Ab Initio Torsion-Wag Surface for the Ethyl Radical

The torsion-wag potential of the ethyl radical has a 6-fold barrier to internal rotation and the minimum energy path involves deviations of the CH$_{2}$ wag angle of 6 to 11 degrees on either side of planar. Partially optimized 2-dimensional surfaces were calculated at the B3LYP, MP2, and CCSD(T) levels with 6-311++G(d,p) and 6-311++G(3df, 2p) basis sets and they were fit to a function containing a polynomial in the wag angle $\tau $ and trigonometric functions of the torsional angle $\alpha $. Comparison is made with the corresponding surfaces for CH$_{3}$NH$_{2}$ and CH$_{3}$OH$_{2}^{+}$. Unlike CH$_{3}$CH$_{2}^{\bullet }$, both have a substantial barrier to inversion. The dominant torsion-wag coupling term in all three cases has the form $\tau $cos3$\alpha $.