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Ab initio calculations give, with an accuracy depending on the sophistication of the method, a bond length as an equilibrium value, r e. The experimental bond lengths are always vibrationally averaged and may be expressed in different ways (r g, r z, r a, etc.). Since high-quality ab initio calculations now are capable of giving bond lengths that are approximately of experimental accuracy, it is important to be able to interconvert these values. We find that the bond lengths optimized at the TZ2P+f CCSD level may be considered as the converged r e values and that the MM3 and MM4 force fields successfully convert r g to r e values. We also evaluated the performance of quantum mechanics at the 6-31G* MP2 and the 6-31G* B3LYP levels and found that the bond lengths (r e) at the 6-31G* B3LYP level are better than these at the 6-31G* MP2 level for molecules with only first-row atoms. However, the bond lengths for the bonds involving second-row atoms are too long at the 6-31G* B3LYP level, and for these, the 6-31G* MP2 level is recommended. An empirical formula is given for the conversion of the theoretical r e values calculated at these levels to the r g values.

The potential functions for simple amides, several peptides and a small protein have been worked out for the MM3 force field. Structures and energies were fit as previously with MM2, but additionally, we fit the vibrational spectra of the simple amides (average rms error over four compounds, 34 cm-I), and examined more carefully electrostatic interactions, including charge-charge and chargedipole interactions. The parameters were obtained and tested by examining four simple amides, five electrostatic model complexes, two dipeptides, six crystalline cyclic peptides, and the protein Crambin. The average root-mean-square deviation from the Xray structures for the six cyclic peptide crystals was only 0.10 A for the nonhydrogen atomic positions, and 0.011 A, 1.0", and 4.9" for bond lengths, bond angles, and torsional angles, respectively. The parameter set was then further tested by minimizing the high resolution crystal structure of the hydrophobic protein Crambin. The resultant root-mean-square deviations for the non-hydrogen atomic data, in the presence of the crystal lattice, are 0.22 A, 0.023 A, 2.0°, and 6.4" for coordinates, bond lengths, bond angles, and torsional angles, respectively.

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 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 Å 3 (11.7%) and signed average error of 0.01 Å 3 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.

A new approach is proposed which allows us to calculate molecular conformations of organometallic molecules within the framework of the MM3 force field. The ligand positions in the coordination sphere of the metal atom are mainly determined by minimization of the interligand nonbonded energy. For a description of the metal-ligand interactions (n-bonding), a very strong but otherwise ordinary (Hill type) van der Waals potential is used. Using this approach, the conformations of the bent sandwich metallocenes MCp2 (where M are metals of main groups I1 or IVA or lanthanides 11) were reproduced. It was shown that, when the interplanar distance between the planes of the Cp ligands are short, the ligands have a parallel orientation. When the distance is large (when the metal atom has a large radius), the interplanar distances become longer and the ligand planes do not stay parallel, but the molecule "bends" so that these planes intersect. The influence of bulky substituents on the bending angle was shown. Calculations were also carried out on crystals of these molecules, to determine the effect of crystal packing. The possibilities for the accurate prediction of the conformations of molecules of this type of structures (not yet investigated experimentally) on the basis of quantum mechanics and molecular mechanics are discussed.

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 alpha and beta 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 alpha and beta 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).