Luther E. Erickson and Kevin F. Morris describe an experimental and computational student project that determines the energy difference, DE, between the minima in the potential energy profile for internal rotation in substituted ethanes by measuring molecular properties that are conformation dependent (J. Chem. Educ. 1998, 75, 900). They follow the traditional procedure (often called the rotational isomeric state (RIS) approximation), which consists of interpreting the observations in terms of an equilibrium mixture of the most stable rotamers, as a substitute for either a classical continuum average over all torsional angles or a quantum mechanical average involving the various torsional eigenfunctions. We feel that the benefit of such an effort would be greatly enhanced if students were also encouraged to appreciate the approximations involved and the conditions under which they can be acceptable.

It has long been known that there is little difference between the dipole moments calculated for 1,2-dichloroethane (perhaps the most studied ethane derivative from the point of view of conformation and internal rotation) for room temperature, using the RIS method and the continuum average approach (1). However, in other cases, large errors can be introduced using the RIS approximation (2, and references therein). In particular, large differences can be found between theoretical DE values for a pair of stable rotamers and the corresponding values (actually DG°) obtained using the RIS method (calculated from an effective equilibrium constant K defined in terms of the fractional populations of the rotamers: K = f_j / f_i).

Two basic sources of difference have been identified and fully characterized in ref 2. One depends on the temperature and on the shape of the potential curve, and especially on the values and relative positions of the maxima in the energy profile E(font face="Symbol"q). The other varies with the way the conformation-dependent property changes with the torsion angle q. For example, this usually varies with cos q for dipole moments of CH₂X-CH₂X or CHX₂-CHX₂ molecules, but with cos²q for vicinal HH coupling constants. As expected, for low temperatures and deep potential troughs the differences are small. However, for realistic energy barriers and profiles, the differences can be as large as ± 40% even at room temperature, in some cases with opposite signs obtained for cos q and cos²q-dependent properties. This is probably the reason why a big difference is found for the DE value for 1,2-dibromoethane in the paper by Erickson and Morris, depending on whether the property used is the dipole moment or the vicinal HH coupling constants.

Literature Cited

1. Mark, J. E.; Sutton, C. J. Am. Chem. Soc. 1972, 94,, 1083.
2. Gil, V. M. S.; Varandas, A. J. C.; Murrell, J. N. Can. J. Chem. 1983, 61, 163.