In his seminal work [5], Berry discovered that after undergoing an adiabatic cyclic evolution, a quantum system attains an additional phase factor independent of the dynamics and depending solely on the geometry of the evolution, since referred to as Berry’s phase. This discovery opened up an entire field of study of the more general concept of geometric phase which has since been found to comprise the underlying mechanism behind a wide variety of physical phenomena, in both the classical and quantum domains. A key example of each is the Pancharatnam phase in classical optics, [72], which has been experimentally verified using experiments involving laser interferometry [6] and the celebrated Aharonov–Bohm effect of quantum mechanics, discovered in 1959 [3] and experimentally verified in the late 1980s [94], which was given a geometric phase interpretation in [5]. One particular discipline which has benefited greatly from the understanding of geometric phase is quantumchemistry,

in which the separation of the molecular wavefunction into nuclear and electronic components gives rise to geometric phase effects in an array of phenomena [67], perhaps most famously including the Jahn–Teller effect [49; 59]. To this day there is extensive research into the role of the geometric phase in quantum systems and in particular the application to molecular dynamics in quantum chemistry [1; 2; 33; 67; 78; 80; 81; 82].