The effective Hamiltonian for the Renner-Teller effect

A derivation of the effective vibronic Hamiltonian for a linear triatomic molecule in a Π electronic state within the harmonic approximation is presented. In addition to the well-established vibrational and Renner-Teller coupling terms, there is a small term which has been overlooked before. The form of this term is derived and the parameter involved, g_K, is related to other observable quantities. Several experimental examples are presented which demonstrate that the extra term is needed to reproduce the vibronic levels in Π electronic states, the contribution being of the order of a few cm ^-1.