Steric Strain and Molecular Mechanics

A system of analyzing the energy differences among molecules and among various geometries of a particular molecule has been developed, based on some fundamental concepts formalized by Westheimer. The method is now known by the term molecular mechanics, although the expressions empirical force field calculations or the Westheimer method are sometimes applied 

The mathematical expressions for the force fields are derived from classical mechanical potential energy functions. The energy required to stretch bonds or to bend bond angles increases as the square of the distortion. 

Westheimer, in Steric Effects in Organic Chemistry, M. S. Newman (ed.), Wiley, New York, 1956, Chap. 12. 

The torsional strain is a sinusoidal function of the torsion angle, (In the context of its use in structural organic chemistry, torsion angle is synonymous with the more familiar, but less precise, dihedral angle ) For molecules with a threefold barrier such as ethane, the form of the torsional barrier is 

For applications of the concept of torsion angle to conformational descriptions, see R. Bucourt, Top. Stereochem. 8, 159 (1974). 

Nonbonded interaction energies are the most difficult contributions to evaluate and may be attractive or repulsive. When two uncharged atoms approach each other. 

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There has been a decisive evolution in the treatment of steric effects in heteroaromatic chemistry. The quantitative estimation of the role of steric strain in reactivity was first made mostly with the help of linear free energy relationships. This method remains easy and helpful, but the basic observation is that the description of a substituent by only one parameter, whatever its empirical or geometrical origin, will describe the total bulk of the substituent and not its conformationally dependent shape. A better knowledge of static and dynamic stereochemistry has helped greatly in understanding not only intramolecular but also intermolecular steric effects associated with rates and equilibria. Quantum and molecular mechanics calculations will certainly be used in the future to a greater extent. 

In molecules with little steric strain but a large number of atoms, attractive steric interactions contribute significantly to the net steric strain and offer an extreme test of whether a molecular mechanics program gives a correct balance of repulsive and attractive van der Waals forces. Molecules which may fall into this class are the medium- to large-ring cycloalkanes. 

An example of the application of molecular mechanics in the investigation of chemical reactions is a study of the correlation between steric strain in a molecule and the ease of rupture of carbon-carbon bonds. For a series of hexasubstituted ethanes, it was found that there is a good correlation between the strain calculated by the molecular mechanics method and the rate of thermolysis. Some of the data are shown in Table 3.3. 

The estimate of relative stabilities via the comparison of total strain energies is in general limited to a series of conformers and isomers (see for instance Chapter 7 and the relevant chapters in Parts I and III). The determination by molecular mechanics calculations of relative stabilities of a series of complexes with metal ions having differing geometric preferences (electronic effects) and preferences in terms of donor atoms is therefore a questionable approach. A comparative study is only useful if the structural preferences of the different metal ions are similar and/or if the electronic effects may be separated from steric effects. 

Molecular mechanics as a minimization of strain energy makes a rigid distinction between steric and electronic effects. Electronic effects are introduced in the form of empirical constants such as characteristic bond lengths and angles, the corresponding force constants, torsional rigidity of even-order bonds, planarity of aromatic systems and the coordination symmetry at transition-metal centres. These constants are accepted, without proof, to summarize the ensual of electronic interactions and used without further optimization. 

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