Berlin 2014 – scientific programme
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MO: Fachverband Molekülphysik
MO 18: Theory 3: Quantum Chemistry
MO 18.5: Talk
Thursday, March 20, 2014, 15:00–15:15, BEBEL SR144
Exact factorization of the time-dependent electron-nuclear wavefunction — Ali Abedi1, •Federica Agostini1, Neepa Maitra2, and E. K. U. Gross1 — 1Max-Planck-Institut für Mikrostrukturphysik, Weinberg 2, 06120 Halle, Germany — 2Department of Physics and Astronomy, Hunter College and the City University of New York, New York, New York 10065, USA
We present an exact factorization of the complete wavefunction into a purely nuclear part and an electronic wavefunction which parametrically depends on the nuclear configuration. We derive equations of motion for the nuclear and electronic wavefunctions. The nuclear dynamics is governed by a time-dependent Schrödinger equation featuring a vector potential and a potential energy surface. These potentials are unique and give a purely nuclear wave-function yielding the true nuclear N-body density and the true nuclear N-body current density of the full electron-nuclear system. Hence, in the classical limit, the gradient of this exact potential energy surface yields the "correct" classical force on the nuclei [3,4]. Therefore, the exact splitting of electronic and nuclear degrees of freedom lends itself as a rigorous starting point for the systematic development of (semi)classical approximations. Here, we present a novel mixed-quantum-classical algorithm to treat the coupled electron-nuclear motion. [1] A. Abedi, N.T. Maitra, E.K.U. Gross, PRL 105, 123002 (2010). [2] A. Abedi, N.T. Maitra, E.K.U. Gross, JCP 137, 22A530 (2012). [3] A. Abedi, F. Agostini, Y. Suzuki, E.K.U. Gross, PRL 110, 263001 (2013). [4] F. Agostini, A. Abedi, Y. Suzuki and E.K.U. Gross, Mol. Phys. 111, 3625 (2013)