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

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Abstract
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 C4H2+2, and its linear isomer have been studied with the 6‐311G(2d,p) basis set and all electron correlation using Mo/ller–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 C4 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.