AbstractWe 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 〈n_4f〉 = 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 f ⁿ–f ⁿ⁺¹ multiplet structure differently hybridized with ligand states in such Racah materials is discussed.