MNDO model limitations

MNDO, AMI, and PM3 are based on the same semiempirical model [12, 13], and differ only in minor details of the implementation of the core-core repulsions. Their parameterization has focused mainly on heats of formation and geometries, with the use of ionization potentials and dipole moments as additional reference data. Given the larger number of adjustable parameters and the greater effort spent on their development, AMI and PM3 may be regarded as methods which attempt to explore the limits of the MNDO model through careful and extensive parameterization. 

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. 

The MNDO model is a very successful model, again with some documented limitations. MNDO produces spurious interatomic repulsions, generally... 

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. 

These specifications define choices (a) and (b) in the MNDO formalism and thus constitute the MNDO model. The original implementation of the model may be summarized as follows [19]. Conceptually the one-center terms are taken from atomic spectroscopic data, with the refinement that slight adjustments of the parameters are allowed in the optimization to account for possible differences between free atoms and atoms in a molecule. Any such adjustments should be minor to ensure that the one-center parameters remain close to their spectroscopic values and thus retain their physical significance. The one-center two-electron integrals derived from atomic spectroscopic data are considerably smaller than their analytically calculated values, which is (at least partly) attributed to an average incorporation of electron correlation effects. For reasons of internal consistency, these integrals provide the one-center limit (/ AB = 0) of the two-center two-electron integrals A o- ),... 

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. 

To that end, Stewart set out to optimize simultaneously parameters for H, C, N, O, F, Al, Si, P, S, Cl, Br, and I. He adopted an NDDO functional form identical to that of AMI, except that he limited himself to two Gaussian functions per atom instead of the four in Eq. (5.16). Because his optimization algorithms permitted an efficient search of parameter space, he was able to employ a significantly larger data set in evaluating his penalty function than had been true for previous efforts. He reported his results in 1989 as he considered his parameter set to be the third of its ilk (tire first two being MNDO and AMI), he named it Parameterized Model 3 (PM3 Stewart 1989). 

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. 

Mulholland and Richards [344-346] have carried out ab initio (MP2/6-31-i-G(d) and RHF/6-31+G(d)) and semiempirical (AMI, PM3 and MNDO) molecular orbital calculations focussing on the enzyme citrate synthase. Their calculations were performed on the first stage of the citrate synthase reaction [344], on the substrate oxaloacetate [345] and on a simple model of the condensation reaction [346]. Their aim was to model the nucleophilic intermediate produced by the rate-limiting step, to examine which form of acetyl-CoA is the likely intermediate and how it is stabilised by the enzyme. They have found that the enolate is the likely nucleophilic intermediate in citrate synthase being stabilised by hydrogen bonds. 

There are known strengths ind weaknesses of each semiempirieal method. The AMI and PM3 models only include s- and p-funetions, which limits their u.sefulncss for most elements of the periodic table that require d-orbitals. Many of the.se elements, however, arc not typically found in most drug-like molecules. More recent advances with MNDO/d include the incorporation of d-functions in the NDDO (neglect of diatomic differential overlap) model."" ""... 

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. 

The main structural features of compound 1 are the seven-membered ring and the orientation of the dimethylallyl group. We believe that it is not possible by calculation accurately to predict the exact conformation of the side chain the usefulness of a crystal structure is also limited concerning this flexible group. The seven-membered ring contains three planar atoms and has some similarity with cyclohexene we expect therefore the existence of two conform-ers that are related to the two twist forms of cyclohexene. A conformational analysis using MNDO [5] supports this assumption. For our model we have used the conformer with the lowest MNDO heat of formation, which is also in agreement with a published X-ray structure of a chloro derivative of TIBO [6]. 

An obvious candidate for a stable noncyclic carbenium ion is the tert-butyl cation observed in superacidic media. Even if the proton affinity of isobutene (Table 22.1) does not make it very likely that tert-butyl cations will exist in zeolites, several quantum chemical studies have localized stationary points for tert-butyl cations in zeolite and found that they are less stable than the adsorption complex, but are similar in stability to surface butoxides. Because of technical limitations vibrational analysis, which could prove that this cation is a local minimum on the potential energy surface, that is a metastable species, have only recently been made. Within a periodic DFT study of isobutene/H-FER a complete vibrational analysis for all atoms in the unit cell was made [48], and as part of a hybrid QM/MNDO study on an embedded cluster model of isobutene/H-MOR a vibrational analysis was made with a limited number of atoms [49]. Both reached the... 

There are, however, two major disadvantages to the finite field procedure. The first is that it is limited to static fields, and hence the method does not give values that can be directly related to most experiments. This is not necessarily a serious problem because as a rule only an estimate or information on relative properties is needed. The second disadvantage is that, like all numerical derivative schemes, the finite field procedure may exhibit severe numerical problems. In the example of this shown in Figure 4, the calculated y value for a biphenyl molecule obtained by a semiempirical method (MNDO) is plotted as a function of the arbitrary choice of the base field strength F used in Eqs. [28] and [29]. The correct value within the model is the limit as F - 0. Note the large dependence of the choice of F in the calculation. As the base field increases, the calculated properties based on E(F) and p(f) deviate more and more from the... 

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