Empirical force field calculations

In spite of its limitations, molecular mechanics (MM) is a technique that is widely used for the computation of molecular structures and relative stabilities. The advantage of MM over quantum mechanical methods is mainly based on the computational simplicity of empirical force field calculations, leading to a comparatively small computational effort for MM calculations. Therefore, even large... 

Altona, C., and Faber, D. H. Empirical Force Field Calculations. A Tool in Structural Organic Chemistry. 45, 1-38 (1974). 

Hydrogen bonding is included in empirical force field calculations in two ways. In the MM series (27). bond dipoles are placed at the centers of the bonds and the Jeans equation is used ... 

Some of the potential energy functions used to calculate the total strain energy of a molecule are similar to the functions used in the analysis of vibrational spectra. Because the parameters used to derive the strain energies from these functions are fitted quantities, which are based on experimental data (for example X-ray structures), molecular mechanics may be referred to as empirical force field calculations (more often the simplification force field calculations is used). The quality of such calculations is strongly dependent on the reliability of potential energy functions and the corresponding parameters (the force field). Thus, the selection of experimental data to fit the force field is one of the most important steps in a molecular mechanics study. An empirical force field calculation is in essence a method where the structure and the strain energy of an unknown molecule are interpolated from a series of similar molecules with known structures and properties. 

It is important to realize that for any arrangement of more than two atoms the strain energy minimized structure does not have ideal (zero strain) distances and angles. This is demonstrated in the case of ethane (Fig. 2.2), where, due to the repulsion of the protons, the experimentally determined C-C distance in ethane of 1.532 A, which is well reproduced by empirical force field calculations, is slightly longer than the ideal C-C separation of 1.523 A used in the MM2 force field1. Further examples are presented in Table 2.1. With increasing substitution of the carbon atoms the C-C separation increases up to 1.611 A in tris(t-butyl)methane. 

The quantitative prediction of the stereochemistry of a chemical reaction by strain energies requires knowledge of the reaction mechanism, i.e., the selective intermediates and/or transition states involved, and an accurate force field for the transient species. As discussed above, these are two demanding problems and so far there are no reports of studies in this area that have used molecular mechanics for quantitative predictions at the same level of accuracy as for conformational analyses. The application of empirical force field calculations to the design of asymmetric transformations clearly is a worthy task, and some examples of studies in this area have been discussed above. On the basis of two examples we will now discuss some general aspects highlighting the limitations of the qualitative considerations emerging horn molecular mechanics calculations for the interpretation and support of assumed reaction pathways. 

We turn to empirical force field calculations in order to choose between these two mechanisms. 44 Such calculations indicate that the two-ring flip mechanism is the lowest-energy pathway, and yield a barrier of 20 kcal/mol for the two-ring flip of 7. 44> The experimental free energy of activation for stereoisomerization derived from the temperature-dependent 1H-nmr spectrum, is AG 67 21.9 kcal/mol 43, in excellent agreement with the calculated value. This high barrier admits of the possibility that 7 is separable into its optical antipodes at moderately low temperatures. 

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