J. Phys. Chem. 1995,99, 8058-8065
8058
A Comprehensive Study of Alkane Nonbonded Empirical Force Fields. Suggestions for Improved Parameter Sets Jenii Nagy$ Donald F. Weaver$*$and Vedene H. Smith, Jr.*>+ Departments of Chemistly and Medicine, Queen's University, Kingston K7L 3N6, Ontario, Canada Received: November 16, 1994; In Final Form: February 14, 1995@
A critical examination of 10 existing alkane nonbonded empirical potential functions has been performed by computating various properties in all three phases. The evaluated properties include methane dimer energies, methane and butane second virial coefficients, liquid methane and butane enthalpies of vaporization, liquid densities, liquid methane C-C correlation functions, crystal unit cell parameters, unit cell volumes, and enthalpy of sublimation data. The potential functions have been selected to cover the widest range of potential functions currently available in molecular mechanics force fields. Ten new parameter sets have also been obtained based on various criteria to fit to ab initio and empirical properties. Bartell's modified Urey-Bradley potential and a reparameterized version of Allinger's MM3 function, termed MM3mc, have emerged as the two most reliable potentials. The relationships between properties in different phases have also been explored.
1. Introduction The functional form and parametrization of nonbonded interactions pose a major difficulty in developing reliable empirical force fields. In apolar alkanes, van der Waals interactions dominate the intermolecular energy. The molecular mechanics programs developed over the past decades have employed various functional forms to describe these interactions. These functions may be placed into three general classes. First, the time-honored Lennard-Jones 12-6 function, despite its welldocumented hardness at short distances, is still widely used in Monte Carlo and molecular dynamics simulations owing to its computational Others have softened the repulsive exponent by using the 9-6 form: and recently, a buffered 14-7 potential has also been ~uggested.~ The second major direction in van der Waals function development is the application of the Born-Mayer formula for the repulsive region, combined with a sixth-power dispersion interaction (exp-6). In its most general form, this potential has three parameters.8-10 Although this confers flexibility on the potential, the meanings of the conventional atomic radius and well depth parameters are lost. A member of this family, the Buckingham potential also includes three parameters but retains 6 and r* explicitly.".'2 A modified form of the Buckingham potential is the Hill potential used in Allinger's MM2 and MM3 force fields with different steepness parameter^.'^.'^ The exp-6 potentials exhibit incorrect asymptotic behavior at very short distances. Thus, an alternative functional form has been suggested to alleviate the need for an auxiliary function at short distances.I5 The third type of van der Waals form is the less widely used three-parameter Morse p ~ t e n t i a l . ' ~ .Although '~ it provides a good description of the potential well, its asymptotic behavior is incorrect at both large and small separations.I8 There are a number of other van der Waals functions in the literature, but they have not come into general use due to their more complicated functional f0rms.'~3'~ Therefore, in this work, attention was focused on the first three categories. Parametrization of van der Waals functions is achieved by fitting the parameters to experimental properties, such as crystal
* To whom correspondence should be addressed.
' Department of Chemistry. @
Department of Medicine. Abstract published in Advance ACS Abstracts, April 1, 1995.
cell and heats of sublimation data6,10,12-'4,20-22 liquid heats of vaporization and d e n ~ i t i e s , alkane ~ . ~ free energies of solution in water,5and virial coefficient^.*^-^^ Semiempiricalpotentials, which combine computational observables, such as ab initio hydrogen or methane dimer energies, with empirical data are also frequently used.9~25-28 No purely theoretical method has been performed to date to determine alkane nonbonded interactions. In most cases, however, parametrization procedures are restricted to one phase only for it is assumed that a force field optimized in one phase will be sufficiently accurate to reliably predict properties in the same phase. It is also very difficult to simultaneously parametrize a potential in different phases. Although one cannot expect a force field to give a perfect representation of all phases, a suitable potential should reproduce experimentally and computationally available data in all phases with at least reasonable accuracy. The aim of this paper is threefold. First, by computing a wide range of properties with 10 well-known alkane potential functions, an attempt has been made to compare their performance and to identify strengths and weaknesses. The computed properties include gas-phase methane dimer energies, methane and butane virial coefficients at several temperatures, liquid methane and butane densities and heats of vaporization, liquid methane C-C radial correlation functions, crystal unit cell parameters, unit cell volumes, and heat of sublimation data for seven alkane molecules. Second, within the realm of the exp-6 and Morse potential forms, several attempts have been made in this study to reparametrize them according to various criteria. The obtained results are analyzed and compared to results based on the first 10 potentials. Third, observing the deviations between computed and experimental data in different phases should help further our understanding of van der Waals interactions. General conclusions about different potential forms as well as the role of electrostatic interactions are also discussed.
2. Models and Parametrization Procedures The 10 alkane force fields evaluated in this work are as follows (see Table 1): MM2,I3 MM3,I4 Schleyer's force field (EAS),'* Bartell's MUB-2,9 Boyd's force field,8 and a recent reparametrization of the potential of Weiner et al.' by Sun et aL2 Since the latter force field was derived by the use of AMBER, the parameters in ref 2 will be henceforth referred to
0022-365419512099-8058$09.00/0 0 1995 American Chemical Society
Alkane Nonbonded Empirical Force Fields
TABLE 1: Previously Determined Alkane van der Waals Potentials That Were Studied in This Work force field
Ab potential form 0.915 ~[2.90x lo5exp(-12.5r/r*) 2.25(r*/r)6] 1.112 0.923
