The Berry phase revisited: application to Born–Oppenheimer molecular systems

doi:10.1088/0953-4075/37/23/003 In this paper, we study the implementation of the Berry approach as expressed in his seminal publication (1984 Proc. R. Soc. Lond. A 392 45) within Born– Oppenheimer molecular systems (1927 Ann. Phys., Lpz. 84 457). This was done with the purpose of revealing the relation between the various time-dependent magnitudes in the adiabatic limit and their time-independent counterparts. The two main results are: (1) in the adiabatic limit, a single Born– Oppenheimer state becomes an eigenstate of the system during the excursion of a system along a given contour, and (2) at the end of a closed contour, the topological phases associated with the states that moved adiabatically along a closed contour are well presented by the diagonal D-matrix as obtained from the time-independent treatment. The theoretical study is supported by a detailed numerical study carried out for two ab initio molecular systems, namely the (Na, H2) and the (H, H2) systems. 1