Particular cases of geometric phases, which are those usually encountered in molecular processes within the Born-Huang representation, are the topological phases. When an electronic adiabatic eigenstate is slowly varied along a closed path in nuclear configuration space encircling the conical intersection, the corresponding wavefunction picks up a phase, in addition to the dynamical phase arising from the Schrödinger equation: if the phase depends on the geometry of the path, it is called geometric, whereas if it depends on the winding number of the path around the conical intersection, it is called topological. For a real-valued adiabatic wavefunction, the topological phase is γ = 0 or π and the phase factor is e iγ = ±1, yielding a change of sign of the electronic wavefunction when transported along the path. This idea of adiabatic transport of the electronic wavefunction in nuclear space implies the BO approximation. In an explicitly dynamical formulation, the BO approximation states that the molecular wavefunction is