The electronic structure of the low-dimensional 4d 5 oxides Sr 2 RhO 4 and Ca 3 CoRhO 6 is herein investigated by embedded-cluster quantum chemistry calculations. A negative tetragonal-like t 2g splitting is computed in Sr 2 RhO 4 and a negative trigonal-like splitting is predicted for Ca 3 CoRhO 6 , in spite of having positive tetragonal distortions in the former material and cubic oxygen octahedra in the latter. Our findings bring to the foreground the role of longerrange crystalline anisotropy in generating noncubic potentials that compete with local distortions of the ligand cage, an issue not addressed in standard textbooks on crystal-field theory. We also show that sizable t 2g 5 −t 2g 4 e g 1 couplings via spin− orbit interactions produce in Sr 2 RhO 4 ⟨ ⟩ = ⟨∑ · ⟩ l s i i i ground-state expectation values significantly larger than 1, quite similar to theoretical and experimental data for 5d 5 spin−orbit-driven oxides such as Sr 2 IrO 4 . On the other hand, in Ca 3 CoRhO 6 , the ⟨ ⟩ values are lower because of larger t 2g −e g splittings. Future X-ray magnetic circular dichroism experiments on these 4d oxides will constitute a direct test for the ⟨ ⟩ values that we predict here, the importance of many-body t 2g −e g couplings mediated by spin−orbit interactions, and the role of low-symmetry fields associated with the extended surroundings. ■ INTRODUCTIONOne of the most difficult problems in electronic structure theory is the correct description of correlated d and f electrons in solid-state compounds. Although density functional theory (DFT) provides results in reasonably good agreement with the experiment for weakly and moderately correlated electron systems, there are many materials, in particular, d-and felectron oxides, whose electronic structures cannot be properly treated within the canonical DFT framework. Extensions of DFT by dynamical mean-field theory (DMFT) led to DFT +DMFT schemes and allowed one to overcome some of the intrinsic limitations of DFT.1,2 Yet the accuracy and predictive power of the DFT+DMFT calculations is to some extent restricted by the use of parametrizations such as the on-site Coulomb repulsion U. It is therefore desirable to explore complementary techniques, e.g., wave-function-based quantum chemistry methods. While early attempts and the first encouraging results go back as early as the 1970s, with the work of Wachters, Bagus, and others, 3,4 the tremendous progress in computer technology nowadays makes possible many-body quantum chemistry calculations on larger and larger embedded clusters with remarkably good results for quantities such as the d-level splittings and intersite spin interactions; see, e.g., refs 5−34.Most of the investigations have been focused on 3d transition-metal compounds 3−24 and very recently, because of novel physics arising from strong spin−orbit coupling (SOC), on 5d oxides. 25−29 The 4d materials, on the other hand, received little attention in this context. Here we investigate with the help of ab initio quantum chemistry methods the...
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