MNDO Parametric Method

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. 

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

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... 

Modified Neglect of Diatomic Overlap Parametric Method Number 3 (MNDO-PM3) 3.10.6 The MNDO/d Method 88 89 5.5 5.6 5.4.5 Correlation Consistent Basis Sets Extrapolation Procedures Isogyric and Isodesmic Reactions 162 164 169... 

Many popular semiempirical methods are based on the original MNDO method. The most prominent of these are Austin Model 1 (AMI) by Dewar et al. [73] and Parametric Method 3 (PM3) by Stewart [74], These three methods represent the semiempirical standard for the calculation of organic molecules and are included in popular program packages such as Gaussian [78], CERIUS [79], SPARTAN [80], MOP AC [81], and AMPAC [82], Recently, AM 1 and PM3 have also been extended for the treatment of transition metal compounds [75-77], In principle, they only differ in the parameterization and in the empirical function fAB [Eq. (42)]. 

NDDO [20] goes beyond INDO in that the ZDO approximation (section 6.2.1, point (3)) is not applied to orbitals on the same atom, i.e. ZDO is used only for atomic orbitals on different atoms. NDDO is the basis of the currently popular semiempirical methods developed by Dewar and coworkers modified NDDO (MNDO), Austin method 1 (AMI) and parametric method (PM3). 

As mentioned (Section 21.3.2), the MNDO-type methods attempt to incorporate the effects of Pauli exchange repulsion in an empirical manner, through an effective atom-pair potential that is added to the core-core repulsion. It would clearly be better to include the underlying orthogonahzation corrections explicitly in the electronic calculation and to remove the effective atom-pair potential from the core-core repulsion. In a semiempirical context, the dominant one-electron orthogonahzation correchons can be represented by parametric funchons that reflect the second-order expansions of the Lowdin orthogonahzation transformation in terms of overlap. These corrections can then be adjusted during the parametrization process. 

Such specialized semiempirical treatments exist (see Ref. [42] for a review on early work), many of which are based on the MNDO model in one of its standard implementations. For example, there are several early MNDO and AMI variants with a special treatment of hydrogen bonds [42], which have recently been supplemented with an elaborate PM3-based parametrization for water-water interactions named PM3-PIF (pair interaction function) [69]. These special approaches exploit the flexibility offered in MNDO-type methods by the presence of the effective core-core repulsion term which can be modified for fine tuning. 

Za and Zg). The SINDOl resonance integrals are also related to overlap integrals, but in a fairly intricate manner [25]. As in MNDO-type methods, the parametrization (d) of SINDOl focuses on ground-state... 

The discussion in Section II.A has shown that many of the currently accepted semiempirical methods for computing potential surfaces are based on the MNDO model. These methods differ mainly in their actual implementation and parametrization. Given the considerable effort that has gone into their development, we believe that further significant overall improvements in general-purpose semiempirical methods require improvements in the underlying theoretical model. In this spirit we describe two recent developments The extension of MNDO to d orbitals and the incorporation of orthogonalization corrections and related one-electron terms into MNDO-type methods. 

The documented successes of MNDO/d (see above) suggest an extension to transition metals. The MNDO/d parametrization has been completed for several transition metals [123] and is in progress for others, but a systematic assessment of the results is not yet feasible. Elsewhere the published MNDO/d formalism for the two-electron integrals [33] has been implemented independently [124] and combined with PM3 in another parametrization attempt for transition metals [125]. Moreover, the SAMI approach is also being parametrized for transition metals [122,126]. Given these complementary activities it seems likely that the performance of MNDO-type methods with an spd basis for transition metal compounds will be established in the near future. 

In the late 1960s and early 1970s, Dewar and co-workers developed the modified INDO (MINDO) methods. In 1976, the modified neglect of diatomic overlap (MNDO) method " was introduced. Further refinements were made to MNDO and improved parametrizations, AMI Austin model 7) PM3 parametric method and PM5 parametric method 5), ... 

In 1989, Stewart re-parametrized AMI to give the PM3 method (parametric method 3, methods 1 and 2 being MNDO and AMI) [J. J. P. Stewart, J. Comput. Chem., 10, 209,221 (1989) 11, 543 (1990) 12, 320 (1991)]. PM3 differs from AMI as follows. The one-center electron-repulsion integrals are taken as parameters to be optimized (rather than being found from atomic spectral data). The core-repulsion function has only two Gaussian terms per atom. A different method was used to optimize the PM3 parameters. PM3 has been parametrized for nearly all the main-group elements and for Zn, Cd, and Hg. 

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 ... 

Thielwas the first to introduce a correlated version of the MNDO model, called MNDOC. The ground state parametri-zation is carried out on the level of second-order perturbation theory equivalent to a Cl with a Cl matrix containing non zero elements only in the diagonal, in the first row and in the first column. It was shown in a statistical analysis of the heats of formation that the results of MNDO and MNDOC are of similar quality, with the latter showing a slight reduction of the absolute error, but no consistent improvement over the former. In an accompanying study on reactive intermediates and transition states, MNDOC turned out to be superior to MNDO for systems that show specific correlation effects. Excited states are then treated by a perturbation Cl approach. Modifications of the parametrization of the MNDO model led eventually to the Austin model 1 (AMI) and parametric method number 3 (PM3) schemes. 

In this article, we summarize the results of our previous OVGF calculations based on the commonly used semiempiri-cal methods (modified neglect of diatomic overlap, MNDO Austin Model 1, AMI and parametric methods, PM3 ) and compare them with the results of the recent semiempirical ab initio method 1 (SAMl) and MNDO/d " semiempirical methods. The focus is on methodology of the method and its performance. 

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. ... 

The established MNDO-type methods, i.e., MNDO, AMl, and PM3 (see AMI MNDO and PM3) employ an sp basis without d orbitals in their original implementation. Therefore, they cannot be applied to most transition metal compounds, and difficulties are expected for hypervalent compounds of main-group elements where the importance of d orbitals for quantitative accuracy is well documented at the ab initio level. To allow for an improved semiempirical description of such compounds, the MNDO formalism has been extended to d orbitals. This extension forms the basis of the MNDO/d method " and the independent PM3/tm parametrization. ... 

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