Perturbative Handling of the Renner–Teller Effect and Spin–Orbit Coupling in Π Electronic States of Triatomic and Tetra-atomic Molecules

Abstract

Second-order perturbative formulae for handling the Renner–Teller effect combined with the spin–orbit coupling in Π electronic states of triatomic and symmetric (ABBA-type) tetra-atomic molecules with linear equilibrium geometry are derived. Two schemes for partition of the model Hamiltonian are employed: In the first the spin–orbit coupling term is treated as a perturbation, in the second it is included in the zeroth-order Hamiltonian. It is demonstrated that both approaches lead to the same results when the spin–orbit coupling constant is small compared to the bending frequency, but much larger than the splitting of potential surfaces upon bending. The perturbative formulae derived for tetra-atomic molecules are used to compute the spectrum of the X2Πu state of the acetylene ion, employing the parameters obtained in ab initio calculations. The results are compared with those generated in corresponding variational computations.