MNDO model accuracy

MNDO, AMI, and PM3 employ an sp basis without d orbitals [13, 19, 20]. Hence, 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 [34], To overcome these limitations, the MNDO formalism has been extended to d orbitals. The resulting MNDO/d approach [15-18] retains all the essential features of the MNDO model. 

In an overall assessment, the established semiempirical methods perform reasonably for the molecules in the G2 neutral test set. With an almost negligible computational effort, they provide heats of formation with typical errors around 7 kcal/mol. The semiempirical OM1 and OM2 approaches that go beyond the MNDO model and are still under development promise an improved accuracy (see Table 8.1). 

To accomplish this large task of optimizing parameters an automatic procedure was introduced, allowing a parameter search over many elements simultaneously. These now include H, C, N, O, F, Br, Cl, I, Si, P, S, Al, Be, Mg, Zn, Cd, Hg, Ga, In, Tl, Ge, Sn, Pb, As, Sb, Bi, Se, Te, Br, and I. Each atom is characterized through the 13-16 parameters that appear in AMI plus five parameters that define the one-center, two-electron integrals. The PM3 model is no doubt the most precisely parameterized semiempirical model to date, but, as in many multiminima problems, one still cannot be sure to have reached the limit of accuracy suggested by the MNDO model. 

A variation on MNDO is MNDO/d. This is an equivalent formulation including d orbitals. This improves predicted geometry of hypervalent molecules. This method is sometimes used for modeling transition metal systems, but its accuracy is highly dependent on the individual system being studied. There is also a MNDOC method that includes electron correlation. 

The Schrodinger equation can also be solved semi-empirically, with much less computational effort than ab initio methods. Prominent semi-empirical methods include MNDO, AMI, and PM3 (Dewar 1977 Dewar etal. 1985 Stewart 1989a Stewart 1989b). The relative computational simplicity of these methods is accompanied, however, by a substantial loss of accuracy (Scott and Radom 1996), which has limited their use in geochemical simulations. Historically, semi-empirical calculations have also been limited by the elements that could be modeled, excluding many transition elements, for example. Semi-empirical calculations have been used to predict Si, S, and Cl isotopic fractionations in molecules (Hanschmaim 1984), and these results are in qualitative agreement with other theoretical approaches and experimental results. 

The methods have been very successful, but they do suffer drawbacks. The lack of parameters for many elements seriously limits the types of problems to which the methods can be applied and their accuracy for certain problems is not very good (for example, both MNDO and AM 1 do not well describe water-water interactions). There are also questions about the theoretical foundations of the models. The parameterization is performed using experimental data at a temperature of 298K and implicitly includes vibrational and correlation information about the state of the system. Therefore, the parameterization is used, in part, to compensate for quantities that the HF method cannot, by itself, account for. But what happens if vibrational or correlation energy calculations are performed With these caveats and if one can be certain of their accuracy in given circumstances, the methods are very useful as calculations can be performed with them much more quickly than ab initio QM calculations. Even so, they are probably still too computationally intensive to treat complete condensed phase systems in a routine manner. 

MNDO, AMI, and PM3 together are all NDDO techniques developed by Dewar and his co-workers, and all use essentially the same model functions. MNDO has been parameterized for 20 elements, AMI for 11, and PM3 for 12. The accuracy of these three methods in reproducing experiment has been examined recently in considerable detail.We review this briefly below and refer in particular to ref. 12. 

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