Molecular Mechanics . The MM 3 Force Field for Hydrocarbons . 2 . Vibrational Frequencies and Thermodynamics *

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-I, of which the largest errors occur in the CC-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 AS* 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 AG* are 2.46 and 1.02 kcal/mol, for seven examples. Force fields can be constructed to reproduce different kinds of data. The MM2 force field was specifically constructed to fit structures and energies of organic molecules.’-3 A few other properties were also fit, but we frankly omitted fitting vibrational spectroscopic data, because we could not see how to fit those data, and fit the other above-mentioned data at the same time, with the same parameter set. Various other force fields have been constructed along similar lines in some cases, and to fit other data, such as spectroscopic data, as Such force fields have fit more things, but they have fit less well to structures and energies4 With the experience now available in the design and construction of force fields, it is possible to fit both structures and energies better, overall, than was done with MM2. The previous paperS described the development of MM3, which does exactly that. This paper will be concerned with the fitting of some of the other kinds of data which went into the development of MM3, namely, vibrational spectra and other properties that depend on the vibrational levels (entropies, thermodynamic functions). The following paper will describe the results obtained with crystallographic data. All of this work was carried out at the same time and employs the same force field and parameter set. As discussed long ago,6 if one can correctly calculate the unit cell constants and heat of sublimation of a crystal, one has an indication that the van der Waals’ properties of the molecules are, on the whole, reasonable. Because there are many more variables in the van der Waals’ parameters than there are cell constants, good fits to crystal data are required if one is to have a good van der Waals’ parameter set, but such data alone do not guarantee that the van *Abstracted mainly from the Ph.D. dissertation submitted by J.-H. Lii to the University of Georgia, 1987. der Waals’ parameter set is, in fact, accurate. Besides the structural, energy, and crystal data mentioned above, we also wanted to fit vibrational spectroscopic data insofar as possible. Vibrational spectra have been studied in great detail ( I ) The MM2 force field for hydrocarbons was first described in ref 2. Extensions to functionalized molecules and other sorts of special problems have been described in subsequent papers, which are summarized in ref 3. The original version of the program (MM2(77)) is available from the Quantum Chemistry Program Exchange, University of Indiana, Bloomington, IN 47405, Program 395. The latest version of the MM2 program, which is referred to as MM2(87), is available to academic users from the Quantum Chemistry Program Exchange, and to commercial users from Molecular Design Limited, 2132 Farallon Dr., San Leandro, CA 94577. The MM3 program is still under development, but it is intended to make it available shortly from Technical Utilization Corp., Inc., 235 Glen Village Ct, Powell, OH 43065, and from MDL. (2) Allinger, N. L. J . Am. Chem. SOC. 1977, 99, 8127. (3) Burkert, U.; Allinger, N. L. Molecular Mechanics; American Chemical Society: Washington, D.C., 1982. (4) (a) Engler, E. M.; Andose, J. D.; Schleyer, P. v. R. J . Am. Chem. SOC. 1973, 95, 8005. (b) Altona, C. L.; Faber, D. H. Top. Curr. Chem. 1974, 45, I . (c) Dunitz, J . D.; Burgi, H. B. MTP International Reviews of Science, Series Two: Chemical Crystallography; Robertson, J. M. R., Ed.; Butterworths: London, 1975; p 81. (d) Allinger, N. L. Adu. Phys. Org. Chem. 1976, 13, 1 , (e ) Ermer, 0. Struct. Bonding (Berlin) 1976, 27, 161. (f) Bartell, L. S. J . Am. Chem. SOC. 1977,99, 3279. (8 ) Niketic, S. R.; Rasmussen, K. The Consistent Force Field; Springer Verlag: Berlin, 1977. (h) Warshel, A. In Modern Theoretical Chemistry; Segal, G. , Ed.; Plenum: New York, 1978; Vol 7, p 133. (i) White, D. N. J . In Molecular Structure by Diffraction Methods; The Chemical Society: London, 1978; Vol. 6, p 38. fJ) Osawa, E.; Musso, H. Top. Stereochem. 1982, 13, 117. (5) Allinger, N. L.; Lii, J.-H.; Yuh, Y. H. J . Am. Chem. SOC., preceding paper in this issue. (6) Allinger, N. L.; Miller, M. A.; Van-Catledge, F. A.; Hirsch, J. A. J . Am. Chem. SOC. 1967, 89, 4345. 0002-7863/89/15l1-8566$01.50/0