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

► The E⊗(b1⊕b2) Jahn-Teller effect in the 2E ground state of the singly-charged cations of ethene and allene is investigated. ► A theoretical model is presented that allows a joint treatment of the Jahn-Teller effect and of the large-amplitude torsional motion. ► The vibronic model is based on the expression of the potential energy surfaces using Fourier series instead of Taylor series.