Molecular geometric phase from the exact electron-nuclear factorization

Abstract

The Born-Oppenheimer electronic wavefunction ${\Phi }_R^{BO}(r)$ picks up a topological phase factor $\pm 1$, 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 $e^{i\gamma }$ if the geometric phase $\gamma =\oint \mathrm{Im}⟨{\Phi }_R|{\nabla }_{\mu }{\Phi }_R⟩\cdot d{\mathbf{R}}_{\mu }$ is evaluated with the conditional electronic wavefunction ${\Phi }_R(r)$ from the exact electron-nuclear factorization ${\Phi }_R(r)\chi (R)$ instead of the adiabatic function ${\Phi }_R^{BO}(r)$. A model of a pseudorotating molecule, also applicable to dynamical Jahn-Teller ions in bulk crystals, provides the first examples of induced vector potentials and molecular geometric phase from the exact factorization. The induced vector potential gives a contribution to the circulating nuclear current which 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 wavefunction.

References in corpus (6)

• The exact forces on classical nuclei in non-adiabatic charge transfer
• The Geometric Phase Appears in the Ultracold Hydrogen Exchange Reaction
• Local electronic structure of Fe${}^{2+}$ impurities in MgO thin films: Temperature-dependent soft x-ray absorption spectroscopy study
• Dynamical Jahn--Teller effect and antiferromagnetism in Cs${}_3$C${}_{60}$
• Anomalous multi-order Raman scattering in LaMnO_3: a signature of a quantum lattice effect in a Jahn-Teller crystal
• Geometric Phase Atom Optics and Interferometry

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