Abstract: Clusters (I_h)-(Cd,Hg, Yb)@(Pb₁₂, Sn₁₂), (C_5v)-(Ag, Au)@BiPb₁₁,(C_5v)-Ag@SbSn₁₁, (D_5d)(Ni, Pd,Pt)@Bi₂Pb₁₀, (D_5d)-Pd@Sb₂Sn₁₀,(C_3v)-(Pb₁₂,Sn₁₂)·(Pb, Sr, Ba), closo-Bi₂Pb₁₀,closo-Bi₂Pb₄,closo-Sb₂Sn₄,(I_h)-Bi₂₀,(I_h)-Kr@Bi₂₀, and(I_h)-Ni₁₂Bi₂₀were studied by the DFT PBE0 method. Structures of (I_h)-(Pb,Sr)@(Pb₁₂, Sn₁₂), (I_h)-Ba@Pb₁₂,(D_5d)-(He,Ne)@Bi₂Pb₁₀, (C_3v)-(Pb₁₂,Sn₁₂)∙Yb, (C_5v)-(Pb₁₂,Sn₁₂)∙Hg, (C_s)-BiPb₁₁∙(Ag,Au), (C_s)-SbSn₁₁∙Ag,(C_s)-p-Bi₂Pb₁₀∙(Ni, Pd,Pt), and (C_s)-p-Sb₂Sn₁₀∙Pdclusters are metastable; structures of (I_h)-Ba@Sn₁₂ and(D_5d)-(Ar, Kr,Rn)@Bi₂Pb₁₀ are unstable. Inthe (I_h)-Ni₁₂Bi₂₀cluster, nickel atoms form η⁵-bonds with the faces ofthe Bi₂₀ dodecahedron. In the isomers (D_4h)- and (C_2v)-(Bi, Sb)₂(Pb,Sn)₄, 6 orbitals of lone electron pairs and 8 bondingthree-center orbitals with populations of 2.00 make up a linearly dependent setof 14 natural orbitals. The oxidation state Ξ_X isassociated with the populations of orthogonal orbitals located outside the Xatom.