Theoretical framework for serial femtosecond crystallography in the presence of non-Born-Oppenheimer effects

Serial femtosecond crystallography (SFX) is a powerful technique for studying ultrafast structural dynamics in matter. However, the analysis of SFX data is challenging and would benefit from a systematic theoretical framework. By employing a quantum-electrodynamics approach, we demonstrate that conventional SFX practices are not only intuitively plausible but also firmly grounded in well-established principles. We show that standard SFX assumptions remain valid even when non-Born-Oppenheimer effects near conical intersections are significant. Through a modal decomposition of diffraction signals in reciprocal space, we derive a corresponding decomposition of the electron density in real space, valid in the limit of small pump excitation probability. This result justifies a key assumption made in a recent study [A. Hosseinizadeh et al., Nature (London) 599, 697 (2021)]. Remarkably, we find that the number of structural modes contributing to the SFX signal near conical intersections depends solely on the number of electronic states involved, regardless of the number of nuclear degrees of freedom. Our work establishes a foundation for accelerating the structural inversion of time-resolved SFX data and provides a rigorous theoretical basis for interpreting ultrafast structural dynamics.