PM3 model

Figure 28. The PM3 models of pyruvate- and pentanedione-bis(oxazoline)-Cu(II) complexes. [Adapted from (235).]...

The Hartree-Fock approximation also provided the basis for what are now commonly referred to as semi-empirical models. These introduce additional approximations as well as empirical parameters to greatly simplify the calculations, with minimal adverse effect on the results. While this goal has yet to be fully realized, several useful schemes have resulted, including the popular AMI and PM3 models. Semi-empirical models have proven to be successful for the calculation of equilibrium geometries, including the geometries of transition-metal compounds. They are, however, not satisfactory for thermochemical calculations or for conformational assignments. Discussion is provided in Section n. 

Additional approximations are introduced in order to further simplify the overall calculation, and more importantly to provide a framework for the introduction of empirical parameters. Except for models for transition metals, parameterizations are based on reproducing a wide variety of experimental data, including equilibrium geometries, heats of formation, dipole moments and ionization potentials. Parameters for PM3 for transition metals are based only on reproducing equilibrium geometries. The AMI and PM3 models incorporate essentially the same approximations but differ in their parameterization. 

The PM3 model qualitatively accounts for equilibrium geometries in these compounds, but does not afford the quantitative descriptions available from density functional models. None of the systems is particularly poorly described, but individual bond length errors are often significant (as reflected in the large mean absolute error). The PM3 model certainly has a role in surveying the geometries of transition-metal inorganic compounds, but it is not a replacement for better models. 

The PM3 model also provides a solid account. In terms of mean absolute error, it is as good as either of the more costly density functional models. It would appear to be an excellent choice for preliminary structure surveys of organometallics. 

There is a very wide variation in the quality of results from the different models. MNDO and AMI semi-empirical models, the ST0-3G model and both local density models are completely unsatisfactory. The 3-2IG model, all density functional models with the 6-3IG basis set and the PM3 model fare better, while 6-3IG ... 

Only local density, BP, BLYP, EDFl and B3LYP density functional all with the 6-3IG basis set and PM3 models have been examined. All produce similar results which closely parallel the known relative acidities of the uncomplexed benzoic acids (see data in Table 6-19), although, the overall range of substituent effects is somewhat reduced. Of special note is the (apparently) favorable performance of PM3, paralleling its behavior for relative acidities in uncomplexed benzoic acids. While experimental data on the acidities of complexed benzoic acids are unavailable, the consistency of results among the various models lends credence to their validity. 

MNDO and AMI semi-empirical models are not successful in reproducing experimental CX stretching frequencies. The PM3 model provides a much better account, and is the method of choice if semi-empirical models need to be utilized. 

Semi-empirical models are completely unsatisfactory. The MNDO model performs worst and the PM3 model performs best (paralleling the behavior that was previously noted in other frequency comparisons), but none is successful in properly ordering the frequencies. 

MNDO, AMI and PM3 models are unsatisfactory for assignment of ground-state conformer and for calculation of conformational energy differences in acyclic systems. While this could have been anticipated, given the poor performance of semi-empirical models for other isodesmic processes (see discussion in Chapter 6), it is nevertheless disappointing. In many cases, semi-empirical models either yield the... 

As with acyclic systems, semi-empirical models provide a poor account of the ground-state conformation and conformational energy differences in cyclic systems. While all three models typically yield reasonable results for hydrocarbons, results for other systems are not acceptable. The performance of the PM3 model with regard to the... 

Semi-empirical models do not provide good descriptions of the energy barrier to ring inversion in cyclohexane. The MNDO model underestimates the barrier by a factor of three, and the AMI and PM3 models by almost a factor of two. This behavior is consistent with previous experience in dealing with single-bond rotation barriers. 

Semi-empirical models generally turn in a respectable account of dipole moments in these compounds. None of the models stand out as being particularly better (or particularly worse) than the others. While there are a few very bad cases (for example, the AMI dipole moment in phosphine is four times larger than the experimental value), most of the calculated moments fall within a few tenths of a debye of their respective experimental values. Comparison of Figure 10-11 (for the PM3 model) with the other figures clearly shows, however, that semi-empirical models are not as successful as the other models in accounting for dipole moments in these compounds. 

Dipole moments for hypervalent molecules calculated from semi-empirical models are generally larger than experimental values (sometimes by a factor of two or more), suggesting descriptions which are too ionic. Figure 10-11 provides an overview for the PM3 model. Semi-empirical models should not be used. 

The SM2/AM1 model was used to examine anomeric and reverse anomeric effects and allowed to state that aqueous solvation tends to reduce anomeric stabilization [58]. Moreover, SM2/AM1 and SM3/PM3 models were accounted for in calculations of the aqueous solvation effects on the anomeric and conformational equilibria of D-glucopy-ranose. The solvation models put the relative ordering of the hydroxymethyl conformers in line with the experimentally determined ordering of populations. The calculations indicated that the anomeric equilibrium is controlled primarily by effects that the gauche/trans 0-C6-C5-0 hydroxymethyl conformational equilibrium is dominated by favorable solute-solvent hydrogen bonding interactions, and that the rotameric equilibria were controlled mainly by dielectric polarization of the solvent [59]. On the other hand, Monte Carlo results for the effects of solvation on the anomeric equilibrium for 2-methoxy-tetrahydropyran indicated that the AM1/SM2 method tends to underestimate the hydration effects for this compound [60]. 

The SM2/AM1 model was successful in studies on alkaline hydrolysis ofcla-vulanic acid - />-lactam antibiotic and / -lactamase inhibitor [86], The SM3/PM3 model was used to study the influence ofthe solvent on the basic hydrolysis of the />-lactame ring, and calculations for a supramolecular complex with 20 molecules of water in the solvation sphere around the solute yielded a potential barrier very close to the experimental value [87, 88],... 

Free energies of solvation in water and chloroform were calculated with the SM5.4/AM1 and SM5.4/PM3 models during a study on the effects of substitution of the hydroxyl group by the fluorine atom for (R,R)-tartaric acid derivatives. The results indicated that the substitution of OH by F results in greater conformational freedom of these compounds, and that solvation tends to decrease conformational diversity [18]. 

SM2/AM1 and SM3/PM3 models were used to study the hydrolysis of pyrophosphate, which is coupled to virtually all biosynthetic reactions. However, the authors concluded that extreme care must be taken when applying semiempirical methods to compounds containing second-row atoms, since they may produce anomalously high atomic charges [98]. On the other hand, a study on syn and anti conformations of solvated cyclic 3 ,5 -adenosine monophosphate indicated that SM3/PM3 and SM2/AM1 models are inexpensive yet accurate approaches... 

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