In this work, we use high-level ab initio procedures to show that the high-energy isomers of C7H2 with a planar tetracoordinate carbon (ptC) atom serve as reactive intermediate leading to the formation of an experimentally known ring-chain carbene, 1-(buta-1,3-diynyl)-cyclopropenylidene (2). Among the experimentally known isomers of C7H2, the latter is the only low-lying ring-chain carbene identified by Fourier-transform microwave spectroscopy. Here we investigate the ring-opening pathways of C-C single bonds connected to the ptC atom in three different C7H2 isomers using coupled-cluster and density functional theory methods. These three isomers [ptCl (C-2v; (X-1) over tildeA(1)), ptC2 (C-s; (X-1) over tildeA'), and ptC3 (C-s; (X-1`) over tildeA')] are found to be local minima on the C7H2 potential-energy surface at both CCSD(T)/cc-pVTZ and B3LYP/6-311+G(d,p) levels of theory. The transition states and minimum-energy pathways connecting the reactants (ptC isomers) and the products have been found via intrinsic reaction coordinate calculations at the B3LYP/6-311+G(d,p) level of theory. The high-energy ptC isomers (ptC2 and ptC3) lead to the formation of 2, while the low-energy ptC isomer, ptCl, rearranges to a bicyclic carbene, bicyclo[4.1.0]hepta-4,6-diene-2-yne-7-ylidene (6). In the latter, we note that both the reactant and the product are yet to be identified in the laboratory. Relative energies, activation energies, reaction energies, and nucleus independent chemical shift values have been calculated to access the thermodynamic and kinetic stabilities and the aromatic nature of these peculiar molecules. Rotational and centrifugal distortion constants have also been estimated for all ptC isomers, which may assist the efforts of microwave spectroscopists.