Diabatic and adiabatic representations: Electronic structure caveats

•Energetically inaccessible conical intersections strongly affect standard single adiabatic state descriptions of nonadiabatic tunneling.•Linked intersections limit the validity of standard treatments of nonadiabatic dynamics involving more than two adiabatic electronic states.•The geometric phase and vector potential needed to describe the Molecular Aharonov Bohm effect can determined from a two state diabatization.•Some properties based diabatizations produce spurious singularities in the derivative couplings.