  We demonstrate that the molecular Berry phase and the corresponding
non-analyticity in the electronic Born-Oppenheimer wavefunction is, in general,
not a true topological feature of the exact solution of the full
electron-nuclear Schr\"odinger equation. For a numerically exactly solvable
model we show that a non-analyticity, and the associated geometric phase, only
appear in the limit of infinite nuclear mass, while a perfectly smooth behavior
is found for any finite nuclear mass.
