Simulating electronic dynamics with Quantum Trajectories by combining exact factorization and Density Functional Theory

Project Information

QT-DFT

Grant agreement ID: 101104947

DOI

10.3030/101104947

Project closed

EC signature date 13 July 2023

Start date 1 October 2023

End date 30 November 2025

Funded under

• Marie Skłodowska-Curie Actions (MSCA)

Total cost

No data

EU contribution

€ 200 141,89

Coordinated by

CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
France

Periodic Reporting for period 1 - QT-DFT (Simulating electronic dynamics with Quantum Trajectories by combining exact factorization and Density Functional Theory)

Reporting period: 2023-10-01 to 2025-11-30

Summary of the context and overall objectives of the project

Understanding and predicting how electrons move inside atoms, molecules or materials is essential for the development of clean-energy technologies, photovoltaic devices, efficient catalysts, and emerging quantum technologies. Many of these processes happen on attosecond to femtosecond timescales and require theoretical tools that can describe fast, correlated electronic motion accurately and at a feasible computational cost.
Today, the most widely used method for electronic-structure simulations is Density Functional Theory (DFT), and its time-dependent extension (TDDFT). While highly successful, standard approximations often fail in situations where electronic motion is strongly correlated—such as molecular dissociation, charge transfer, ionization, and relaxation of electronically excited states. In these scenarios, key features of the exact Kohn–Sham potential, such as peaks and steps, are essential for a correct description but are not captured by existing approximations.
The QT-DFT project set out to address these long-standing challenges by combining insights from two powerful theoretical frameworks:
Exact Factorization, which provides a rigorous way to separate parts of a many-electron wavefunction and identify the potentials that govern electronic dynamics; and
Trajectory-based quantum algorithms, originally developed for electron–nuclear coupled motion, adapted here to the purely electronic problem.
The project pursued three overarching objectives:
(O1) Develop a new density-functional approximation able to capture peaks and steps in the Kohn–Sham potential during bond breaking.
(O2) Explore, for the first time, the electronic vector potential arising from the factorization of complex electronic wavefunctions, a quantity expected to play an essential role in excited-state dynamics.
(O3) Extend a state-of-the-art mixed quantum–classical algorithm so that it can be applied directly to electrons, opening a new pathway to simulate ultrafast purely electronic processes.
By improving our ability to simulate excited-state phenomena central to photochemistry, attosecond spectroscopy, and quantum materials, the project contributes to EU priorities in sustainable energy, advanced materials, and next-generation digital technologies.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

The research carried out during the fellowship produced three key scientific outcomes, including two major planned milestones and one additional peer-reviewed result linked to the project’s aims.
Milestone M1.1 – New density-functional approximation for dissociation (achieved)
The project successfully developed and demonstrated an orbital-independent approximation capable of reproducing the signature peaks and steps of the exact Kohn–Sham potential during molecular dissociation. The proof-of-principle was published as:
Giarrusso & Agostini, J. Chem. Phys. 162, 091103 (2025).
This represents a significant advance toward overcoming one of DFT’s best-known failures and provides a foundation for future functional development.
Milestone M2.1 – First explicit calculation of the electronic vector potential (achieved)
The project performed the first explicit calculation of the electronic vector potential emerging from the exact factorization of a complex electronic wavefunction. This work clarifies the structure and physical meaning of this previously unexplored quantity and opens up a new line of investigation for excited-state and electronic dynamics.
Published as:
Giarrusso, Gori-Giorgi & Agostini, ChemPhysChem 25, e202400127 (2024).
Progress toward Milestone 3 – Adapting the CTMQC code to electrons (substantial progress)
The intended extension of the Generalized Coupled-Trajectory Mixed Quantum-Classical (G-CTMQC) algorithm to the fully electronic case proved numerically extremely challenging. Unlike the electron–nuclear problem, electrons all have the same small mass, and replacing the nuclear mass by an electronic one in the code leads to instabilities and convergence issues.
Despite these difficulties, major preparatory work was completed:
the bottlenecks were identified and analysed;
alternative propagation strategies were explored;
the insights gained have direct relevance for polaritonic chemistry, where photons play a role analogous to electrons and have an effective mass of 1.
This effort has generated new research directions that will continue beyond the fellowship.
Additional relevant scientific output
The fellow also co-authored a publication on an excited-state-specific Kohn–Sham formalism for the asymmetric Hubbard dimer:
Loos & Giarrusso, J. Chem. Phys. 162, 144104 (2025).
While not originally foreseen as a deliverable, this work directly contributes to understanding excited-state DFT—one of the core scientific themes of the project.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

QT-DFT generated results that push the theoretical frontier in several directions:
i) Advances in density-functional theory
The newly developed proof-of-principle approximation demonstrates, for the first time, that peaks and steps—essential features previously considered inaccessible to efficient DFT models—can be reproduced without orbitals. This opens the door to a new generation of non-empirical, physically grounded functionals for challenging processes such as charge transfer and bond breaking.
ii) New fundamental insights in exact factorization
The explicit computation of the electronic vector potential represents a conceptual leap beyond existing literature, which had only addressed the nuclear counterpart. This establishes a foundation for incorporating vector potentials into excited-state theories, potentially improving simulations of ultrafast electronic phenomena.
iii) Towards a new simulation paradigm for electrons
Although the full implementation of the electron-CTMQC scheme requires further developments, the project established the theoretical framework and practical understanding necessary for its future realization. Success in this direction would enable simulations where one electron follows trajectory-like dynamics while the remainder are treated quantum-mechanically—an unprecedented capability with major implications for attosecond science.

Needs for further uptake
To fully exploit these advances, future work will require:
improved numerical strategies for stable propagation of light-mass degrees of freedom;
further theoretical development of approximate vector potentials;
integration with existing TDDFT and quantum-chemistry software;
exploration of new applications in photochemistry and polaritonic chemistry;
possible medium-term collaborations for code development and benchmarking.