The reaction of acetylene (Ac) with its radical cation (Ac.+) is studied at the CCSD(T)/cc-pVTZ//QCISD/6-31G* level of theory and by the B3LYP/6-31G* density functional method. Contrary to earlier claims, we find that vertical ionization of the neutral acetylene dimer leads to a bound state which relaxes to a T-shaped ion-molecule complex 8.3 kcal/mol below the separated fragments. Once Ac and Ac.+ have approached to less than an approximate to 3 Angstrom center to center distance, spin and charge begin to delocalize and the complex collapses smoothly to the cyclobutadiene radical cation (CB) via a linear complex (LC1) and/or a cyclopropenylcarbene cation (CC). Rearrangements to other stable C4H4.+ isomers require H shifts which are promoted by localization of the positive charge on one C atom. From LC1 this leads directly to the transition state LC2 for formation of a pivotal intermediate, H2C=C=CHCH.+ (methyleneallene, MA), which in turn collapses with E-a approximate to 3 kcal/mol to the methylenecyclopropene radical cation (MCP), the most stable C4H4.+ isomer. Additional [1,2] H shifts which require higher activation energies lead to the radical cations of butatriene (BT, E-a approximate to 17 kcal/mol from MA) or vinylacetylene (VA, E-a approximate to 20 kcal/mol from MA) which are of stability similar to that of CB. These findings are in accord with condensed phase experiments on alkylated acetylenes, where the corresponding CB derivatives were the only products observed. However, in gas phase studies other C4H4.+ isomers were observed in Ac + Ac.+ reactions. Perhaps these arise through bifurcations leading to structures with localized charge without passing through the stationary points located in this study. B3LYP/6-31G* results were found to be in close agreement with the reference coupled cluster calculations for most parts of the C4H4.+ potential energy surface probed in this study. However, it should be noted that density functional methods may give a wrong dissociation behavior for radicals because they fail to localize the spin (and the charge in the present case) when this is required and therefore cannot be used in the loosely bound region for ion-molecule complexes.