Force-field Energies and Thermodynamics

Even with the various simplifications one may envision to reduce die number of parameters needed, a vast number remain for which experimental data may be too sparse to permit reliable parameterization (thus, for example, die MMFF94 force held has about 9000 defined parameters). How does one find the best parameter values There are three typical responses to this problem. 

The most common response nowadays is to supplement the experimental data with the highest quality ab initio data that can be had (either from molecular orbital or density functional calculations). A pleasant feature of using theoretical data is that one can compare regions on a PES that are far from equilibrium structures by direct computation rather than by trying to interpret vibrational spectra. Furthermore, one can attempt to make force-field energy derivatives correspond to those computed ab initio. The only limitation to this approach is the computational resources that are required to ensure that the ab initio data are sufficiently accurate. 

We have alluded above that one measure of the accuracy of a force field can be its ability to predict heats of formation. A careful inspection of all of the formulas presented thus far, however, should make it clear that we have not yet established any kind of connection between the force-field energy and any kind of thermodynamic quantity. 

What is necessary to compute a heat of formation, then, is to define the heat of formation of each hypothetical, unstrained atom type. The molecular heat of formation can then be computed as the sum of the heats of formation of all of the atom types plus the strain energy. Assigning atom-type heats of formation can be accomplished using additivity methods originally developed for organic functional groups (Cohen and Benson 1993). The process is typically iterative in conjunction with parameter determination. 

Eor some atom types, thermodynamic data may be lacking to assign a reference heat of formation. When a molecule contains one or more of these atom types, the force field cannot compute a molecular heat of formation, and energetic comparisons are necessarily limited to conformers, or other isomers that can be formed without any change in atom types. 

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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. 

Another important property of thiepine is the equilibrium between thiepine (1) and its valence isomer, benzene episulflde (9). Benzene episuliides are found to be so unstable that they can not be detected hence theoretical treatment should provide helpful information. MNDO molecule force field calculations of the zero point energy, potential energy, and thermodynamic parameters for the valence tautomerization of benzene episulflde (9) and thiepine (1) show that (9) is more stable than (1) both in the gas phase and in polar media (Equation (1)). The equilibrium is shifted towards (1) in polar media. The vapor phase inversion barrier for (1) is 3-5 kJ mol , and is reduced to zero by polar solvents <83MI 903-01 >. 

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