Semiempirical Heats of Formation

A major weakness of semiempirical methods is that they must be assumed to be unreliable outside molecules of the kind used for their training set (the set of molecules used to parameterize them), until shown otherwise by comparison of their predictions with experiment or with high-level ab initio (or probably DFT) calculations. Although, as Dewar and Storch pointed out [125], the reliability of ab initio calculations, too, should be checked against experiment, the situation is somewhat different for these latter, at least at the higher levels studies of exotic species, in particular, are certainly more trustworthy when done ab initio than semiempirically. Semiempirical heats of formation are subject to errors of tens of kJ mol-1, and thus heats (enthalpies) of reaction and activation could be in error by scores of kJ mol-1. AMI and PM3 underestimate steric repulsions, overestimate basicity and underestimate nucleophilicity, and can give unreasonable charges and... 

Repasky, M.P., Chandrasehar, J., and Jorgensen, W.L., Improved semiempirical heats of formation through the use of bond and group equivalents, J. Computational Chem., 23, 498-510, 2002a. 

In other analytical work, Shevchenko et al. [80] found excellent agreement between theoretical and experimental ionization potentials. Semenov and Khodyreva (81) compare photoelectron spectra with CNDO/S3 calculations and found good resnlts. Semiempirical calculations, on a number of lignin model compounds have also been nsed as an aid in the interpretation of ESR spectroscopy [34]. In more general research on substituted aromatic systems [82] correlated experimental p/f valnes to semiempirical heats of formation and HOMO energies, with correlations in the 0.7-0.9 range. 

Stability (cubane is veiy strained, but perfectly stable kinetically at room temperature). The easiest way to calculate a heat of formation for a compound is to use a semiempirical method which has been parmeterized to give molecular energies as heats of formation. Currently the most popular such methods are AMI and PM3. The heat of formation of pyramidane from AMI and PM3 are 1047 and 916kJ mol respectively. Unfortunately, semiempirical heats of formation, although trivial to calculate, thus rendering such calculations useful for some purposes, are subject to considerable errors, often tens or occasionally even hundreds of kJ mol. ... 

Semiempirical methods are parameterized to reproduce various results. Most often, geometry and energy (usually the heat of formation) are used. Some researchers have extended this by including dipole moments, heats of reaction, and ionization potentials in the parameterization set. A few methods have been parameterized to reproduce a specific property, such as electronic spectra or NMR chemical shifts. Semiempirical calculations can be used to compute properties other than those in the parameterization set. 

Many semiempirical methods compute energies as heats of formation. The researcher should not add zero-point corrections to these energies because the thermodynamic corrections are implicit in the parameterization. 

Thermodynamic properties such as heats of reaction and heats of formation can be computed mote rehably by ab initio theory than by semiempirical MO methods (55). However, the Hterature of the method appropriate to the study should be carefully checked before a technique is selected. Finally, the role of computer graphics in evaluating quantum mechanical properties should not be overlooked. As seen in Figures 2—6, significant information can be conveyed with stick models or various surfaces with charge properties mapped onto them. Additionally, information about orbitals, such as the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), which ate important sites of reactivity in electrophilic and nucleophilic reactions, can be plotted readily. Figure 7 shows representations of the HOMO and LUMO, respectively, for the antiulcer dmg Zantac. 

A particularly useful property of the PX monomer is its enthalpy of formation. Conventional means of obtaining this value, such as through its heat of combustion, are, of course, excluded by its reactivity. An experimental attempt was made to obtain this measure of chemical reactivity with the help of ion cyclotron resonance a value of 209 17 kJ/mol (50 4 kcal/mol) was obtained (10). Unfortunately, the technique suffers from lack of resolution in addition to experimental imprecision. It is perhaps better to rely on molecular orbital calculations for the formation enthalpy. Using a semiempirical molecular orbital technique, which is tuned to give good values for heat of formation on experimentally accessible compounds, the heat of formation of /5-xylylene has been computed to be 234.8 kj/mol (56.1 kcal/mol) (11). 

These findings accord with the semiempirical AMI calculations [92JCS(P1)2779] of the heats of formation of all theoretically possible tautomeric forms of 4-aminoimidazole 53. The most stable are the tautomers 53a AHf = 213 kJ mol ) and 53d AHf = 215 kJ mol ) (Scheme 29). All... 

Quantum-chemical calculations have been carried out for 123 [R = Me, = (CH2) , = 3, 4] using two semiempirical methods AMI and PM3 [94JCS(P2)1561], The heats of formation (AH ) and the population of each tautomer were calculated, the latter being in good agreement with experimental data. 

Molecular orbital calculations, whether by ab initio or semiempirical methods, can be used to obtain structures (bond distances and angles), energies (such as heats of formation), dipole moments, ionization energies, and other properties of molecules, ions, and radicals—not only of stable ones, but also of those so unstable that these properties cannot be obtained from experimental measurements." Many of these calculations have been performed on transition states (p. 279) this is the only way to get this information, since transition states are not, in general, directly observable. Of course, it is not possible to check data obtained for unstable molecules and transition states against any experimental values, so that the reliability of the various MO methods for these cases is always a question. However, our confidence in them does increase when (1) different MO methods give similar results, and (2) a particular MO method works well for cases that can be checked against experimental methods. ... 

