Periodic Reporting for period 1 - MEDYNA (Memory effects in Electron DYNamics: a connector Approach)
Reporting period: 2021-10-01 to 2023-09-30
Understanding the behavior of many electrons in interaction is one of the greatest challenges of modern quantum physics, called the quantum N-body problem. Part of the issue for describing the quantum behavior of the electronic density comes from the description of excitations in a system. Formally, the description of excited states can be understood as coupling in time, i.e. the history-dependence of materials properties, also called non-adiabatic effects. These can show up in the most diverse manner, such as satellites in photoemission spectra of solids or double excitation in molecules. Non-adiabatic effects are at the origin of phenomena that enter modern technologies, such as charge migration and multiple exciton generation, that is a promise for photovoltaic applications.
From the theoretical point of view, a full description of the N-electron system would ask for the solution of the full Schrödinger equation, which is not feasible for more than a few electrons. In practice, the full wave function contains much more information than the observables of interest.
One way to circumvent this issue is to focus on compact quantities (electronic density, density matrix, one-body Green's function, spectral function, etc.) to develop functionals that simplify calculations and make them tractable for realistic systems.
Most approximations used to compute these reduced quantities have strong limitations concerning these non-adiabatic effects. For example, in quantum chemistry, a lot of work focuses on the electronic density as the reduced quantity and the method of choice to describe excited states is the Time-Dependent Density Functional Theory (TDDFT), where most functionals are purely adiabatic. In solids, the one-body Green’s function computed within the GW approximation is the standard. Green's function methods rapidly meet their limits when it comes to the description of non-adiabatic coupling between excitations. For instance, GW approximation to the electron self-energy is not able to well describe plasmon satellites that are observed in photoemission spectra. Also, because Green’s functions are a bigger object than the density, Green's functions-based approaches would mostly require a computational effort that is still out of reach in many systems.
In this project, the philosophy is to use data on precomputed model systems and explore various reduced quantities to retrieve non-adiabatic effects. The overall objective is to advance the understanding and prediction of non-adiabatic effects in materials and spectroscopies, in order to identify novel phenomena and enhance theoretical frameworks.
From the theoretical point of view, a full description of the N-electron system would ask for the solution of the full Schrödinger equation, which is not feasible for more than a few electrons. In practice, the full wave function contains much more information than the observables of interest.
One way to circumvent this issue is to focus on compact quantities (electronic density, density matrix, one-body Green's function, spectral function, etc.) to develop functionals that simplify calculations and make them tractable for realistic systems.
Most approximations used to compute these reduced quantities have strong limitations concerning these non-adiabatic effects. For example, in quantum chemistry, a lot of work focuses on the electronic density as the reduced quantity and the method of choice to describe excited states is the Time-Dependent Density Functional Theory (TDDFT), where most functionals are purely adiabatic. In solids, the one-body Green’s function computed within the GW approximation is the standard. Green's function methods rapidly meet their limits when it comes to the description of non-adiabatic coupling between excitations. For instance, GW approximation to the electron self-energy is not able to well describe plasmon satellites that are observed in photoemission spectra. Also, because Green’s functions are a bigger object than the density, Green's functions-based approaches would mostly require a computational effort that is still out of reach in many systems.
In this project, the philosophy is to use data on precomputed model systems and explore various reduced quantities to retrieve non-adiabatic effects. The overall objective is to advance the understanding and prediction of non-adiabatic effects in materials and spectroscopies, in order to identify novel phenomena and enhance theoretical frameworks.
The project, led by fellow Lionel LACOMBE with the mentorship of Lucia REINING at École Polytechnique, aimed to develop a new non-adiabatic functional for TDDFT, based on the Connector Theory (COT). Our research has highlighted the intricate challenges involved in extending COT to non-adiabatic and non-local regimes. Through systematic exploration of non-adiabatic phenomena within a model system, the Hubbard Dimer, we have formulated a robust methodology for selecting the most suitable approximation and model when deriving a new connector approach. We have identified which key reduced quantities are relevant when deriving a new functional for these phenomena. While our methodology provides valuable insights, further refinement is necessary to fully capture the dynamics of double charge transfer and the description of double excitations. Our findings lay the groundwork for future advancements in accurately predicting non-adiabatic effects within density functional theory, marking a significant step forward in computational chemistry.
We explored the use of a new reduced quantity: the diagonal of the Green’s function in reciprocal space. This allows us to derive a generalized TDDFT-like approach with non-adiabaticity already baked in at the fundamental level. Furthermore, quantities of physical interest in photoemission spectra, such as the spectral function, are directly related to our reduced quantity. The subsequent formalism provides a straightforward expansion of observables around the homogeneous electron gas reference. The prospect of formulating functionals of the diagonal of the Green’s function, rather than the entire Green’s function, holds promise in calculating an exchange-correlation kernel that balances the accuracy of Bethe-Salpeter Equation with the simplicity of TDDFT’s exchange-correlation kernel. Our research represents significant progress in extracting valuable information and observables from angle-resolved photoemission spectroscopy experiments.
