Geometric phases are ubiquitous in physics and chemistry, and some of the most fascinating phenomena such as topological insulators or ferroelectricity are closely retated to the occurrence of Berry phases. Geometric phases may arise when the Hamiltonian of a system depends on a set of parameters. For example, the electronic Hamiltonian in Born-Oppenheimer approximation depends parametrically on the nuclear coordinates. 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 Schroedinger equation. For a numerically exactly solvable model we show [1] that a non-analyticity, and the associated geometric phase, only appears in the limit of infinite nuclear mass, while a perfectly smooth behavior, and hence no Berry phase, is found for any finite nuclear mass.

[1] S.K. Min, A. Abedi, K.S. Kim, E.K.U. Gross, Phys.Rev.Lett. 113, 263004 (2014).