Feynman's way is used to calculate total-energy curves for the X-1 Sigma(g)(+), a(3) Pi(u), b(3) Sigma(g)(-), A(1) Pi(u), c(3) Sigma(u)(+), 1(1) Delta(g), 2(1) Sigma(g)(+), d(3) Pi(g), C-1 Pi(g), e(3) Pi, D-1 Sigma(u)(+), and C'(1) Pi(g) valence states of C-2. Lewis structures are derived for each state. Average (maximum) deviations of calculated spectroscopic constants from experiment are 1.9 (4.3) pm for R-e, 18 (32) kJ/mol for D-e, 12 (36) kJ/mol for T-e, 62 (162) cm(-1) for omega(e), and 16 (31) kJ/mol for asymptotic excitation energies.