Time-dependent potential energy surfaces from the exact factorization: A predictive first-principles approach to ultra-fast non-adiabatic dynamics

Some of the most fascinating phenomena in physics and chemistry, such as the process of vision, as well as exciton dynamics in photovoltaic systems involve the coupled motion of electrons and nuclei beyond the adiabatic approximation, i.e. processes not captured by the dynamics on a single Born-Oppenheimer surface. To go beyond the adiabatic approximation is notoriously difficult as one has to start from the full Hamiltonian of interacting electrons and nuclei. We deduce an exact factorization [1] 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 of these two wave functions provide an ideal starting point to develop efficient algorithms for the study non-adiabatic phenomena. The successful prediction of ultrafast laser-induced isomerization processes [2], the description of decoherence [3], calculations of the molecular Berry phase without invoking the Born-Oppenheimer approximation [4] and accurate predictions of vibrational spectroscopy [5], especially dichroism, will demonstrate the power of this new approach. To tackle non-adiabatic phenomena in solids, such as laser-induced phase transitions, the equations of motion of the exact factorization are “density-functionalized” [6], leading to a coupled set of Kohn-Sham equations for electrons and phonons [7].

[1] A. Abedi, N.T. Maitra, E.K.U. Gross, PRL 105, 123002 (2010).
[2] F. Agostini, S.K. Min, I. Tavernelli, E.K.U. Gross, J Phys Chem Lett 8, 3048 (2017).
[3] S.K. Min, F. Agostini, E.K.U. Gross, PRL 115, 073001 (2015).
[4] S.K. Min, A. Abedi, K.S. Kim, E.K.U. Gross, PRL 113, 263004 (2014).
[5] A. Scherrer, F. Agostini, D. Sebastiani, E.K.U. Gross, R. Vuilleumier, Phys. Rev. X 7, 031035, (2017).
[6] R. Requist, E.K.U. Gross, PRL 117, 193001 (2016).
[7] R. Requist, C.R. Proetto, E.K.U. Gross, Phys Rev B 99, 165136 (2019).