The structure and thermodynamic stabilities of a range of cations sharing the C4H2+ composition were investigated with ab initio quantum chemical methods. Four species found as the most stable ones (namely the diacetylene cation, 4- and 3-carbon ring structures, and a Y-shaped vinylidene-like arrangement) were selected for an in-depth analysis, providing molecular parameters relevant to rotational, vibrational, and electronic spectroscopy. (C) 2013 Elsevier B.V. All rights reserved.