Quantum dynamics and geometric phase in E⊗e Jahn-Teller systems with general C_nv symmetry

E ⊗ e Jahn-Teller (JT) systems are considered the prototype of symmetry-induced conical intersections and of the corresponding geometric phase effect (GPE). For decades, this has been analyzed for the most common case originating from C_3v symmetry and these results usually were generalized. In the present work, a thorough analysis of the JT effect, vibronic coupling Hamiltonians, GPE, and the effect on spectroscopic properties is carried out for general C_nv symmetric systems (and explicitly for n = 3-8). It turns out that the C_3v case is much less general than often assumed. The GPE due to the vibronic Hamiltonian depends on the leading coupling term of a diabatic representation of the problem, which is a result of the explicit n, α, and β values of a C_nvE_α ⊗ e_β system. Furthermore, the general existence of n/m (m∈N depending on n, α, and β) equivalent minima on the lower adiabatic sheet of the potential energy surface (PES) leads to tunneling multiplets of n/m states (state components). These sets can be understood as local vibrations of the atoms around their equilibrium positions within each of the local PES wells symmetrized over all equivalent wells. The local vibrations can be classified as tangential or radial vibrations, and the quanta in the tangential mode together with the GPE determine the level ordering within each of the vibronic multiplets. Our theoretical predictions derived analytically are tested and supported by numerical model simulations for all possible E_α ⊗ e_β cases for C_nv symmetric systems with n = 3-8. The present interpretation allows for a full understanding of the complex JT spectra of real systems, at least for low excitation energies. This also opens a spectroscopic way to show the existence or absence of GPEs.