The two lowest 1A[superscript]' potential energy surfaces (PES) of the ozone molecule are determined and analyzed using accurate ab-initio MCSCF calculations;As appropriate internal coordinates, the shape-scale perimetric coordinates for triatomic molecules are discussed and further developed;Because the previously determined intersection between these two surfaces of like symmetry is unusual, much of the present work involves this intersection. The relevant theory of intersections is reviewed, and a method for characterizing intersections according to the topology of the surfaces in their vicinity is developed;Furthermore, the reasons for this particular crossing in ozone are investigated. The analysis is based on a novel method for transforming the adiabatic states produced by quantum chemical calculations into diabatic states. The method is founded on the idea that a diabatic state should be dominated throughout coordinate space by a single set of configurations. Accordingly, the transformation to diabatic states is derived by maximizing the contribution of these configurations to their respective states. It is shown that the crossing in ozone is due to an additional exchange in dominance of configurations within each diabatic state;The intersection point in C[subscript] 2v symmetry is part of a larger, 1-dimensional intersection seam in C[subscript] s symmetry. This seam is shown to consist of four branches, one of which is a closed loop. The three other branches lie entirely in C[subscript] 2v restricted subspaces and connect to the first branch at nodes. Additional intersections must exist. A new method for determining an intersection point in a two-dimensional coordinate space, based on the wavefunction phase-change theorem of Herzberg-Longuet-Higgins, is also developed;Finally, global mappings of the two potential energy surfaces in the scale-shape perimetric coordinates are determined. The minima of the two surfaces, their dissociation and rearrangement paths, and the map of the energy difference between them are all discussed. It is shown that direct formation of the ring structure of ozone from O[subscript]2 and O is improbable and that there is no rearrangement pathway on the ground state representing the interchange of two atoms.