Kuo-Hsiang Chen

An improved force field (MM4) for saturated hydrocarbons

A new force field has been developed for alkanes and cycloalkanes, excluding small rings, to improve the calculation of vibrational frequencies, rotational barriers, and numerous relatively small errors that were observed to result from the use of the MM3 force field.

MOLECULAR MECHANICS (MM4) CALCULATIONS ON ALKENES

The MM4 force field has been extended to alkenes. It retains most of the formalism and computational schemes that were present in MM3. Several additional cross‐terms have been added in MM4 that were not present in MM3, mainly to improve vibrational frequencies but also to improve structures and energies. About 100 molecules have been examined, many in multiple conformations. Geometries are fit for the most part to within the following ranges: 0.004 Å for bond lengths, 1° for bond angles, 4° for torsion angles, and 0.5% for moments of inertia (r2). Conformational energy differences/barriers are generally fit to within 0.5 kcal/mol unless they are very large. The vibrational frequency rms error for 7 alkenes is 25 cm−1.

Hyperconjugative effects on carbon—Carbon bond lengths in molecular mechanics (MM4)†

The hyperconjugative result of bond stretching in alkenes has been studied with MM4. A low‐temperature crystallographic study of 1,2‐diarylindane[a]indane has been carried out, together with ab initio (MP2/6‐31G*) calculations on model systems. The results are well reproduced with a force field designed to explicitly include hyperconjugation (MM4), and they show beyond doubt that hyperconjugative bond elongations exist both in theory and by experiment.

Alcohols, ethers, carbohydrates, and related compounds. IV. Carbohydrates.

Ab initio calculations [B3LYP/6‐311++G(2d,2p)] have been carried out on 84 conformations of 12 different sugars (hexoses), in both pyranose and furanose forms, with the idea of generating a data base for carbohydrate structural energies that may be used for developing the predictive value of molecular mechanics calculations for carbohydrates. The average value for the apparent gas phase anomeric effect for a series of 31 pairs of pyranose conformations was found to be 1.83 kcal/mol (vs. 2.67 kcal/mol with a smaller basis set used in earlier calculations). In developing MM4 to reproduce these data, it was necessary first to have good energies for simple alcohols and ethers, together with an adequate treatment of hydrogen bonding, and then to include the anomeric effect, and the ethylene glycol type system, as was previously recognized. It was also found that the so‐called delta‐2 effect, long recognized in carbohydrates, must be explicitly included, in order to obtain acceptable results. When a force field that included all of these items as developed from the small molecules based on the MM4 hydrocarbon force field was applied without any parameter adjustment to the set of hexopyranose and furanose conformations mentioned earlier, the Eβ − Eα was found to have an average value of 1.88 kcal/mol, versus 1.74 for the quantum calculations. The signed average and RMS deviations of the MM4 from the QM results were +0.15 and 0.87 kcal/mol.

Alcohols, ethers, carbohydrates, and related compounds. I. The MM4 force field for simple compounds

Simple alcohols and ethers have been studied with the MM4 force field. The structures of 13 molecules have been well fit using the MM4 force field. Moments of inertia have been fit with rms percentage errors as indicated: 18 moments for ethers, 0.28%; 21 moments for alcohols, 0.22%. Rotational barriers and conformational equilibria have also been examined, and the experimental and ab initio results are reproduced substantially better with MM4 than they were with MM3. Much of the improvement comes from the use of additional interaction terms in the force constant matrix, of which the torsion–bend and torsion–torsion are particularly important. Induced dipoles are included in the calculation, and dipole moments are reasonably well fit. It has been possible for the first time to fit conformational energetic data for both open chain and cyclic alcohols (e.g., propanol and cyclohexanol) with the same parameter set. For vibrational spectra, over a total of 82 frequencies, the rms error is 27 cm−1, as opposed to 38 cm−1 with MM3. Both the α and β bond shortening resulting from the presence of the electronegative oxygen atom in the molecule are well reproduced. The electronegativity of the oxygen is sufficient that one must also include not only the α and β electronegativity effects on bond lengths, but also on angle distortions, if structures are to be well reproduced. The heats of formation of 32 alcohols and ethers were fit overall to within experimental error (weighted standard deviation error 0.26 kcal/mol).

