Spin-Orbit Coupling Changes the Identity of the Hyper-Open-Shell Ground State of Ce⁺, and the Bond Dissociation Energy of CeH⁺Proves to Be Challenging for Theory

Cerium (Ce) plays important roles in catalysis. Its position in the sixth period of the periodic table leads to spin-orbit coupling (SOC) and other open-shell effects that make the quantum mechanical calculation of cerium compounds challenging. In this work, we investigated the low-lying spin states of Ce+ and the bond energy of CeH+, both by multiconfigurational methods, in particular, SA-CASSCF, MC-PDFT, CASPT2, XMS-PDFT, and XMS-CASPT2, and by single-configurational methods, namely, Hartree-Fock theory and unrestricted Kohn-Sham density functional theory with 34 choices of the exchange-correlation functional. We found that only CASPT2, XMS-CASPT2, and SA-CASSCF (among the five multiconfigurational methods) and GAM, HCTH, SOGGA11, and OreLYP (among the 35 single-configuration methods) successfully predict that the SOC-free ground spin state of Ce+ is a doublet state, and CASPT2 and GAM give the most accurate multireference and single-reference calculations, respectively, of the excitation energy of the first SOC-free excited state for Ce+. We calculated that the ground doublet state of Ce+ is an intra-atomic hyper-open-shell state. We calculated the spin-orbit energy (ESO) of Ce+ by the five multiconfigurational methods and found that ESO calculated by CASPT2 is the closest to the experimental value. Taking advantage of the availability of an experimental D0 for CeH+ as a way to provide a unique test of theory, we showed that all the multiconfigurational methods overestimate D0 by at least 246 meV (5.7 kcal/mol), and only three functionals, namely, SOGGA, MN15, and GAM, have an error of D0 that is less than 200 meV (5 kcal/mol).