Chemical Bonding in Isoelectronic NdO₂and SmO₂²⁺

Neodymium dioxide (NdO₂) and samarium dioxide cation (SmO₂²⁺) are isoelectronic molecules. Here we used calculations of the spin-orbit-free wave functions to study and compare their geometries, spin states, and bonding. We used Kohn-Sham density functional theory with the B97-1 exchange-correlation functional to optimize the geometries and found that the two molecules have different ground spin states and structures. NdO₂ favors a linear ONdO triplet structure, and SmO₂²⁺ favors a linear SmOO²⁺ quintet structure. We then used state-averaged complete-active-space self-consistent-field (SA-CASSCF) calculations to investigate the bonding characteristics of NdO₂ and SmO₂²⁺ in various geometries. We found that in NdOO, one electron is transferred from Nd to O, while in SmO₂²⁺, there is no electron transfer between Sm and O. The SA-CASSCF calculation also shows that ONdO has a stronger bonding orbital between a 4f orbital of Nd and a p_z orbital of oxygen atoms. We compared three multireference methods, namely, extended multistate complete active space second-order perturbation theory (XMS-CASPT2), extended multistate pair-density functional theory (XMS-PDFT), and compressed multistate pair-density functional theory (CMS-PDFT), for calculating the spin-orbit-free energies of various isomers of both molecules. We found that although XMS-PDFT and CMS-PDFT are at the same cost level as SA-CASSCF, they give results with the same accuracy as given for the much more demanding XMS-CASPT2 calculation. Between the two multistate PDFT methods, CMS-PDFT is better at giving good degeneracies for states that should be degenerate.