Alcohols, ethers, carbohydrates, and related compounds. II. The anomeric effect†

The anomeric effect has been studied for a variety of compounds using the MM4 force field, and also using MP2/6‐311++G(2d,2p) ab initio calculations and experimental data for reference purposes. Geometries and energies, including conformational, rotational barriers, and heats of formation were examined. Overall, the agreement of MM4 with the experimental and ab initio data is good, and significantly better than the agreement obtained with the MM3 force field. The anomeric effect is represented in MM4 by various explicit terms in the force constant matrix. The bond length changes are accounted for with torsion‐stretch elements. The angle changes are accounted for with torsion‐bend elements. The energies are taken into account with a number of torsional terms in the usual way. A torsion‐torsion interaction is also of some importance. With all of these elements included in the calculation, the MM4 results now appear to be adequately accurate. The heats of formation were examined for a total of 12 anomeric compounds, and the experimental values were fit by MM4 with an RMS error of 0.42 kcal/mol.

A molecular mechanics study of alkyl peroxides

Studies have been carried out on alkyl peroxides with MM3 that have led to a parameter set that allows the calculation of geometries, energies, vibrational frequencies, and heats of formation for alkyl hydroperoxides (ROOH) and dialkyl peroxides (R1OOR2). The results obtained are in agreement with the available experimental and theoretical data. A similar, although less good, parameter set has been developed for MM2.

Alcohols, ethers, carbohydrates, and related compounds. III. The 1,2-dimethoxyethane system†

Ethylene glycol, its dimethyl ether, and some related compounds have been studied using the MM4 molecular mechanics force field. The MM4 calculated structural and energetic results have been brought into satisfactory agreement with a considerable number of experimental data and MP2/6‐311++G(2d,2p) ab initio calculations. The heats of formation of these compounds are also well calculated. The MM4 ethylene glycol conformations in particular are in good agreement, both geometrically and in terms of energy, with those from the ab initio calculations. The corresponding dimethyl ether is of special interest, because it has been suggested that the trans‐gauche conformation is unusually stable due to the hydrogen bonding of a hydrogen on a methyl group with the more distant oxygen. It is shown in the present work that while this conformation is more stable than might have been expected, the energy is adequately calculated by MM4 without using any hydrogen bonding between the CH bond and the oxygen. If such hydrogen bonding occurs, it amounts to no more than about 0.5 kcal/mol in energy, and is too small to detect with certainty. Additionally, energetic relationships in trans‐1,2‐dimethoxycyclohexane, 1,3,5,7‐tetraoxadecalin, and 3‐methoxytetrahydropyran have been studied, and the calculated results are compared with experimental information, which is adequately reproduced.

Heats of formation of organic molecules calculated by density functional theory: II. Alkanes

Heats of formation of alkanes have been calculated with an accuracy of better than 0.36 kcal/mol by using the total energy calculated by density functional theory, plus bond and group equivalents and statistical mechanical corrections. The necessary equivalents were assigned to bonds and groups in molecules. Once such equivalents have been derived from the fit to available experimental values for a large and diverse set of compounds, they can be used to predict heats of formation for compounds of the same class for which these quantities are not experimentally available. Expanding the method to a new class of compounds requires that only new groups of equivalents for that class be added to the scheme. This provides a path for the systematic expansion of the model to new classes of compounds, and gives us a computational method for getting around the lack of experimental information about systems of interest. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1421–1430, 1998

Molecular mechanics calculations (MM3) on conjugated ketones

Abstract The MM3 force field has been extended to cover compounds in which a carbonyl group (aldehyde or ketone) is conjugated with either a double bond or a benzene ring. Molecular structures, conformational energies, moments of inertia, dipole moments, and vibrational spectra have all been examined. The agreement with experiment is mostly good, although for the dipole moments somewhat less so, because induced moments are not taken into account. The vibrational spectra have been calculated for four compounds, and over this set, the average r.m.s. error is 39 cm −1 .