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

✍ Scribed by Miljenko Perić; Sigrid D. Peyerimhoff

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 160 KB
• Volume: 212
• Category: Article
• ISSN: 0022-2852
• DOI: 10.1006/jmsp.2002.8533

✦ Synopsis

Second-order perturbative formulae for handling the Renner-Teller effect combined with the spin-orbit coupling in 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 X 2 u state of the acetylene ion, employing the parameters obtained in ab initio calculations. The results are compared with those generated in corresponding variational computations.