The exact factorization part I: Non-adiabatic molecular dynamic
Eberhard K.U. Gross, Fritz Haber Center Institute of Chemistry, Israel
Thursday, October 14, 2021 at 11 AM at Casali 253
Many fascinating phenomena in chemistry and physics, such as laser-induced structural phase transitions in solids or photochemical processes in molecules like the process of vision, occur in a regime where the coupled motion of electrons and nuclei beyond the adiabatic approximation is essential. The adiabatic approximation is among the most fundamental components in modern quantum chemistry and condensed-matter physics. It describes the dynamics of the system as the motion of a nuclear wave packet on as single static Born-Oppenheimer surface. This approximation not only makes computations feasible, it also provides us with an intuitive picture of many chemical processes. To go beyond the adiabatic approximation is notoriously difficult because one has to start from the full many-body Hamiltonian of interacting electrons and nuclei. In this seminar, we deduce an exact factorization  of the full electron-nuclear wave function into a purely nuclear wave packet and a many-electron wave function which parametrically depends on the nuclear configuration and which has the meaning of a conditional probability amplitude. The equations of motion for these two wave functions provide an ideal starting point to develop efficient algorithms for the study of non-adiabatic phenomena. The successful prediction of laser-induced isomerization processes , the description of decoherence [2,3], and the evaluation of local electronic currents associated with nuclear motion , will demonstrate the power of this new approach.
 A. Abedi, N.T. Maitra, E.K.U. Gross, PRL 105, 123002 (2010).
 F. Agostini, S.K. Min, I. Tavernelli, E.K.U. Gross, J Phys Chem Lett 8, 3048 (2017).
 S.K. Min, F. Agostini, E.K.U. Gross, PRL 115, 073001 (2015).
 A. Schild, F. Agostini, E.K.U. Gross, J. Phys. Chem. A 120, 3316 (2016).