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Quantum Dynamics Beyond the Born-Oppenheimer Picture: Making the most of wave function and trajectory-based approaches

Periodic Reporting for period 1 - BeBOP (Quantum Dynamics Beyond the Born-Oppenheimer Picture: Making the most of wave function and trajectory-based approaches)

Reporting period: 2017-10-01 to 2019-09-30

The Born-Oppenheimer 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 Born-Oppenheimer potential energy surface 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 Born-Oppenheimer approximation leads to many fascinating phenomena in physics, chemistry and biology. For example, electron-nuclear correlation is a key player in processes such as Joule heating in atomic devices, vision, photovoltaics, proton transfer and hydrogen-storage. These processes include some of the most difficult phenomena to theoretically model, viz. an accurate calculation of the time-resolved dynamics of electrons and ions while their correlations and quantum features of the nuclear motion are critical. One of the future challenges will be, e.g. to learn how to produce artificial light-harvesting complexes for photovoltaic systems. It has been recently shown that the charge separation mechanism in a prototypical artificial light-harvesting system is driven by “a correlated wavelike motion of electrons and nuclei”.
The overall objective of the BeBOP research has been to develop an efficient algorithm that implement the core ideas of the so-called conditional wavefunction approach to treat large systems. BeBOP’s research should lead to a new predictive and practical method that is mathematically rigorous and overcomes the difficulties that current methods have in treating the coupled electron-nuclear dynamics in processes such as photovoltaics or vision.
The research work has culminated in the development of a stochastic wavefunction ansatz that has yielded an ab-initio algorithm for quantum dynamics simulations that reformulates the traditional “curse of dimensionality” that plagues all state-of-the-art techniques for solving the time-dependent Schrödinger equation. More specifically, the difficulty of the many-body problem becomes dominated by the number of trajectories needed to describe the process, rather than simply the number of degrees of freedom involved.
This novel theoretical framework has yielded a highly parallelizable technique that achieves quantitative accuracy for situations in which mean-field theory drastically fails to capture qualitative aspects of the dynamics, such as quantum decoherence or the reduced probability densities, using orders of magnitude fewer trajectories than a mean-field simulation. The performance of this novel method has been proven for two fundamental non-equilibrium processes: a photoexcited proton-coupled electron transfer problem, and nonequilibrium dynamics in a cavity bound electron-photon system in the ultrastrong-coupling regime.
These developments provide a general framework to approach the many-body problem in a variety of contexts. For example, using the resulting method in a form compatible with time-dependent density functional theory is a particularly appealing route to follow in this respect, and work in this direction is already in progress. At the moment, the developed method is being implemented in the OCTOPUS code with the help of a PhD student and the technician in charge of the software maintenance.
Main results during the two years of the reasearch project include 3 peer-reviewed publications, 4 more papers currently under revision and 1 book chapter (see publications list).
Describing nonequilibrium processes in molecular and condensed-phase systems continues to pose significant challenges due to the overwhelming computational costs of the structural and dynamical aspects of the problem. Yet, this is a problem that is increasingly topical, especially with the advent of attosecond lasers and ultrafast electron diffraction techniques that allow to visualize the “molecular movie”. Up to now, most of the methods to describe the correlated electron-nuclear motion have been based on the Born-Huang expansion that fails to meet the appropriate trade-off between accuracy and efficiency for large systems.
The results of BeBOP research have yield an efficient algorithm for performing ab-initio quantum dynamics simulations that is based on the conditional decomposition of the many-body wavefunction. This highly parallelizable technique achieves quantitative accuracy using orders of magnitude fewer trajectories than the corresponding mean-field calculation. The degree of computational efficiency of this method opens the possibility to treat dynamics in larger quantum systems with unprecedented accuracy and constitutes an alternative to available methods for systems of interacting fermions/bosons.
Furthermore, the developed method could also lead to a paradigm change in how nonadiabatic molecular dynamics is numerically approached: (i) unlike methods based on the Born-Huang expansion of the molecular wave function (e.g. Ab- Initio Multiple Spawning or Tully surface hopping), the developed tool provides direct access to electron dynamics, (ii) the newly derived method goes beyond standard time-dependent density-functional theory for fixed nuclei and accounts for electron-nuclear correlations beyond the time-dependent density-functional theory+Ehrenfest method.
We expect the new method to help understand important processes such as Joule heating in atomic devices, vision, photovoltaics, or proton transfer and hydrogen- storage. These processes include some of the most difficult phenomena to theoretically model, viz. an accurate calculation of the time-resolved dynamics of electrons and ions while their correlations and quantum features of the nuclear motion are critical.
Furthermore Dr. Albareda has been very active in the dissemination of results in numerous conferences and workshops (13) where he has given talks on his research topics (selected):

Participation to Conferences and Workshops
i. Coupled electron-nuclear dynamics without Born-Oppenheimer surfaces. XXXIII Scientific Meetings in the Mediterranean. 18th-20th October 2017 Mahó, Spain. Invited.
ii. Ab-initio nonadiabatic dynamics without Born-Oppenheimer potential-energy surfaces. Non-Adiabatic Quantum Dynamics: From Theory to Experiments. 2th-6th July 2018. Lausanne, Switzerland. Invited.
iii.Trajectory Approaches for Nonequilibrium Quantum Dynamics in Light-Matter Systems. Scientific Advisory Board Meeting of the MPSD. 9th-11th January 2019. Hamburg, Germany. Invited.
iv. Approaches to nonadiabatic quantum dynamics without potential-energy surfaces. Recent developments in quantum dynamics. 17th–21th July 2019. Lyon, France. Invited.

Contributions to Conferences and Workshops
i. Non-Universality of Quantum Dynamics Computed from Time-Correlation Functions. International Conference on Quantum Frontiers and Fundamentals. 30th April-4th May, 2018 Bengaluru, India. Talk.
ii. Eliminating quantum uncertainty in quantum electron devices: Leveraging classical and quantum computing. The International Workshop on Computational Nanotechnology. 20th-24th May 2019 Illinois, USA. Talk
iii. Biradical Species induced by Valence Tautomerism: a challenge for Electronic Structure Methods. International Conference on Molecular Electronic Structure. 28th–31th May 2018 Metz, France. Talk.
"Schematic representation of the ""conditional wavefunction"" approach to molecular dynamics."