The intersection of potential energy surfaces in polyatomic molecules

It is proved that if the wave function of a given electronic state changes sign when transported adiabatically round a loop in nuclear configuration space, then the state must become degenerate with another one at some point within the loop. I t is further shown that this condition is satisfied by certain unsymmetrical triatomic systems, thereby disposing of a recent claim that the non-crossing rule for diatomic molecules applies also to polyatomic molecules.