The global potential energy surface, determined in the first paper [1] for the groundstate ring opening of cyclopropylidene to allene, is complemented by accurate calculations of its key regions. The basis set is extended and polarization functions are included. The full configuration space of four electrons in four reactive orbitals is enlarged to the full configuration space of eight electrons in eight active orbitals by including correlations in the unbroken, but stretched CC sigma bonds. The effect of further single and double excitations is examined. The geometries and relative energies of the critical regions are found to change only little except for the ring-opening energy barrier which is lowered to about 7 kcal/mol, in good agreement with the experimental estimate of about 6 kcal/mol. Furthermore, the bifurcation is shown to occur after the transition state, in the neighborhood of a conical intersection on the steepest descent path from the ring-opening transition state to the allene isomerization transition state. The steepest descent paths and the conical intersection are documented in detail. The cogwheel-like free internal rotation of the two methyl groups is confirmed by the accurate calculations. A similar richness of features is believed to exist on many potential energy surfaces governing chemical reactions.