The potential energy surface (PES) for the singlet 1,2-dilithioethene and acetylenic C2H2Li2 isomers was carefully surveyed using ab initio quantum mechanical methods. Three previously unreported minima (including, remarkably, the global minimum) were located, a planar, monobridged trans-1,2-dilithioethene and two acetylenic structures. A total of seven minima and ten transition states for interconversion of minima were investigated (seven transition states are reported here for the first time). Vibrational frequencies were evaluated for all structures through the coupled-cluster method including all single and double excitations with a double-zeta plus polarization basis set (CCSD/DZP). An acetylenic isomer (11), namely, a C,complex between lithioacetylene and LiH, is the global minimum on the C2H2Li2 PES. This was 34 kcal/mol more stable at CCSD/DZP (+ZPVE) than the two lowest lying singlet 1,2-dilithioethene structures, a trans planar C-2h form with acute CCLi angles (1) and a cis doubly bridged C-2v structure(5). The other singlet 1,2-dilithioethene minima, cis planar monobridged C-s (14), cis planar dibridged C-2v (3), and trans planar monobridged C-s (7), are 4.3, 8.4, and 19.4 kcal/mol higher lying than 1 at CCSD/DZP (+ZPVE), respectively. The carbon-lithium bonding is ionic in character in all these species.