Racah materials: role of atomic multiplets in intermediate valence systems

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We address the long-standing mystery of the nonmagnetic insulating state of the intermediate valence compound SmB₆. Within a combination of the local density approximation (LDA) and an exact diagonalization (ED) of an effective discrete Anderson impurity model, the intermediate valence ground state with the f-shell occupation n₄f =5.6 is found for the Sm atom in SmB₆. This ground state is a singlet, and the first excited triplet state 3 meV higher in the energy. SmB₆ is a narrow band insulator already in LDA, with the direct band gap of 10 meV. The electron correlations increase the band gap which now becomes indirect. Thus, the many-body effects are relevant to form the indirect band gap, crucial for the idea of ``topological Kondo insulator" in SmB₆. Also, an actinide analog PuB₆ is considered, and the intermediate valence singlet ground state is found for the Pu atom. We propose that [Sm,Pu]B₆ belong to a new class of the intermediate valence materials with the multi-orbital ``Kondo-like" singlet ground-state. Crucial role of complex spin-orbital fⁿ-fⁿ⁺¹ multiplet structure differently hybridized with ligand states in such Racah materials is discussed.