Can four-center two-electron bonding alone provide stability of a molecule?

Ab initio calculations on the Li₄²⁺ and Na₄²⁺ T_d structures show that two valence electrons are capable of binding four alkali metal centers. These structures have positive binding energies (E_b/n = 4.62 (Li₄²⁺, QCISD-(T)(full)/6-311G(2d)//MP2(full)/6-311G(2d); 4.74 MP4SDQ(full)/6-31+G(3d)//MP2(full)6-311G(2d)) and 1.66 kcal/mol (Na₄²⁺, QCISD(T)(full)/6-31G(d)//MP2(full)/6-31G(d)). However, they are thermodynamically unstable with respect to the dissociations into different two sets of cations, i.e. into M₃⁺ (D_3h) and M⁺ and into 2M₂⁺. The decomposition barriers into M₃⁺ and M⁺ are 3.4 kcal/mol for Li₄²⁺ (QCISD(T)(full)/6-311G(2d)//MP2(full)/6-311G(2d) + ZPE(MP2/6-31G(2d)) and 2.3 kcal/mol for Na₄²⁺ (MP4SDTQ(fc)/6-31G(2df)/6-31G(d)//MP2(full)/6-31G(d) + ZPE(HF/6-31G(d))), respectively. Four-center, two-electron (4c-2e) bonding suffices to stabilize an otherwise unsupported molecule. Alternative geometries of the M₄²⁺ clusters (e.g., linear (D_∞h), Y-type (D_3h), square (D_3h), and rhombus (D_2h)) are not minima. In contrast to H₄²⁺, the relative stabilities of the Li₄²⁺ forms strongly disagree with the expectations based on the charge alternation model. Effective 4c-2e bonding in Li₄²⁺ (T_d) depends on the 2p lithium orbitals. When these orbitals are excluded from the basis set, Li₄²⁺ behaves somewhat similarly to H₄²⁺; in particular, the T_d form is not a minimum. Topological analysis (AIM) of the electron charge density shows the existence of a nonnuclear maximum (attractor, in this case pseudoatom) in the center of the Li₄²⁺ tetrahedron. There is no direct Li-Li bonding. The electronic structure analysis shows that Li₄²⁺ (T_d) is not very stable; this is consistent with the low dissociation barrier.