A general theoretical description of "distonic" radical anions is presented, along with an account of an extensive series of ab initio molecular orbital and density functional theory calculations on the negative ions of o-, m- and p-benzyne. The performance of several different computational methods is evaluated with respect to artifactual symmetry-breaking. QCISD(T), CCSD(T), CASPT2N, and DFT(B3LYP) calculations employing double-zeta quality basis sets predict that o-, m-, and p-benzyne anions all have high-symmetry, delocalized radical anion ground electronic states : B-2(2) (C-2 nu), B-2(2) (C-2 nu), and (2)A(g) (D-2h), respectively. The meta and pam isomers also exhibit low-lying, localized radical anion forms with distorted geometries that arise by pseudo Jahn-Teller interactions (vibronic coupling) : (2)A’ (C-s) for m-benzyne anion and (2)A(1) (C-2 nu) for p-benzyne anion. Broken-symmetry wave functions are obtained at symmetrical geometries from MCSCF and CISD calculations for p-benzyne anion, but not for o- and m-benzyne anions. The calculated potential energy surfaces for in-plane distortion of m- and p-benzyne anions are found to be quite flat. An isodesmic reaction approach is used to calculate the electron, proton, and hydrogen atom-binding energies for each of the minimum energy states. Good agreement is achieved between the experimental estimates for these quantities and the calculated values for the lowest-energy anion states. The implications of the theoretical findings for negative ion photoelectron spectroscopic measurements with the m- and p-benzyne anions are discussed.