The A 2g and B 2g states in D 4h symmetry can be distinguished based on the occupation number of the spinor, as shown in eq 9. For IrF 6 , a Fermionic system (odd number of electrons) in O h symmetry, the quadruply degenerate states are always in U 3/2 symmetry. The doubly degenerate states (E 1/2 and E 5/2 ) can be distinguished from a doublet-like electronic configuration (one open-shell orbital, the others are closed-shell) in the CI wavefunction. The electronic configuration [u 3/2 (4), e 1/2,6s (1)] contributes to the E 1/2 state, where Ir's 6s orbital contributes to e 1/2,6s . In the E 5/2 state, a Kramers pair (two spinors) of four spinors in u 3/2 are occupied, and another electron occupies the e 5/2 spinor. The assignment at the SF level, which has been extensively investigated and thus will not be described here, was carried out based on the orbital occupation number under the C 2v symmetry using Bethe's method and the phase of the Slater determinants of the CI wavefunctions. Although the experimental UV/vis spectra were reported , vibrational calculations using more sophisticated electronic structure theory would be essential to compare with the experimental spectra. Further efforts are also needed to assign the experimental spectra. They are beyond the scope of the present study and will be pursued in future studies. Finally, the SO effect of the MF 6 is analyzed from the viewpoint of the atomic SO splitting. Figure shows a schematic diagram of the ligand field splitting of the atomic d orbitals at the SF and SO levels as well as the gross population of the PtF 6 . This figure is similar to Figures 19.4 and 19.5 of ref 58, but we added the gross population of PtF 6 obtained by the projection analysis at the X2C/HF/dyall.v3z level of theory in this study. The projection analysis is a method to obtain the contribution from the atomic orbital to the molecular orbital (MO) based on the two-or four-component Hamiltonian that can work with the one-component basis sets, as demonstrated in refs. .