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

Abstract

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 timedependent 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, H 2 ) and the (H, H 2 ) systems.

A study of conical intersections for the H3+ system

“…[10][11][12][13][14][15][16][17] In our present calculations, we used the flexibility of the DIM approach to eliminate unnecessary discrepancies with ab initio results. As we shall see, since the conical regions lie at infinite distances, they do not give rise to geometrical phases 7-9 since nuclear paths do not surround the seams.…”

Introducing time-dependent molecular fields: a new derivation of the wave equations

“…1-8, 10-12, 14-59). In particular I refer to studies by Englman and Vertesi (46) who, employing Berry's adiabatic Phase, analyzed some of the topological phases calculated by Baer et al (30) enhancing the connection between the two approaches. Also, I would like to mention a recent interesting approach, named Factorization, by Gross et al (47,48) who treat the BOH approach, while replacing the BH expansion by a single BOlike term (obviously  interpreted differently).…”

“…  pq pq pq     ττ τ (30) and the corresponding time derivative of t τ (see Eqs. ( 19)), i.e., / t t   τ .…”

On the aspect of plane of appearance of Jahn‐Teller and Renner‐Teller intersections in tetra‐atomic system—A case study with HCNO+

“…Hence, it was believed necessary to obtain a diabatic framework through adiabatic to diabatic transformation (ADT). In this regard, although the works of Hobey and Mclachlan and Smith are historically important, in what follows, we follow the theoretical framework first introduced by Baer and later championed by Baer with collaborators and several other groups …”