The project strategically evolved towards investigating non-adiabatic charge transfer and energy absorption within photovoltaic systems, broadening its scope and fostering collaboration with external partners. It became part of a collaborative effort with the Institut Photovoltaïque d’Île-de-France. This collaboration involves understanding, predicting and tailoring charge transfer at interface. This can only be achieved with a deeper understanding of non-adiabatic and correlation effects in solar cells.
In our research, we have implemented numerical methods for simulating real-time propagation including a large bosonic bath, and conducted thorough analyses of time propagation to observe energy transfer dynamics. Additionally, we have calculated time-dependent local energy distributions within the Hamiltonian and evaluated charge density evolution during the propagation process. Our findings highlight the limitations of the linear response approximation in accurately describing charge transfer dynamics and time propagation. Exact propagation has proven to offer insights into energy transfer mechanisms, indicating the necessity of exploring quadratic response for better approximation on physical systems.
We explored the use of a new reduced quantity: the diagonal of the Green’s function in reciprocal space. This allows us to derive a generalized TDDFT-like approach with non-adiabaticity already baked in at the fundamental level. Furthermore, quantities of physical interest in photoemission spectra, such as the spectral function, are directly related to our reduced quantity. The subsequent formalism provides a straightforward expansion of observables around the homogeneous electron gas reference. The prospect of formulating functionals of the diagonal of the Green’s function, rather than the entire Green’s function, holds promise in calculating an exchange-correlation kernel that balances the accuracy of Bethe-Salpeter Equation with the simplicity of TDDFT’s exchange-correlation kernel. Our research represents significant progress in extracting valuable information and observables from angle-resolved photoemission spectroscopy experiments.
The project strategically evolved towards investigating non-adiabatic charge transfer and energy absorption within photovoltaic systems, broadening its scope and fostering collaboration with external partners. It became part of a collaborative effort with the Institut Photovoltaïque d’Île-de-France. This collaboration involves understanding, predicting and tailoring charge transfer at interface. This can only be achieved with a deeper understanding of non-adiabatic and correlation effects in solar cells.
In our research, we have implemented numerical methods for simulating real-time propagation including a large bosonic bath, and conducted thorough analyses of time propagation to observe energy transfer dynamics. Additionally, we have calculated time-dependent local energy distributions within the Hamiltonian and evaluated charge density evolution during the propagation process. Our findings highlight the limitations of the linear response approximation in accurately describing charge transfer dynamics and time propagation. Exact propagation has proven to offer insights into energy transfer mechanisms, indicating the necessity of exploring quadratic response for better approximation on physical systems.
Our exploration of non-adiabatic effects spans from studying existing approximations and methods, and assessing their impact on real systems like photovoltaic cells, to devising new approximations and methodologies to improve simulations, based on a Connector approach. Additionally, our work involves crafting entirely new frameworks that concentrate on reduced quantities directly associated with experimental data.
The project makes significant progress in the little explored field of constraints on Green Functions, with the example of the diagonal of the Green’s function in reciprocal space. By demonstrating the uniqueness of the diagonal in describing physical systems and developing techniques to extract valuable information from it, our research opens up new avenues for exploring frequency-dependent effects in physical systems. This could also lead to more efficient algorithms for simulating electronic structure and dynamics, reducing computational costs and storage requirements, and enabling the study of larger and more complex systems.
Moreover, the project has direct relevance to photovoltaic applications by enhancing our understanding of charge transfer dynamics in solar cells. By investigating non-adiabatic and correlation effects in photovoltaic systems, the project contributes to the development of more efficient and functional solar devices. Insights gained from the study of charge separation dynamics could lead to the design of novel materials and interfaces optimized for solar energy conversion, ultimately advancing the design of sustainable energy technologies.
The project makes significant progress in the little explored field of constraints on Green Functions, with the example of the diagonal of the Green’s function in reciprocal space. By demonstrating the uniqueness of the diagonal in describing physical systems and developing techniques to extract valuable information from it, our research opens up new avenues for exploring frequency-dependent effects in physical systems. This could also lead to more efficient algorithms for simulating electronic structure and dynamics, reducing computational costs and storage requirements, and enabling the study of larger and more complex systems.
Moreover, the project has direct relevance to photovoltaic applications by enhancing our understanding of charge transfer dynamics in solar cells. By investigating non-adiabatic and correlation effects in photovoltaic systems, the project contributes to the development of more efficient and functional solar devices. Insights gained from the study of charge separation dynamics could lead to the design of novel materials and interfaces optimized for solar energy conversion, ultimately advancing the design of sustainable energy technologies.