with mean absolute deviations being around 3-5 kcal/mol. For the second-row compounds, MNDO/d is currently the most accurate among the semiempirical methods considered. This performance has been attributed [16-18] to the use of an spd basis which allows a balanced description of normalvalent and hypervalent molecules. OM1 and OM2 have not yet been parameterized for second-row elements. 

FMO theory according to calculated electron densities at different carbon atoms of the HOMO of the radical cation (Hiickel and MNDO programmes). 

Finally, Nudelman and coworkers examined the effects of temperature, reagent concentration, reaction time, a radical trap, light and solvent on the formation of radical byproduct, in the reaction of PhLi with fi-cinnamaldehyde. It was claimed that the PhLi dimer is the reacting species with the aldehyde and that the reaction is initiated by an FT from the PhLi dimer to the cinnamaldehyde. MO calculations at the MNDO level of theory were claimed to be consistent with the participation of a dimer species. ... 

MNDO or ab initio calculations (Table 5.3). Further confirmation for the preference of 1,2-addition was established by ab initio calculation of the C-H bond energy in hydrogenated fullerenes [35]. Hybrid density functional theory using the B3LYP functional with the 6-31 G(d,p) basis set leads to the bond energies shown in Table 5.3. The most stable bond is found in 1,2 adducts with a bond energy of 2.86 eV, followed by a bond energy of 2.69 eV in 1,4-adducts. All the other addition patterns such as 1,3 addition or addition to a [5,6] bond lead to less stable C-H bonds (Table 5.3). 

M. R. Silva-Junior and W. Thiel. Benchmark of electronically excited states for semiempirical methods MNDO, AMI, PM3, OMl, OM2, OM3, INDO/S, and INDO/S2, J. Chem. Theory Comput., 6 1546-1564 (2010). 

Calculations by the MNDO (modified neglect of diatomic overlap) method with full optimization of geometry were carried out for [Zn, N, C, H]+ ions indicating the possible existence of four stable isomers (Figure 7). According to the same semi-empirical method, [Zn, N, C2, H3]+ ions can form nine stable isomeric stmctnres (Fignre 7) In a separate study by density functional theory, self-assembled helicate architectures have been proposed for ions of the [Zn (CN)2 +i] series. ... 

Semi-empirical molecular orbital, MO, theory uses a combination of experimental data and quantum mechanical MO methods to model the valence electronic structure of molecules. In the MNDO (8) method each atom is parameterized using experimental data. This calculation provides molecular orbital descriptions of the valence electrons, as well as effective charges of each atom in the molecule. 

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