Frequency-resolved ultrafast electron diffraction: visualizing vibrational dynamics in frequency- and real-space

Ultrafast electron diffraction (UED) provides direct information on changes in molecular structure following photoexcitation. However, identifying the individual vibrational motions contributing to these structural dynamics remains challenging from time-dependent electron scattering and pair distribution functions alone, particularly when multiple vibrational motions contribute over similar internuclear distances. Moreover, the ∼100 fs temporal resolution of current gas-phase UED experiments further limits the vibrational dynamics that can be resolved. In this work, we introduce frequency-resolved UED, where Fourier transformation of the time-dependent difference pair distribution function (ΔPDF) along the pump-probe delay axis gives a two-dimensional frequency-distance representation of the photoinduced structural dynamics. To demonstrate the utility of frequency-resolved UED, we study the ultrafast vibrational dynamics in allene and its methylated derivative 1,2-butadiene following photoexcitation to its S₁(ππ*) state at 200 nm. We simulate the electron scattering signals from previously-published ab initio multiple spawning (AIMS) trajectories (S. P. Neville et al., J. Chem. Phys., 2016, 144, 014305). Through the frequency-distance representation, we identify the CC stretching and CCC bending motions in both molecules and their internuclear distances over which these frequency components contribute. We further separate overlapping CH₂ vibrational motions and identify contributions from multiple vibrational frequencies at the same internuclear distance. We show the delay times at which specific frequency components contribute during the excited-state dynamics by changing the pump-probe delay range used for the Fourier transform of the ΔPDF signal. In both molecules, the CCC bending motion contributes predominantly before substantial S₁ → S₀ population transfer occurs by 70-90 fs, whereas the CC stretching motion persists at all delays. We find that methyl substitution reduces the CC stretching and CCC bending frequencies, while an additional frequency component appears in 1,2-butadiene and contributes primarily during the first 90 fs. Finally, we investigate the impact of the total instrument response function (IRF) on the retrieval of these frequency components and show the importance of reaching sub-20-fs, and ultimately few-femtosecond, temporal resolution. Frequency-resolved UED therefore provides a route to identify the vibrational frequencies that contribute to photoinduced structural dynamics, the internuclear distances associated with these frequencies, and the reaction times at which they are present.