Molecular geometric phase from the exact electron-nuclear factorization

Ryan Requist*, Falk Tandetzky, E. K.U. Gross

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

55 Scopus citations


The Born-Oppenheimer electronic wave function ΦRBO(r) picks up a topological phase factor ±1, a special case of Berry phase, when it is transported around a conical intersection of two adiabatic potential energy surfaces in R space. We show that this topological quantity reverts to a geometric quantity eiγ if the geometric phase γ= ®Im(ΦR| μΦR)·dRμ is evaluated with the conditional electronic wave function ΦR(r) from the exact electron-nuclear factorization ΦR(r)χ(R) instead of the adiabatic function ΦRBO(r). A model of a pseudorotating triatomic molecule, also applicable to dynamical Jahn-Teller ions in bulk crystals, provides examples of nontrivial induced vector potentials and molecular geometric phase from the exact factorization. The induced vector potential gives a contribution to the circulating nuclear current that cannot be removed by a gauge transformation. The exact potential energy surface is calculated and found to contain a term depending on the Fubini-Study metric for the conditional electronic wave function.

Original languageAmerican English
Article number042108
JournalPhysical Review A
Issue number4
StatePublished - 13 Apr 2016
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2016 American Physical Society.


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