Electron spin-torsion coupling in open shell molecules displaying a large amplitude torsional motion

Following a recent publication by Coudert et al., Phys. Rev. Lett. 134, 173001 (2025), where the electron spin-torsion coupling was theoretically and experimentally evidenced for the first time, an effective fitting Hamiltonian is retrieved for modeling the high-resolution spectrum of non-rigid 2Σ open-shell molecules displaying internal rotation of a methyl group. A molecular Hamiltonian in which the nuclear and electronic degrees of freedom are treated simultaneously is first derived and includes the mass polarization and translational energy terms. The operator describing the new electron spin-torsion coupling is deduced, and an effective 4-D Hamiltonian allowing us to treat simultaneously the fine interaction and the large-amplitude torsional motion is selected and accounts for the electron spin-rotation, the rotation-torsion, and the electron spin-torsion couplings. The procedure to be used for computing electron spin-rotation-torsion energy levels is presented, and the effects of the electron spin-rotation and spin-torsion couplings are numerically investigated. The unreduced effective 4-D fitting Hamiltonian accounting for distortion effects is built using symmetry considerations.