Relativistic Framework for Attosecond Pump-Probe Induced Dynamics

Project Information

RAPPID

Grant agreement ID: 101152113

DOI

10.3030/101152113

Project terminated on 31 March 2026

EC signature date 22 April 2024

Start date 1 August 2024

End date 31 July 2026

Funded under

• Marie Skłodowska-Curie Actions (MSCA)

Total cost

No data

EU contribution

€ 165 059,52

Coordinated by

UNIVERZITA KOMENSKEHO V BRATISLAVE
Slovakia

Periodic Reporting for period 1 - RAPPID (Relativistic Framework for Attosecond Pump-Probe Induced Dynamics)

Reporting period: 2024-08-01 to 2026-07-31

Summary of the context and overall objectives of the project

Recent advances in attosecond laser technology and ultrafast X-ray spectroscopy allow direct observation of electron dynamics in molecules and materials on their natural timescale. Modern pump–probe experiments can probe charge transfer, ionization processes, and ultrafast changes in molecular chirality. However, the interpretation of these experiments requires theoretical methods capable of describing relativistic effects, non-equilibrium electron dynamics, and strong light–matter interactions in a computationally efficient way, particularly for heavy-element systems where spin–orbit effects are essential.

The primary objective of the RAPPID project is to develop an open-access relativistic real-time time-dependent density functional theory (RT-TDDFT) framework for simulating out-of-equilibrium processes observed in attosecond pump–probe spectroscopies. The project will combine relativistic exact two-component Hamiltonians with semiclassical electron–nuclear Ehrenfest dynamics approach to enable simulations beyond the Born–Oppenheimer approximation.

A central component of the project is the modern atomic mean-field exact two-component (amfX2C) Hamiltonian, which achieves near four-component relativistic accuracy at a fraction of the computational cost, enabling simulations of chemically realistic systems in both valence and core energy regions. The developed methodology will be applied to time-resolved X-ray circular dichroism (TR-XCD), charge-transfer dynamics, and related ultrafast spectroscopies, including simulations beyond the electric-dipole approximation and spin–orbit-driven dynamics in open-shell systems.

All methods will be implemented in the open-access relativistic quantum-chemistry program ReSpect and made freely available to the scientific community. The project aims to provide the theoretical and computational tools necessary for interpreting next-generation ultrafast X-ray experiments and to strengthen expertise in relativistic quantum chemistry and computational spectroscopy.

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

A major achievement of the project was the implementation of relativistic RT-TDDFT methodologies within the open-access ReSpect program package, including circularly polarized laser fields, time-resolved electronic circular dichroism (TR-ECD) protocols, and sudden-ionization approaches for describing ultrafast non-equilibrium dynamics. Additional developments included the implementation of charge, spin, and current density analysis tools at nonrelativistic, amfX2C, and fully relativistic four-component Hamiltonian levels.

The project also resulted in the development of the open-access ReSpect Visualization Lab (RVL), a web-based platform for visualization and post-processing of real-time spectroscopic simulations. The developed methodologies were successfully applied to simulations of ultrafast spectroscopic phenomena and charge migration processes in representative heavy-element molecular systems.

The main outcomes of the project include:
* implementation of relativistic Ehrenfest RT-TDDFT methodologies and relativistic gradients;
* development of TR-ECD and ultrafast charge-migration simulation protocols;
* implementation of visualization and analysis tools for charge, spin, and current density dynamics;
* development of the open-access RVL visualization platform;
* publication of project results in peer-reviewed scientific journals.

Overall, the project significantly expanded the capabilities of the ReSpect program for simulations of relativistic ultrafast spectroscopy and non-equilibrium electron dynamics.

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)

The project delivered new methodologies and software tools for relativistic simulations of ultrafast electronic and spectroscopic processes in heavy-element systems. The main results include the implementation of relativistic real-time TDDFT methodologies, Ehrenfest-type electron–nuclear dynamics, circularly polarized laser-field protocols, sudden-ionization approaches, and analysis tools for charge, spin, and current density dynamics within the open-access ReSpect program package. The project also resulted in the development of the ReSpect Visualization Lab (RVL), a web-based platform for visualization and post-processing of real-time spectroscopic simulations.

These developments significantly expand the capabilities of relativistic quantum chemistry for simulations of modern ultrafast spectroscopies, including time-resolved electronic circular dichroism and charge migration dynamics. The developed methodologies provide computationally efficient approaches for studying non-equilibrium processes in heavy-element systems where relativistic and spin–orbit effects are essential.

The project is expected to contribute to computational spectroscopy, relativistic quantum chemistry, and ultrafast science by supporting interpretation of next-generation pump–probe and X-ray spectroscopy experiments. Future uptake of the project outcomes will require continued methodological development, benchmarking, and access to HPC infrastructures for large-scale simulations. The open-access nature of ReSpect and RVL ensures broad availability of the developed tools to the international scientific community.