Parameterization of a force field

Understanding how the force field was originally parameterized will aid in knowing how to create new parameters consistent with that force field. The original parameterization of a force field is, in essence, a massive curve fit of many parameters from different compounds in order to obtain the lowest standard deviation between computed and experimental results for the entire set of molecules. In some simple cases, this is done by using the average of the values from the experimental results. More often, this is a very complex iterative process. 

The parameterization of a force field can be based on any type of experimental data that is directly related to the results available from molecular mechanics calculations, i. e., structures, nuclear vibrations or strain energies. Most of the force fields available, and this certainly is true for force fields used in coordination chemistry, are, at least partially, based on structural data. The Consistent Force Field (CFF)197,106,1071 is an example of a parameterization scheme where experimentally derived thermodynamic data (e. g., heats of formation) have been used to tune the force field. Such data is not readily available for large organic compounds or for coordination complexes. Also, spectroscopic data have only rarely been used for tuning of inorganic force field parameters113,74,1081. 

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 development of such a specific force field is a tedious task, and thousands of individual computations in conformer search procedures must be performed, as has been the case in the above-mentioned study. To date, the strategy of using quantum chemical data for the parameterization of a force field is the most feasible route. Previously, such an investigation, without the use of a specialized force field, would have been impossible due to the excessive amount of time needed for the large number of quantum-chemical calculations. 

To reliably describe PT reactions in the gas and condensed phases, the usual parameterization of a force field in terms of harmonic bonded interactions is not sufficient. H-bonded systems are quite anharmonic around the bottom of the well for bond-stretching motions, and angular bending vibrations are equally affected. Furthermore, the hydrogen motion between the donor and acceptor atoms is strongly coupled to the donor-acceptor motion. These aspects need to be taken into account for a reliable model of hydrogen or proton motion between a donor-acceptor pair. 

Validation of a force field is typically done by showing how accurately it reproduces reference data, which may or may not have been used in the actual parameterization. Since different force fields employ different sets of reference data, it is difficult to compare their accuracy directly. Indeed there is no single best force field, each has its advantages and disadvantages. They perform best for the type of compounds used in the parameterization, but may give questionable results for other systems. Table 2.6 gives some typical accuracies for AH( that can be obtained with the MM2 force field. 

The vast majority of potential users of molecular mechanics have two primary, related questions How do I pick the best force field for my problem and, How will I know whether I can trust the results The process of testing the utility of a force field for molecules other than those over which it was parameterized is known as validation . 

A significant issue widi modem force fields is that it can be difficult to simultaneously address both generality and suitability for use in condensed-phase simulations. For example, the MMFF94 force field is reasonably robust for gas-phase conformational analysis over a broad range of chemical functional groups, but erroneously fails to predict a periodic box of n-butane to be a liquid at —0.5 °C (Kaminski and Jorgensen 1996). The OPLS force field, on the other hand, is very accurate for condensed-phase simulations of molecules over which it is defined, but it is an example of a force field whose parameterization is limited primarily to functionality of particular relevance to biomolecules, so it is not obvious how to include arbitrary solutes in the modeling endeavor. 

If molecular mechanics is to be a valid modeling tool for the design of new compound and the interpretation of experimental results, the compounds under consideration must belong to a class for which the molecular mechanics model is well defined. In other words, the accuracy of the results obtained depends critically on the parameterization of the force field and how this has been obtained (Fig. 5.1). 

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. 

Jorgensen has parameterized by fitting properties of bulk liquids to Monte Carlo simulations to give the AMBER/OPLS force field (26,157, 158). Conceptually, one is attracted ly the use of liquids and their observable properties as constraints during the derivation of a force field that is destined to study the properties of solvated molecules. 

Many systems of interest are too large to be tackled using ab initio methods and here force field methods can be useful. Force field methods do not explicitly include the electrons, rather the energy of a system is a function only of the nuclear coordinates. The main application of molecular mechanics modelling is in the area of big systems (thousands of atoms are not uncommon). The calculations can be performed in a fraction of the computer time that would be required for an ab initio calculation. Their accuracy is determined by the quality of the parameterization of the force field. 

Typically, force field parameters are determined by fitting calculated results to experimental data. This may sound straightforward, but there are many problems involved in parameter development, especially with respect to conformational energies. Ideally, gas phase enthalpy data should be used. Such data are scarce, however, and very often it is necessary to use free energy data in solution for the parameterization (and validation) of a force field. In some cases, moreover, there are large variations in experimental data, and it is not an easy task to select data from which to parameterize the force field. 

Following the introdnction of a directional hydrogen bonding potential function into MM3, the parameterization of the force field for the ammonia dimer was undertaken anew . Three conformers were considered, namely 28, 29 and a bifurcated structure 31, and were calcnlated ab initio at the 6-31G level. The results (after corrections for Basis Set Superimposition Error BSSE) favor the linear dimer over the cyclic one by 0.4 kcalmol and yield dimerization energies of —2.49, —2.09 and —0.62 kcalmol for 28, 29 and 31, respectively. A comparison of force field (original MM3 and MM3 with the directional hydrogen bonding function) and ab initio resnlts for the three ammonia... 

---