Relativistic Jahn–Teller Effect ²T_g × e_g in Octahedral Molecules with a Heavy Central Atom

Abstract

This analysis is based on taking into account the spin–orbit interaction in the form of the Breit–Pauli operator in the electron Hamiltonian of the molecule. As the latter, we consider the Hamiltonian of the octahedral molecule $\tilde {Y}~{{X}_{6}}$ with an odd number of electrons and a heavy central atom $\tilde {Y}$ in the orbital ²D state with one outer electron and six X-ligand atoms forming a closed electron shell. The key element of the analysis is the construction of symmetrized combinations of products of e_g modes and Pauli matrices, followed by the expansion of the electron Hamiltonian in a Taylor series in terms of the mentioned symmetrized combinations. In this case, the contributions of the main, first, and second orders in terms of powers according to the e_g mode of normal vibrations are taken into account. A 6 × 6 vibronic matrix dependent on two e_g modes is calculated in the diabatic electron basis constructed from the products of the components of the orbital D states and electronic spin functions. The vibronic matrix includes four electrostatic parameters and four parameters of spin–orbit origin. The eigenvalues of the vibronic matrix (i.e., potential energy surface) are invariant under the operations of the molecular symmetry group $O_{h}^{'}.$