We address the long-standing mystery of the nonmagnetic insulating state of the intermediate valence compound $SmB_{6}$. 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 $\sim3$ meV higher in the energy. $SmB_{6}$ is a narrow band insulator already in LDA, with the direct band gap of $\sim10$ 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 $SmB_{6}$. Also, an actinide analog PuB6 is considered, and the intermediate valence singlet ground state is found for the Pu atom. We propose that $[Sm, Pu]B_{6}$ 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.