Relativistic Effects in Ligand Field Theory (II): Optical and Magnetic Properties of d1 Atoms in Cubic and Tetragonal Symmetries.

The relativistic motion of an electron in the nd atomic subshell subjected to an electrostatic ligand field and a magnetic field is studied. The ligand and magnetic fields are treated as perturbations on equal footing, employing the atomic Dirac spinors nd3/2 and nd5/2 as basic vectors according to relativistic ligand field theory. The parametrized ligand field allows for the description of C4v', D4h', Oh', and Td' symmetries as particular cases. The wave functions of the ground state manifold Γi(2D3/2) are employed to calculate the Zeeman coefficients and consequently the Curie constant according to Van Vleck's theory of paramagnetism. The theoretical framework is illustrated in Rb2TaCl6, ReF6, Ba2NaOsO6, VO(R-acac)2, and Cs[MoOCl4] d1-systems. It is indicated how correlating the optical transition energies with the magnetic susceptibility enables experimental determination of the theory's parameters: the relativistic ratio p/q, the spin-orbit coupling constant ξnd, and the ligand field strengths Dq, Ds, and Dt. Then, from the deduced parameters, the X-band signals of the electron paramagnetic resonance spectrum are predicted. A strong dependency of the magnetic properties upon the relativistic ratio p/q is observed. Energies of the well-separated (ca. 330 cm-1) optical transitions Γ6(2D3/2) ← Γ7(2D3/2) and Γ7(2D5/2) ← Γ7(2D3/2) for Cs[MoOCl4] are predicted. Our results suggest that the reported spin-orbit coupling constant ξ5d for ReF6 might have been overestimated by more than 1000 cm-1, offering valuable insights into the accuracy of previous experimental and theoretical studies.