Internal Rotation in Ethane and Substituted Analogs

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

Rotation about C-C single bonds has been a topic of interest in chemistry since the 1870s [1]. It has been found that the rotation is often hindered by torsional forces arising from interactions among the substituents on the carbon atoms. The potential energy of interaction for the torsional motion of ethane , or substituted ethanes such as , can be approximated by a potential energy of the form

[more]

,

,

where is the reduced moment of inertia of the two counterrotating methyl groups. This can be put into a standard form of Mathieu's equation,

,

with the substitutions ( to ), . The physically significant solutions are two families of Mathieu functions. One class is periodic in and transforms according to the representation of the symmetry group ; the other is periodic in and belongs to the doubly degenerate species. If not for tunneling, each energy level would be three-fold degenerate. In reality, a small splitting is observed, which increases with increasing torsional quantum number . The and levels are colored blue and red, respectively. As decreases, the number of discrete levels decreases, as the higher levels are absorbed into the continuum. The actual results using Mathieu functions are quite complicated and the results have been distilled into approximate formulas for the energy levels.

[less]

Contributed by: S. M. Blinder (May 2018)
Open content licensed under CC BY-NC-SA


Snapshots


Details

References

[1] R. M. Pitzer, "The Barrier to Internal Rotation in Ethane," Accounts of Chemical Research, 16(6), 1983 pp. 207–210. doi:10.1021/ar00090a004.

[2] L. C. Krisher, "Inversion and Internal Rotation," in Encyclopedia of Physics (R. G. Lerner and G. L. Trigg, eds.), 2nd ed., New York: Wiley-VCH, 1991 pp. 557–558.



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send