Rhombic C₄. Does it contain the shortest nonbonding C-C distance?

In this ab initio molecular orbital study the bonding properties between the inverted carbons in rhombic C₄ and [1.1.1]propellane are discussed. Rhombic C₄, its protonated forms C₄H ⁺ and C₄H₂²⁺, and its linear isomer have been studied with the 6-311G(2d,p) basis set and all electron correlation using Møller-Plesset perturbation theory at second order. The rhombic form of C₄ is estimated to be essentially isoenergetic with the linear form; the estimated harmonic vibrational frequencies for both are compared with experimental data. The molecular orbital and topological one-electron density analyses show that the cross-ring bond of rhombic C ₄ is topologically unstable (at various levels of theory) which suggests a frozen transition for C-C bond making/breaking. At MP4 (SDTQ) this cross-ring distance is only 1.546 Å. The stabilizing properties of rhombic C₄ (and C₄H⁺, and C₄H²⁺) are compared with those of the well known [1.1.1] propellane, which at MP2/6-31G* has a longer cross-ring bond.