MX 6 -type complexes, where M is a central metal element and X is a ligand, serve as excellent models for introducing ligand field splitting -an essential factor in predicting the electronic and spin states of transition metal complexes. This subject is frequently discussed in inorganic chemistry books . While some MX 6 complexes exhibit the expected O h symmetry based on their molecular formula, the Jahn-Teller (JT) effect can induce distortions that lead to another molecular structure such as D 4h symmetry. The smallest and most extensively reported MX 6 complexes would be MF 6 . This complex garners attention not only in introductory chemistry texts but also due to its environmental impact of SF 6 , notable oxidation properties when M is a third-row transition metal ) and UF 6 in nuclear fuel reprocessing . A comprehensive overview of the history and physical and chemical properties of MF 6 is provided in ref Traditional ligand field theory, developed for light elements, does not adequately capture the intricate electronic behaviors exhibited by heavy transition metals. The relativistic effect is significant when describing the chemistry of heavy elements . The relativistic effect can be classified into the following two effects: i) scalar relativistic effect, where the s and p orbitals are contracted while the d and f orbitals are expanded, and ii) spin-orbit coupling (SOC), which is the interaction of the electron spin and the magnetic field induced by a charge in relative motion, leading to the splitting of the degenerate orbitals with l ≥ 1, where l is the quantum number of the electronic angular momentum. The former effect can be sufficiently taken into account by introducing a pseudo-potential , where core electrons are replaced with a fitted potential for valence molecular properties. The latter effect can become small in molecules with low symmetry even if heavy elements are included because of the orbital angular momentum quenching , and thus this effect can often be ignored. However, the SOC can become significant and has to be carefully considered in complexes with high symmetry, which is the target of our study.