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Fully relativistic, four-component, density functional theory calculations (4c-DFT) were performed for [MO 4 (OH) 2 ] 2-  and Na 2 [MO 4 (OH) 2 ], where M=Ru, Os, and Hs. The electronic structure of the Hs complex ion was shown to be similar to that of the Os complex ion, though [HsO 4 (OH) 2 ] 2-  should be more covalent than the lighter congeners in group 8, by analogy with MO 4 . The calculations of the free energy change, Δ  G  r , of the [MO 4 (OH) 2 ] 2-  and Na 2 [MO 4 (OH) 2 ] formation reactions from the volatile tetroxides and NaOH have shown that HsO 4  should be slightly less reactive than OsO 4 , with the difference in Δ G  r  being less than 52 kJ/mol. In the experimental study of the deposition of OsO 4  and HsO 4  on the surface of NaOH in the presence of water, such a difference in reactivity has not yet been clearly revealed. The anionic complex of Ru(VIII) was found to be much less stable than those of Os and Hs. Also, Delta; G  r  for the formation of [RuO 4 (OH) 2 ] 2-  from RuO 4  was found to be ∼300 kJ/mol more positive than Δ G  r  for analogous reactions of Os and Hs, which explains why the Ru(VIII) complex is not known. The ionic radii, IR(Hs 8+ )=0.454 Å for CN=4, IR(Os 8+ ) = 0.49 Å and IR(Hs 8+ ) = 0.54 Å for CN=6, have been obtained on the basis of the calculations of bond lengths in MO 4 , as well as  via  a correlation between  R  max  of the outer  np  obitals and IR of the 5 d  and 6 d  elements, respectively.

Theoretical investigations of the reactivity of MO 4 and the electronic structure of Na 2 [MO 4 (OH) 2 ], where M=Ru, Os, and Hs (element 108)