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).
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We thank Zoltan Varga and Chen Zhou for help with the calculations and useful discussions. This work was supported in part by the Air Force Office of Scientific Research by grant FA9550-16-1–0134.
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