The energy difference between the three lowest-lying isomers of C-6, the linear (3) Sigma(g)(-), state, and the two ring forms, the benzene structure ((1)A(1g)) possessing D-6h symmetry and a distorted cyclic form ((1)A’(1), D-3h symmetry) have been calculated using various ab initio methods. Variational methods such as multireference configuration interaction (MR-CI) and complete active space second order perturbation treatment (CASPT2) have been applied, as well as perturbational treatments and coupled cluster calculations (CCD). The correlation of all valence shell electrons is found to be important for a balanced description of the isomers of C-6. Methods which do not account for higher-order effects appropriately proved to be unsuitable for calculating the energy difference correctly. The results from multireference configuration interaction methods show that the isomers are close in energy with the cyclic forms somewhat lower than the linear form. The ring form possessing D-3h symmetry ((1)A’(1)) is found to be the lowest-lying structure.