## Abstract

The Renner-Teller vibronic-coupling problem of a ^{2}Π electronic state of a linear molecule is analyzed with the inclusion of spin-orbit coupling effects. In contrast to previous investigations, the microscopic expression for the spin-orbit coupling operator is employed in the single-electron approximation. It is pointed out that there exists a linear, albeit relativistically small, vibronic-coupling term, which has not been considered so far in Renner-Teller theory. The consequences of the existence of two integrals of motion, the time-reversal operator and the relativistic vibronic angular momentum operator, are worked out. It is shown that the adiabatic electronic wave functions of the relativistic Renner-Teller problem carry a nontrivial topological phase, despite the absence of a conical intersection of the adiabatic potential-energy surfaces. The equation of motion for the nuclear amplitudes is derived in the diabatic as well as in the adiabatic representation. The nonadiabatic coupling effects in the relativistic Renner-Teller problem are analyzed and shown to be considerably more complex than in the nonrelativistic case.

Original language | English |
---|---|

Pages (from-to) | 111-127 |

Number of pages | 17 |

Journal | Chemical Physics |

Volume | 301 |

Issue number | 1 |

DOIs | |

State | Published - 31 May 2004 |

## Keywords

- Renner-Teller effect
- Spin-orbit coupling
- Vibronic coupling