A new molecular mechanics force field (called MM3) for the treatment
of aliphatic hydrocarbons has been developed and is presented here. This
force field will enable one to calculate the structures and energies,
including heats of formation, conformational energies, and rotational energies,
for hydrocarbons more accurately than was possible with earlier force field.
In addition to simple molecules, a great many highly strained molecules have
been studied, and the results are almost always of experimental accuracy.
In the development of the MM3 force field, vibrational frequencies were considered for a set of eight relatively simple hydrocarbons. The 213 observed experimental frequencies over this set were fit to within a root-mean-square error of 35 cm-1 of which the largest errors occur in the C-C-H bending frequencies. The torsional frequencies are generally calculated to a much higher accuracy, which allows the calculation of entropies near room temperature for a variety of alkanes and cycloalkanes with errors of less than 1%. A number of rotational barriers in hindered compounds were also calculated. The values of d(S#) are usually more negative than -4 eu in congested molecules, and consequently the entropy contribution to rotational barriers can be appreciable. The largest and average discrepancies between the calculated and found values for d(G#) are 2.46 and 1.02 kcal/mole, for seven examples.
The van der Waals' potentials used for interactions between carbon and hydrogen in both aliphatic and aromatic system have been improved from those available in MM2, and the new values are used in MM3. The atoms are slightly larger and somewhat softer than they were with MM2. These values were optimized by fitting to the crystal parameters (six cell constants) and the heats of sublimation for the normal alkanes from C6 to C10, plus C12, and also diamond, graphite, benzene, biphenyl, and hexamethylbenzene, in addition to fitting structural and energy data on congested molecules as reported earlier. The parameters developed give good crystal structures and heats of sublimation for these molecules. Biphenyl is calculated to be twisted about 40 degree in the gas phase, but lattice forces cause it to flatten into a planar conformation in the crystal.
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-1), and examined more carefully electrostatic interactions, including charge-charge and charge- dipole 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 X-ray structures for the six cyclic peptide crystals was only 0.10 A for the non-hydrogen atomic positions, and 0.011 A, 1.0 degree, and 4.9 degree 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 degree, and 6.4 degree for coordinates, bond lengths, bond angles, and torsional angles, respectively.
The MM3 molecular mechanics program calculates a fair representation of vibrational frequencies for molecules. To make this information more useful, a qualitative intensity calculation has been added, as is described herein. Because each bond in the molecule is assigned a dipole moment, and the vibrational amplitudes are known from the frequency calculation, the change in dipole moment corresponding to each normal mode is readily calculated. In some cases a charge flux has to be added empirically for bond stretchings. This relatively simple calculation has been applied to a number of different functional groups, and gives band intensities adequate for dividing the bands into very strong, strong, medium, weak, or very weak (forbidden) categories.
The MM3 molecular mechanics program calculates a fair representation of hydrogen bonding interactions, but to improve the MM3 hydrogen bond potential, a directional term has been added to the hydrogen bonding function. The resulting total function was reoptimized. Comparison of the hydrogen bonding potential functions from ab initio, the original MM3, the current MM3(92) force field and the reoptimized MM3 force field MM3(94) for a variety of C,N,O systems are described.
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 (pi-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 main group II or IVA or lanthanides II) 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 distance become longer and the ligand planes do not stay parallel, but the molecule "bends" so that these planes intersect. The influence of the 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.