MNDO parametrization

An alternative strategy was to develop methods wherein the two-electron integrals are parameterized to reproduce experimental heats of formation. As such, these are semi-empirical molecular orbital methods—they make use of experimental data. Beginning first with modified INDO (MINDO/1, MlNDO/2, and MINDO/3, early methods that are now little used), the methodological development moved on to modified neglect of diatomic differential overlap (MNDO). A second MNDO parameterization was created by Dewar and termed Austin method 1 (AMI), and finally, an "optimized" parametrization termed PM3 (for MNDO, parametric method 3) was formulated. These methods include very efficient and fairly accurate geometry optimization. The results they produce are in many respects comparable to low-level ab initio calculations (such as HF and STO-3G), but the calculations are much less expensive. 

The AMI method (Austin Model 1) [63] is a novel semiempirical scheme. It has been developed under Dewar s guidance and, like the MNDO method, is based on the NDDO approximation. Apart from original MNDO parametrization, the AM 1 method differs from the MNDO method in that the function ... 

Finally, several special MNDO parametrizations are available for certain classes of compounds or for specific properties. These treatments retain the original MNDO approach (a)-(c), but use parameters (d) that have been optimized for the intended applications. It is obvious that such specialized methods ought to be more accurate in their area of applicability than the original general-purpose MNDO method. Samples of this kind include the special MNDO variants for small carbon clusters, fullerenes, and hydrogen-bonded systems as well as special parametrizations for electrostatic potentials. ... 

A new parametric quantum mechanical model AMI (Austin model 1), based on the NDDO approximations, is described. In it the major weakness of MNDO, in particular the failure to reproduce hydrogen bonds, have been overcome without any increase in eoraputer time. Results for 167 molecules are reported. Parameters are currently available for C, H, O and N. 

Modified Negiect of Diatomic Overlap, Parametric Method Number 3 (MNDO-PM3)... 

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. 

With the intermediate NDO method ZDO is not assumed between a.o. s on the same atom in one-centre electron repulsion integrals. Various other schemes based on different ZDO assumptions together with different schemes of semi-empirical parametrization have been developed. These have become known by their acronyms such as CNDO/1, CNDO/2, INDO, MINDO/3 (m - modified), NDDO (d - diatomic), MNDO etc.. 

Thiel and Voityuk (1992, 1996) described the first NDDO model with d orbitals included, called MNDO/d. For H, He, and the first-row atoms, the original MNDO parameters are kept unchanged. For second-row and heavier elements, d orbitals are included as a part of the basis set. Examination of Eqs. (5.12) to (5.14) indicates what is required parametrically to add d orbitals. In particular, one needs and /ij parameters for the one-electron integrals, additional one-center two-electron integrals analogous to those in Eq. (5.11) (there are... 

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. 

Let us compare the SCF dipole moments obtained by MNDO type methods either from the NDDO or the quasi ab initio wavefunctions to the experimental dipole moments. Since experimental results were taken into account in the parametrization of MNDO type methods [32-34], it is more appropriate to... 

The MNDO (modified NDDO) parametrization [64] involves the core-core repulsion in the form ... 

The AMI and PM3 parametrizations can be characterized as the MNDO ones with the core-core energy terms further modified ... 

The highly specific behavior of transition metal complexes has prompted numerous attempts to access this Holy Grail of the semi-empirical theory - the description of TMCs. From the point of view of the standard HFR-based semiempirical theory, the main obstacle is the number of integrals involving the d- AOs of the metal atoms to be taken into consideration. The attempts to cope with these problems have been documented from the early days of the development of semiempirical quantum chemistry. In the 1970s, Clack and coworkers [78-80] proposed to extend the CNDO and INDO parametrizations by Pople and Beveridge [39] to transition elements. Now this is an extensive sector of semiempirical methods, differing by expedients of parametrizations of the HFR approximation in the valence basis. These are, for example, in methods of ZINDO/1, SAMI, MNDO(d), PM3(tm), PM3 etc. [74,81-86], From the... 

In our paper [133] we have performed calculations of the heats of formation using all three parametrizations (MNDO, AMI, PM3) and both types of the variation wave function (SLG and SCF). Empirical functions of distribution of errors in the heats of formation [141] for the SLG-MNDO and SCF-MNDO methods are remarkably close to the normal one. That means that the errors of these two methods, at least in the considered data set, are random. In the case of the SLG-MNDO method, the systematic error practically disappears for the most probable value of the error... 

In Fig. 1 we show the correlation between E and experimental heats of formation for the (complete) set of C22H14 benzenoid isomers. For comparison we also present some recent data for the same set of compounds, obtained by a semiempirical MNDO method [21] and by the MMX/PI version of molecular mechanics calculations [22], The only conclusion we wish to draw from Fig. 1 is that HMO theory is capable of reproducing the experimental enthalpies of benzenoid hydrocarbons with an accuracy which is not much worse than that of the much more sophisticated (and highly parametrized) molecular orbital and molecular mechanics approaches. 

We undertook a quantum chemical study of the protonation of monocyclic and benzannulated five-membered heterocyclic systems with one heteroatom (03KGS38). The initial calculations, carried out by the semi-empirical CNDO/2 method (81ZOR1129), gave values for the differences in energy of the cations formed on protonation of the a- and yS-positions iAEa-p) that corresponded with the available experimental data on the sequence of change in positional selectivity furan > thiophene > pyrrole. However, the place of selenophene between thiophene and pyrrole in this series predicted by these calculations was contradicted by the experimental results obtained later (95JHC53). The results of calculations by the MNDO and PM3 methods also did not fit the experimental data, possibly linked with poor parametrization for selenium atom (97M12). 

Latest version of parametrized MNDO-level approximate SCF method (see MNDO)... 

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