Jenn-Huei Lii

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.

IMPORTANCE OF SELECTING PROPER BASIS SET IN QUANTUM MECHANICAL STUDIES OF POTENTIAL ENERGY SURFACES OF CARBOHYDRATES

An extensive quantum mechanical study of a water dimer suggests that the introduction of a diffuse function into the basis set, which significantly reduces the basis set superposition error (BSSE) in the hydrogen bonding energy calculation, is the key to better calculations of the potential energy surfaces of carbohydrates. This article examines the potential energy surfaces of selected d‐aldo‐ and d‐ketohexoses (a total of 82 conformers) by quantum mechanics (QM) and molecular mechanics (MM) methods. In contrast to the results with a smaller basis set (B3LYP/6‐31G** 5d), we found at the higher level calculation (B3LYP/6‐311++G(2d,2p)//B3LYP/6‐31G** 5d) that, in most cases, the furanose forms are less stable than the pyranose forms. These discrepancies are mainly due to the fact that intramolecular hydrogen bonding energies are overestimated in the lower level calculations. The higher level QM calculations of the potential energy surfaces of d‐aldo‐ and d‐ketohexoses now are more comparable to the MM3 results. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1593–1603, 1999

Directional hydrogen bonding in the MM3 force field: II

Extensive calculations on hydrogen bonded systems were carried out using the improved MM3 directional hydrogen bond potential. The resulting total function was reoptimized. Comparisons of the hydrogen bonding potential function from ab initio calculations (MP2/6‐31G**); the original MM3(89); and the reoptimized MM3 force field MM3(96), for a variety of C, N, O, and Cl systems including the formamide dimer and formamide–water complex, are described herein. Hydrogen bonding is shown to be a far more complicated and ubiquitous phenomenon than is generally recognized. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1001–1016, 1998

Molecular polarizabilities and induced dipole moments in molecular mechanics

Molecular polarizabilities may be divided into either atomic contributions or bond contributions. The common way to estimate molecular polarizabilities is to assign atomic or bond parameters for each atom or bond type to fit experimental or quantum mechanical results. In this study we have taken a different approach. A general formula based on MM3 force constants and bond lengths was used to compute bond polarizabilities and molecular polarizabilities. New parameters for polarizabilities are not required. A fair agreement between experimental and computed molecular polarizabilities was obtained, with a RMS deviation of 0.82 Å3 (11.7%) and signed average error of 0.01 Å3 for a broad selection of 57 molecules studied. Two methods, the many‐body interaction and the pair‐interaction approaches, have been used to study induced dipole moments using the bond polarizabilities estimated from the new formula. The pair‐interaction approximation, which involves much less computation than the many‐body interaction approach, gives a satisfactory representation of induced dipole interaction.

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.

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.

Molecular mechanics calculations on carbonyl compounds. III. Cycloketones

Molecular mechanics (MM4) calculations were carried out on cycloketones for ring sizes ranging from 4 to 11 carbon atoms. The MM4 relative energies for the various conformations of the cycloketones were compared to density functional theory (DFT) calculations (B3LYP/6‐31G*), which were also carried out in this work. For small ring sizes (n=4–6), calculated molecular geometries, dipole moments, moments of inertia, and vibrational spectra were compared to experimental data. The axial–equatorial energy differences in methyl‐substituted cyclohexanones were also calculated by MM4 and compared to ab initio, DFT, and experimental results. The results of the MM4 studies on cycloketones showed significant improvement from those of MM3 calculations performed in parallel with the MM4 calculations.

The important role of lone-pairs in force field (MM4) calculations on hydrogen bonding in alcohols.

An expanded treatment of hydrogen bonding has been developed for MM4 force field calculations, which is an extension from the traditional van der Waals-electrostatic model. It adds explicit hydrogen-bond angularity by the inclusion of lone-pair directionality. The vectors that account for this directionality are placed along the hydrogen acceptor and its chemically intuitive electron pairs. No physical lone-pairs are used in the calculations. Instead, an H-bond angularity function, and a lone-pair directionality function, are incorporated into the hydrogen-bond term. The inclusion of the lone-pair directionality results in improved accuracy in hydrogen-bonded geometries and interaction energies. In this work is described hydrogen bonding in alcohols, and also in water and hydrogen fluoride dimer. The extension to other compounds such as aldehydes, ketones, amides, and so on is straightforward and will be discussed in future work. The conformational energies of ethylene glycol are discussed.