Internal rotation in Jahn–Teller coupled systems: The ethene and allene cations

Abstract The electronic ground state of singly-charged cations of the cumulene family (H 2 CC n CH 2 , n  = 0, 1, …) is doubly degenerate at the D 2d geometry and is subject to an E ⊗ b or E ⊗ (b 1  ⊕ b 2 ) Jahn–Teller effect. One of the Jahn–Teller active modes is the torsion, i.e., the disrotatory motion of the two terminal CH 2 entities. The 2 π periodicity of the torsional motion and the presence of maxima in the potential energy path along the torsional coordinate at planar geometries poses problems in the usual treatment of the Jahn–Teller effect of these cations, which relies on a Taylor expansion of the potential energy surfaces at the point of electronic degeneracy ( D 2d ). A vibronic Hamiltonian has been derived to treat the E ⊗ b and E ⊗ (b 1  ⊕ b 2 ) Jahn–Teller effects in molecules in which one of the Jahn–Teller active modes is the torsion or an internal rotation. The potential energy surfaces are expressed using Fourier series instead of Taylor series which enables a joint treatment of the Jahn–Teller effect and of hindered internal rotations. The resulting Hamiltonian has been used to predict the vibronic energy level structure of C 2 H 4 + and C 3 H 4 + and intensity distributions in the photoelectron spectra of C 2 H 4 and C 3 H 4 . In particular, splittings arise from tunneling through the potential energy barrier at the D 2h geometry. The predictions are compared with available spectroscopic data.