Conical intersections - phase

Can anyone explain why at a conical intersection the wavefunction changes sign? My understanding is that it is a test to see if the crossing IS indeed a conical intersection or just a coincidence of potential energy surfaces, which do not exhibit such phase changes upon periodic cycling. If this is correct ... why? Further what can we gain from knowing that?




A rather quick googling shows up that there is some Longuet-Higgins theorem, which states almost what you are looking for. For instance, the abstract of [this paper](http://rspa.royalsocietypublishing.org/content/344/1637/147) says:



> 
> 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.
> 
> 
> 


In the paper itself it is further stated that this in turn implies that 



> 
> [the corresponding] potential energy surface intersects one of another electronic state
> 
> 
> 


and that the theorem 



> 
> makes it possible to diagnose the presence of an intersection between potential energy surfaces from the behaviour of the electronic wave function as it is transported adiabatically round a closed loop remote from the intersection
> 
> 
> 


which answers both your questions, if I understand them correctly.


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