Molecular geometric phase from the exact electron-nuclear factorization

摘要: The Born-Oppenheimer electronic wave function ${\mathrm{\ensuremath{\Phi}}}_{R}^{\text{BO}}(r)$ picks up a topological phase factor $\ifmmode\pm\else\textpm\fi{}1$, special case of Berry phase, when it is transported around conical intersection two adiabatic potential energy surfaces in $R$ space. We show that this quantity reverts to geometric ${e}^{i\ensuremath{\gamma}}$ if the $\ensuremath{\gamma}=\ensuremath{\oint}\mathrm{Im}\ensuremath{\langle}{\mathrm{\ensuremath{\Phi}}}_{R}|{\mathbf{\ensuremath{\nabla}}}_{\ensuremath{\mu}}{\mathrm{\ensuremath{\Phi}}}_{R}\ensuremath{\rangle}\ifmmode\cdot\else\textperiodcentered\fi{}d{\mathbf{R}}_{\ensuremath{\mu}}$ evaluated with conditional ${\mathrm{\ensuremath{\Phi}}}_{R}(r)$ from exact electron-nuclear factorization ${\mathrm{\ensuremath{\Phi}}}_{R}(r)\ensuremath{\chi}(R)$ instead ${\mathrm{\ensuremath{\Phi}}}_{R}^{\text{BO}}(r)$. A model pseudorotating triatomic molecule, also applicable dynamical Jahn-Teller ions bulk crystals, provides examples nontrivial induced vector potentials and molecular factorization. gives contribution circulating nuclear current cannot be removed by gauge transformation. surface calculated found contain term depending on Fubini-Study metric for function.