Barrier to Internal Rotation in Ethane Using the Hellman—Feynman Theorem

The Hellman—Feynman theorem permits the calculation of the barrier to internal rotation in ethane and related molecules from the electron density corresponding to a single rotational configuration. Previous results, using an extended Hückel calculation and a modification of the Pitzer—Lipscomb wavefunction to approximate the electron density, gave too low a barrier. It appears from the present work that this is characteristic of the method. We have used a MO LCAO function containing a single parameter α which may be fixed in several different ways unrelated to the barrier calculation. We also consider the effect of variation of the exponential parameter ζH for 1s orbitals centered on the protons. The result is that all calculations (corresponding to different choices of α and ζH) give a barrier of the proper sign, but much lower than the experimental value. Not considered in the preceding work was the effect of polarization of the charge density. Part of this effect is estimated here, but seems to lower the barrier further. It appears that the present method is not capable of giving good results unless the polarization and other corrections are considered carefully. Comparisons are made with the Integral Hellman—Feynman theorem.