The potential energy functions for all states of ozone correlating with the lowest O(P-3)+O-2(X (3)Sigma(g)(-)) asymptote have been calculated in the asymptotic region employing correlated electronic wave functions. For linear ozone, the (s)Sigma states (s=1,3, and 5) lie above the corresponding (s)Pi states. For bent geometries the Pi states split into Renner-Teller components with A(') and A(') symmetry, respectively. While the (1)Pi and (3)Pi states lead to bent-bent Renner-Teller pairs, the (5)Pi state gives rise to a linear/linear pair of states. The different spin multiplets emerging from the Pi states cross for valence angles around 160degrees and the (1)A(') component becomes the lowest one. The matrix elements of the spin-orbit operator have also been calculated. They are dominated by the atomic P-3 contributions and their dependence on the mutual orientation of the O-2 molecule and the O atom is small. In the regions where the states correlating to the linear (1,3,5)Pi cross, i.e., for valence angles between 150degrees and 180degrees and close to 90degrees, the mixing among the singlet, triplet, and quintet states is strong and the electron spin quantum number is no longer a good quantum number.