Improving Gaussian Wavepacket Propagation for Non-adiabatic Molecular Dynamics based on a Rigorous Error Analysis

• Applicant: Dr. Antonia Freibert
• Subject Area: Theoretical Chemistry: Electronic Structure, Dynamics, Simulation
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 567563701

This project addresses the numerical challenges of quantum dynamics simulations by integrating rigorous error analysis to enable the precise and efficient treatment of complex chemical systems using Gaussian wave-packet propagation. A key focus is on improving the variational multi-configurational Gaussian (vMCG) method and its direct dynamics variant (DD-vMCG), which are particularly promising for simulating photo-excited molecular responses. However, these methods face efficiency issues due to approximations in the integration schemes and basis set expansions. This project aims to enhance the accuracy and efficiency of (DD-)vMCG by implementing a posteriori error estimates, thereby developing new adaptive time step integration and dynamic basis expansion schemes. Additionally, we will implement error estimates for expectation values in quantum dynamics simulations, which are crucial for linking simulations to spectroscopic observables. Benchmark calculations will be conducted on four molecular systems, each representing different photochemical mechanisms, providing a consistent comparison set for other research groups. By bridging the gap between mathematics and theoretical chemistry, this project aims to significantly advance quantum dynamics simulations. This will enable more accurate and efficient studies of fundamental chemical processes and promote the broader dissemination and adoption of enhanced quantum dynamics methods through the project’s interdisciplinary approach. To ensure optimal outcomes during the mathematically intensive phases of the project, several short visits are planned at the Department of Mathematics at the Technical University of Munich.

• DFG Programme: WBP Fellowship
• International Connection: United Kingdom
• Host: Professor Dr. Graham Worth