SAMOP 2021 – scientific program
PV V: Plenary Talk
Thursday, September 23, 2021, 09:00–09:45, Audimax
Potential energy surfaces and Berry phases from the exact factorization — •E.K.U. Gross — Fritz Haber Center for Molecular Dynamics, The Hebrew University of Jerusalem, Israel
Some of the most fascinating phenomena in physics and chemistry, such as the process of vision, or laser-induced structural phase transitions occur in the so-called non-adiabatic regime where the coupled motion of electrons and nuclei beyond the Born-Oppenheimer approximation is essential. The Born-Oppenheimer approximation is among the most fundamental ingredients of condensed-matter theory and theoretical chemistry. It not only makes computations feasible, it also provides us with an intuitive picture of chemical reactions. Yet it is an approximation. To go beyond it is notoriously difficult because one has to start from the full many-body Hamiltonian of interacting electrons and nuclei. We deduce an exact factorization of the full electron-nuclear wave function into a purely nuclear part 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 lead to a unique definition of exact potential energy surfaces as well as exact geometric phases and, hence, 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 ab-initio description of decoherence, calculations of the molecular Berry phase beyond the Born-Oppenheimer approximation and accurate predictions of vibrational dichroism will demonstrate the power of the new approach.