Molecular geometric phase from the exact electron-nuclear factorization Article Swipe
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· 2016
· Open Access
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· DOI: https://doi.org/10.1103/physreva.93.042108
· OA: W747256263
The Born-Oppenheimer electronic wavefunction $\\Phi_R^{BO}(r)$ picks up a\ntopological phase factor $\\pm 1$, a special case of Berry phase, when it is\ntransported around a conical intersection of two adiabatic potential energy\nsurfaces in $R$-space. We show that this topological quantity reverts to a\ngeometric quantity $e^{i\\gamma}$ if the geometric phase $\\gamma = \\oint\n\\mathrm{Im} \\langle \\Phi_R |\\nabla_{\\mu} \\Phi_R\\rangle \\cdot d\\mathbf{R}_{\\mu}$\nis evaluated with the conditional electronic wavefunction $\\Phi_R(r)$ from the\nexact electron-nuclear factorization $\\Phi_R(r)\\chi(R)$ instead of the\nadiabatic function $\\Phi_R^{BO}(r)$. A model of a pseudorotating molecule, also\napplicable to dynamical Jahn-Teller ions in bulk crystals, provides the first\nexamples of induced vector potentials and molecular geometric phase from the\nexact factorization. The induced vector potential gives a contribution to the\ncirculating nuclear current which cannot be removed by a gauge transformation.\nThe exact potential energy surface is calculated and found to contain a term\ndepending on the Fubini-Study metric for the conditional electronic\nwavefunction.\n
