Vibronic and Spin-Orbit Couplings of 3Π and 3Σ+ Electronic States in Linear Triatomic Molecules

A two-electron model describing vibronic and spin-orbit couplings of 3Π and 3Σ+ electronic states in linear triatomic molecules is proposed. The analysis is based on the use of an ab initio Breit–Pauli form of the spin-orbit coupling operator. Electronic Hamiltonian symmetry operators are shown to involve both spatial operations (acting on electronic coordinates) and matrix operations (acting on electron spins). In our analysis, we take into account only deformation π-modes, and the resulting 9 × 9 vibronic matrix actually describes the relativistic Renner pseudo-effect (3Π + 3Σ+) × π. The eigenvalues of the vibronic matrix (i.e., potential energy surfaces) have an axial symmetry, however, they cannot be represented by analytical expressions. The calculated vibronic Hamiltonian contains six electrostatic and 16 spin-orbit real parameters.