The relativistic Renner-Teller effect revisited

The Renner-Teller vibronic-coupling problem of a (2)Pi 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. (C) 2004 Elsevier B.V. All rights reserved.