Why is the eclipsed form of dimethylacetylene more stable than its staggered form?

Abstract

In organic molecules that exhibit conformational isomers—namely, a staggered and an eclipsed arrangement, as observed in compounds such as ethane or propane—the staggered conformation generally represents the equilibrium structure. This preference is commonly attributed to steric hindrance, Pauli repulsion or hyperconjugation. Surprisingly, in 2-butyne or dimethylacetylene the eclipsed form is lower in energy, but only by 0.017 kcal mol⁻¹ or 5.98 cm⁻¹. The present study shows that in this case neither ‘Pauli repulsion’ nor ‘hyperconjugation’ plays the decisive role, but the kinetic energy of the electrons. A rigid rotation around the linear C–CC–C axis from the eclipsed equilibrium structure to the staggered one increases the electronic kinetic energy by as much as 0.126 kcal mol⁻¹, while the increase of the total energy is rather small. The rotationally symmetric ring of the π-orbitals around the acetylenic CC bond is modulated at three angles in the eclipsed conformer, but at six angles in the staggered one, and this causes the larger electronic kinetic energy. Of course, an increase of both the total energy and the electronic kinetic energy violates the virial theorem. This is then restored by a small increase of only 0.0008 Å in the C–C bond distances, which leads to an elongation and smoothing of the σ-orbitals at the C–CC–C axis and to a reduction of their kinetic energy. In addition to the explanation, why the energy of the eclipsed form of 2-butyne is lower than that of the staggered form, our calculations confirm the experimental observation that the rotation barrier in 2-butyne is very small, only about 6 cm⁻¹.