Semiempirical and ab initio calculations were performed on the cyclodimerization of 1-methylphosphole oxide (86). The relative order of the values of the heat of formation for the transient states leading to the possible isomers (87-94) confirmed that the formation of the isomer prepared (87) is indeed favored to a high extent (Scheme 24) [67], The selectivity can be explained by steric reasons and kinetic factors. 

One might add that the failure of CNDO/2 is probably mainly due to the method of parametrization. If a semiempirical method is to be used to estimate heats of formation and molecular geometries, the parameters in it should be chosen accordingly rather than to mimic the results of an approximation known to give unsatisfactory estimates of energies. Recent studies suggest that CNDO/2 may in fact prove useful if properly parametrized. u>... 

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. 

This procedure is normally followed in ab initio studies and could equally well be applied in semiempirical work. However, in MNDO-type methods, heats of formation at 298 K are traditionally derived in a simpler manner [1, 13]. By formally neglecting the zero-point vibrational... 

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). 

In our own validation sets, experimental heats of formation are preferentially taken from recognized standard compilations [38-40]. If there are enough experimental data for a given element, we normally only use reference values that are accurate to 2 kcal/mol. If there is a lack of reliable data, we may accept experimental heats of formation with a quoted experimental error of up to 5 kcal/mol. This choice is motivated by the target accuracy of the established semiempirical methods. If experimental data are missing for a small molecule of interest, we consider it legitimate [18] to employ computed heats of formation from high-level ab initio methods as substitutes. 

In the course of the MNDO/d development [15-18] we have generated new validation sets for second-row and heavier elements. Those for Na, Mg, Al, Si, P, S, Cl, Br, I, Zn, Cd, and Hg have been published [16-18], The corresponding statistical evaluations for heats of formation [18] are summarized in Table 8.3. It is obvious that MNDO/d shows by far the smallest errors followed by PM3 and AMI. All four semiempirical methods perform reasonably well for normalvalent compounds, especially when considering that more effort has traditionally been spent on the parameterization of the first-row elements. For hy-pervalent compounds, however, the errors are huge in MNDO and AMI, and still substantial in PM3, in spite of the determined attempt to reduce these errors in the PM3 parameterization [20], Therefore it seems likely that the improvements in MNDO/d are due to the use of an spd basis set [16-18]. 

The statistical evaluations of the preceding section indicate that the semiempirical MO methods can predict heats of formation with useful accuracy and at very low computational costs. When comparing with... 

A semiempirical procedure based on isodesmic reactions is used to determine unknown heats of formation. The choice of the isodesmic reaction is critical for the validity of the approach. By definition, all the bonds are conserved in number and nature in this type of process. Also, the bond lengths of equivalent bonds in reactants and products should be as similar as possible. The stabihzation energies are based on the type of isodesmic reaction which is given for the influence of amino- and cyano-groups in a captodative radical in equation (3). Only radicals appear as reactants and... 

The semiempirical AMI MO method has been used to calculate heats of formation of a series of m- and p-substituted benzene and toluene derivatives ArY and ArCHaY, and their phenyl or benzyl cations, anions, and radicals heterolytic and homolytic bond dissociation energies (BDEs) and electron transfer energies for the ions have also been calculated and the relationship A//het = A//et-I-AWhomo has been confirmed (it being noted that A//homo is insensitive to ring substituents). The linear relationship found between and the appropriate HOMO or LUMO... 

For chemical purposes, substitution of total energy hypersurfaces by those based on the heat of formation seems more reasonable, with the difference given by the zero point energy corrections. However, their calculations from first principles can be rather cumbersome (12) and, moreover, for a given variation of some nuclear coordinates it usually can be assumed that the change in zero point energy is small compared to that of the total energy. On the other hand, se eral semiempirical quantum chemical procedures which are appropriately parametrized often yield satisfactory approximations for molecular heats of formation (10) and, therefore, AH hypersurfaces have become rather common. 

Semiempirical methods, on the other hand, utilize minimum basis sets to speed up computations, and the loss in rigor is compensated by the use of experimental data to reproduce important chemical properties, such as the heats of formation, molecular geometries, dipole moments, and ionization potentials (Dewar, 1976 Stewart, 1989a). As a result of their computational simplicity and their chemically useful accuracy, semiempirical methods are widely used, especially when large molecules are involved (see, for example, Stewart, 1989b Dewar et al., 1985 Dewar, 1975). 

The most important uncertainty associated with the determination of is related to our ability to predict heats of formation of species. At present, AH( values for stable species can be predicted within 5kcal/mol using various forms of additivity principles, provided these rules are applicable. Estimations based on semiempirical quantum mechanics are more general and can be as accurate. Although ab initio calculations can be more accurate, they are computationally prohibitive. For radical species, the associated uncertainties in AHf generally are larger. 

In an effort to understand the formidable-appearing output of many computations for a wide variety of C-H-N-O explosives at various initial loading densities, we have investigated interrelationships between such properties as pressure, velocity, density, heat of reaction, etc. These studies have led to a number of interesting observations, important among which were the facts that much simpler semiempirical formulas could be written for desk calculation of detonation velocities and detonation pressures, with about the same reliance on their answers as one could attach to the more complex computer output. These equations require as input information only the explosive s composition and loading density and an estimate of its heat of formation, and, in their comparative simplicity,... 

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