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, but identifying the individual vibrational motions contributing to these dynamics remains challenging. Here, we introduce frequency-resolved UED, where Fourier transformation of the time-dependent difference pair distribution function ($\mathrm{\Delta }$PDF) gives a two-dimensional frequency-distance representation of the structural dynamics. We apply this approach to allene and 1,2-butadiene following photoexcitation to the $S_1(\pi {\pi }^{\ast })$ state at 200 nm, using electron scattering signals simulated from previously-published ab initio multiple spawning trajectories (S. P. Neville et al., J. Chem. Phys., 2016, 144, 014305). We identify C=C stretching and CCC bending motions and the internuclear distances over which they contribute, and separate overlapping CH${}_2$ vibrational motions. By changing the pump-probe delay range used for the Fourier transform, we identify when specific frequency components contribute during the excited-state dynamics. Methyl substitution reduces the C=C stretching and CCC bending frequencies and introduces an additional frequency component in 1,2-butadiene during the first 90 fs. We further show the importance of sub-20-fs, and ultimately few-femtosecond, temporal resolution for retrieving these frequency components. Frequency-resolved UED therefore provides the vibrational frequencies, internuclear distances, and reaction times associated with photoinduced structural dynamics.