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Correlated Electron-Nuclear Dynamics: A novel mixed quantum-semiclassical approach

Periodic Reporting for period 1 - CoEND (Correlated Electron-Nuclear Dynamics: A novel mixed quantum-semiclassical approach)

Reporting period: 2016-04-01 to 2018-03-31

The Born-Oppenheimer (BO) approximation is among the most basic approximations in the quantum theory of molecules and solids. It is based on the fact that electrons usually move much faster than the nuclei. This allows us to visualize a molecule or solid as a set of nuclei moving on a potential energy surface (PES) generated by electrons in a specific electronic state. This picture breaks down when the electronic and nuclear motions become correlated. The interplay between the nuclear and electronic dynamics beyond the BO approximation leads to many fascinating phenomena in physics, chemistry and biology. For example, in the processes such as Joule heating in atomic devices, vision, photovoltaic, proton transfer and hydrogen-storage, that are of fundamental importance in the workings of solar-cell devices, molecular electronics and energy storage, the electron-nuclear correlation is a key player. These processes include some of the most difficult phenomena to theoretically model including an accurate calculation of the time-resolved dynamics of the electrons and ions, while their correlations and quantum features of the nuclear motion are indispensable. For example, one of the future key challenges will be to learn how to produce artificial light-harvesting complexes for photovoltaic systems.

The CoEND project’s aim was to develop an efficient and accurate first-principle method to treat the correlated electron-nuclear dynamics. The project’s goal was to provide a theoretical tool to study a wide range of phenomena that lie beyond the capability of existing methods in terms of efficiency and/or accuracy. For example, in the processes such as Joule heating in atomic devices, vision, photovoltaic, proton transfer and hydrogen-storage, the electron-nuclear correlation is a key player, hence, these processes cannot be described within the standard Born-Oppenheimer approximation and existing mean-field approaches such as Ehrenfest method.
Towards achieving the project’s objective, we have developed a new method for correlated electron-nuclear as well as electron-photon dynamics based on the Exact Factorization (EF) framework in its reverse form. This important fundamental development emerged from the successful collaboration between the researcher, Prof. Tokatly and Dr. Khosravi and was built on the researcher’s previous works on the EF framework, Prof. Tokatly’s works on the Time-Dependent Density-Functional-Theory (TDDFT) for cavity QED and Dr. Khosravi’s works on quantum dynamics and TDDFT. In particular, the productive interplay between the two MSCA-IF projects of CoEND (Dr. Abedi/Prof. Rubio) and AMO-Dance (Dr. Khosravi/Prof. Rubio) was crucial and led to the establishment of TDDFT for electron dynamics within the EF framework that is coupled to non-classical nuclear dynamics.
For the nuclear dynamics part, we have implemented the conditional wave function approach that is an efficient trajectory based method. This part was carried-out in collaboration with Dr. Albareda and Prof. Rubio and together with the TDDFT part forms the pillars of the CoEND method.
We have investigated the performance of the developed methods for model systems and proved that the method has a desirable balance between the accuracy and efficiency and therefore it is ready to be implemented into the OCTOPUS code as planed in the proposal.
There are numbers of scientific achievement beyond the state of the art that have been resulted from the CoEND project. The most significant one is the CoEND method that is a first-principle approach. Although it is originally developed to study the correlated electron-nuclear dynamics it is beyond that: the CoEND method can be used to describe the electronic dynamics that is correlated to other degrees of freedom such as vibrational (such as phonons and photons), spin. We have also reported numbers of other fascinating results such as a new mean of interpreting and understanding the strong-field ionization by introducing a new dynamical measure we dubbed time-resolved R-resolved ionization probability. We have furthermore, shedded light on the correlated electron-photon states in cavity QED and showed the mechanism of polaritonic squeezing of the electronic states. Furthermore, we have proved how the two alternative formally exact approaches of conditional wavefunction and Exact Factorization are linked.
Sketch of the Conditional Wave Function Dynamics