En el Aula Seminario, 2do piso, Pab. I,

                        Lunes 18/12, 14hs:

 

Correlated Electron-Nuclear Dynamics

The coupling between electronic and nuclear motion plays an important role in many fascinating phenomena, such as superconductivity, the process of vision, as well as photo-synthesis. There are standard approximations such as Ehrenfest dynamics or surface hopping that partially capture the non-adiabatic effects. As a first step towards a full ab-initio treatment of the coupled electron-nuclear system, we deduce an exact factorization of the complete wavefunction into a purely nuclear part and a many-electron wavefunction which parametrically depends on the nuclear configuration. We derive formally exact equations of motion for the nuclear and electronic wavefunctions [1-3]. These exact equations lead to a rigorous definition of time-dependent potential energy surfaces (TDPES) as well as time-dependent geometric phases. We analyze features of the TDPES in two topically demanding situations: 
molecules in strong fields [1-3] and splitting of a nuclear wave-packet at avoided crossings [5] Born-Oppenheimer potential energy surfaces. In addition, by studying a numerically exactly solvable model we demonstrate that the molecular Berry phase and the corresponding non-analyticity in the electronic Born-Oppenheimer wavefunction is, in general, not a true topological feature of the exact solution of the full electron-nuclear Schroedinger equation and only appear in the limit of infinite nuclear mass [4].

Finally, we present a novel mixed quantum-classical approach [5] to the coupled electron-nuclear dynamics based on the equations of motion for the electronic and nuclear subsystems within the exact factorization framework. The nuclear equation is a standard Schroedinger equation containing a TDPES as well as a time-dependent vector potential. Starting from these equations, the correct classical limit of the nuclear dynamics is worked out by taking the classical limit of the exact time-dependent Schroedinger equation satisfied by the nuclear wave function. The effect of the time-dependent scalar and vector potentials, representing the exact electronic back-reaction on the nuclear subsystem, is consistently derived within the classical approximation. Using a model system, we examine the performance of the proposed mixed quantum-classical scheme in comparison with exact calculations, in the presence of strong non-adiabatic coupling between the electronic and nuclear motion.

References:
[1] A. Abedi, N. T. Maitra, and E. K. U. Gross, Physical Review Letters 105 123002 (2010). 
[2] A. Abedi, N. T. Maitra, and E. K. U. Gross, Journal of Chemical Physics 137 22A530 (2012)
[3] A. Abedi, F. Agostini, Y. Suzuki, E. K. U. Gross, Physical Review Letters 110 263001 (2013).
[4] S. K. Min, A. Abedi, K. S. Kim, and E. K. U. Gross, Physical Review Letters 113 263004 (2014).
[5] A. Abedi, F. Agostini, and E. K. U. Gross, Europhysics Letters 106 33001 (2014).