OPLS parameter set

The quality of a force field can be established only through extensive test simulations. A large number of force fields that are widely used for biomolecu-lar simulations are available in the literature. These have been used to simulate a variety of systems. For example, the OPLS parameter set developed by Jorgensen et al. ° has been shown to be satisfactory for the simulation of a large number of neat liquid hydrocarbons and polar molecules. Similarly, the AMBER force field nd the CHARMM force field have been used for a variety of protein and nucleic acid simulations. 

The OPLS parameters (charges and Lennard-Jones terms) were obtained primarily via Monte Carlo simulations with particular emphasis on reproducing the experimental densities and heats of vaporization of liquids. Those simulations were performed iteratively as part of the parametrization, so better agreement with experiment is obtained than in previous studies where the simulations were usually carried out after the parametrization. Once the OPLS parametrization was completed, further simulations were also performed in order to test the new set of parameters in the calculation of other thermodynamic and structural properties of the system, besides its density and its heat of vaporization. Parameters have now been generated, among others, for water, alkanes, alkenes, alcohols, amides, alkyl chlorides, amines, carboxylic esters and acids, various sulfur and nitrogen compounds, and nitriles. A protein force field has been established as well. 

The derivatives of these energies with respect to the coordinates of the QM and MM atoms are easily formulated. The remaining term Emm in Eq. (17-18) is composed from two-body electrostatic and LJ interactions and can be computed by utilizing the parameter set of potential field such as Amber, Charmm, or OPLS. 

Examples are the Tripos force field (22), the COSMIC force field (23), and that of White and Bovill (24), which uses only two atom types, those at the end of the bond to parameterize the torsional potential rather than the four types of the atoms used to define the torsional angle. One has only to consider the number of combinations of 20 atom subtypes taken four at time (160,000) versus two at a time (400) to understand the explosion of parameters that occurs with increased atom sub-types. The simplifying assumption in parameterization of the torsional potential reduces to some extent the quality of the results (25), but allows the use of the simplified force fields (22) in many situations where other force fields would lack appropriate parameters. The situation can become complicated, however. For example, the amide bond is normally represented by one set of parameters, whether the configuration is cis or trans. Experiments data are quite compelling that the electronic state is different between the two configurations, and different parameter sets should be used for accurate results (Fig. 3.1). Only AM-BER/OPLS currently distinguishes between these two conformational states (26). Certainly, the limited parameterization of simplified force fields would not allow accurate prediction of spectra that is more reflective of the dynamic behavior of the molecule. 

The third force field parameter set developed within the spirit of the OPLS-AA model and thus oriented toward the calculation of equilibrium thermodynamic and structural properties was presented [73], The parameter sets concerned the cations alkylimidazolium, tetraalkylphosphonium, and /V-alkylpyridinium, and the anions [Cl]-, [Br], and the [DCA] . Validation of the force field consisted of comparison with experimental crystal structure and liquid density data [73], The fourth parameterization of a force field was published only recently. The ions modeled were the 1,2,3-trialkylimidazolium and alkoxycarbonyl imidazolium cations and alkylsul-fate and alkylsulfonate anions [74],... 

The OPLS 2005 force field describes this torsion using a wildcard, denoted by XX . CA is an atom type for an SP2 aromatic carbon atom, originally described by Jorgensen and Severance [54]. S is for the sulfur. OPLSj denotes the OPLS 2005 parameter set containing the new torsion type. 

The intramolecular parameters kf,ro, kg, and 0q from the AMBER force field [21, 22] were used. The oxygen atoms of alcohols and ethers were described by the OPLS parameters [17,18]. The Lennard-Jones parameters for halogens and the atoms of the aliphatic groups were optimized to reproduce the experimentally measured solubilities of methane and its halogenated derivatives in water and hexane, separately [23]. The resulting parameters do not follow the standard combination rules because we were unable to find a set of parameters consistent with the rules which would yield sufficiently accurate solubilities of the solutes in both phases. A similar difficulty was encountered in other studies of interfacial systems, in which the united atom representation was used to describe nonpolar molecules [24, 25]. 

Our Poisson-Boltzmann calculations are currently carried out with the atomic charges and radii of the PARSE parameter set, developed by Honig et al. or the CHARMM22 parameter set. ° The PARSE parameter set is attractive because when used with a solvation model based on the PB equation, it yields accurate solvation energies for a variety of small molecules. The CHARMM parameter set has the advantage of including parameters for more molecules and is also more easily accessible. Other possible charge/radii sets are from CVFF and OPLS. Use of nonstandard sets also has been reported. 

An extensive reparameterization of the Coulomb and Leonard-Jones terms of the AMBER force field led to the development of the OPLS (see OPLS Force Fields) parameter set. In OPLS the majority of bond, angle, and torsion terms were kept at their standard AMBER values however, the atomic partial charges were empirically determined for small molecules and assumed to be transferable to larger molecules. This treatment of partial charge differs significantly from the approach used in AMBER, in which a unique set of partial charges is derived for each molecule from fitting to the quantum mechanical ESP. 

The input and output information are similar to those for standard molecular simulations. Only microscopic parameters are usually required. A very standard set of parameters such as OPLS is sufficient to perform the computations. In this sense, the theory does not require any kind of adjustable parameters. 

Careful consideration was taken in the parameterization process to insure that the parameters were deemed reasonable for the atom types, using the OPLS-AA force field atom types as a comparison. As one of the goals of this project was to ensure that robustness was achieved in many different calculated properties of the newly developed model, several sets of simulations were also performed to ensure that the parameters could achieve a reasonable agreement with experiment. Some of the properties calculated included the gas phase density, the partial molar volume in aqueous solution, and the bulk solvent structure as well. The calculation of the solubility was discussed in the previous section for the parameterization process and the viewing of these results, the solubility will be reported in log S values, as many of the literature values are reported as log S values, and therefore, the comparison would not lose any sensitivity due to rounding error from the log value. 

Ionic liquids share parts of their molecular architectures with molecules that had been parameterized by existing force-field frameworks (AMBER, OPLS, CHARMM, etc.) for example imidazolium rings are present in hystidine, an amino acid. However ionic liquids have one essential difference they are composed of ions, and although they may be built by the same functional groups, the distributions of electrostatic charge will be specific. In order to represent correctly the structure and interactions of these new compounds, the sets of parameters that determine charge distributions and conformations (at the least) had to be developed for this class of substances. 

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