Observation of the molecular response to light upon photoexcitation

The study investigates how electron density in a molecule redistributes immediately after photoexcitation—the first step underlying photochemical and photophysical processes. Using 1,3-cyclohexadiene (CHD) as a model system, the authors aim to directly observe changes in electron density upon excitation, rather than inferring excited-state character indirectly from spectroscopy or secondary structural effects. Advances in x-ray free-electron lasers (XFELs) enable ultrafast, non-resonant x-ray scattering to probe electron distributions with high temporal and spatial resolution. The authors excite CHD to a long-lived (≈200 fs) 3p Rydberg state using 200 nm light, where structural changes are minimal and electronic differences from the ground-state HOMO are pronounced, allowing clean identification of electronic-state signatures in the scattering data.

Prior ultrafast x-ray and electron scattering studies have resolved structural dynamics in molecules during vibrations and reactions, while theoretical work suggested sensitivity to electron-density changes upon excitation. Historically, excited states have been identified indirectly from spectroscopic transitions or via manifestations such as alignment with transition dipole moments or geometry changes of intermediates. A recent x-ray scattering study indicated that reproducing coherent vibrational motion required theoretical inclusion of electron-density changes, but those details were obscured by larger structural changes. CHD has been extensively studied: ring opening upon 267 nm excitation has been monitored using ultrafast x-ray and electron scattering, photoelectron spectroscopy, and x-ray spectroscopy. Electronic spectra and state populations for CHD Rydberg states are known from prior experimental and theoretical work, which inform the excitation scheme and theoretical modeling here.

Experimental: A time-resolved gas-phase non-resonant x-ray scattering experiment was performed at the CXI instrument of LCLS. CHD gas (~6 Torr in the interaction region) at room temperature was excited by 200 nm UV pulses (fourth harmonic of Ti:Sapphire, ~80 fs, ~1 μJ/pulse) and probed by 9.5 keV x-ray pulses (~30 fs) at 120 Hz. Pump and probe were collinear, with spot sizes ≈50 μm (laser) and ≈30 μm (x-rays). The excitation fraction was kept low (<10%; determined globally as 6.0%). Timing jitter was monitored by a spectrally encoded cross correlator (≈30 fs resolution). Scattered x-rays were recorded on a 2.3-megapixel CSPAD in vacuum; detector calibration and decomposition into isotropic and anisotropic components followed established procedures. The isotropic component was analyzed. Fractional difference signals ΔS(q, t) were computed from laser-on/off data to minimize background and noise. A sine transform of the difference signal yielded the real-space difference radial distribution function ΔRDF(r). Time-dependent signals were examined in q-windows 0.3–1.6 Å−1 and 1.7–2.5 Å−1 to separate electronic and nuclear contributions. The excited-state lifetime was extracted from scans over wider delays, comparing to a convolution of a Heaviside step with a Gaussian instrument function near time zero. Theoretical: Ground-state and cation-reference geometries were optimized with CASPT2 using CASSCF active spaces including valence π/π* and Rydberg orbitals: CASSCF(4,4)/aug-cc-pVDZ for neutral; CASSCF(3,4)/aug-cc-pVDZ for cation; followed by multi-state CASPT2 with a state-averaged CAS(4,8)-SCF over seven states. Diffuse Rydberg character was enhanced by uncontracted 3s/3p basis functions at the cation center of charge. A level shift of 0.3 Hartree avoided intruders. Elastic scattering patterns were computed via analytical Fourier transforms of Gaussian-based densities; inelastic contributions used tabulated atomic form factors. Signals for 3p_x and 3p_y were computed and combined in a 1:0.8 ratio (3p_z ≈ 0 initial population). Theoretical fractional difference signals ΔS_exc(q, R′) were decomposed into electronic and nuclear components without approximation by adding and subtracting I_X(q, R′).

• Direct experimental evidence of electron-density redistribution upon photoexcitation of CHD to the diffuse 3p Rydberg state was obtained.
• ΔRDF(r) at 25 fs shows depletion at small inter-electron distances (r < 3 Å) and increased probability at larger distances (4–9 Å), consistent with population of a diffuse excited orbital.
• The experimental fractional difference signal ΔS(q) at 25 fs matches the theoretical 3p-state prediction ΔS_3p(q, R⁺) with excellent agreement, including thermal geometry sampling; discrepancies at large q arise mainly from low photon counts at detector edges.
• Time-resolved analysis reveals a rapid onset in small-q (0.3–1.6 Å−1), dominated by changes in electron density, followed by a slower onset in large-q (1.7–2.5 Å−1), attributed to nuclear structural changes.
• The excited-state lifetime extracted from broader delay scans agrees with previous estimates of approximately 200 fs for the 3p state.
• Decomposition shows both nuclear and electronic contributions are of order ~4% in magnitude. The electronic 3p contribution is distinctly negative at low q (0–1.6 Å−1), whereas the nuclear contribution is small there and grows at larger q.
• As q → 0, the molecular ion signal approaches −4.5%, consistent with removal of 1 electron from 44 in CHD; for q > 1.0 Å−1 the ion and 3p signals are largely parallel, indicating dominance by core-electron effects.
• The electronic contribution of the 3p state is nearly geometry-independent: differences computed at two geometries are ~0.1%, at least an order of magnitude smaller than other effects.

The results directly address the core question of whether ultrafast, non-resonant x-ray scattering can resolve initial electron-density changes during photoexcitation. The observed ΔRDF and ΔS(q) unambiguously identify population of a diffuse 3p Rydberg state in CHD and separate electronic from nuclear contributions via q-space behavior. Excellent agreement with multi-state CASPT2-based predictions validates the theoretical approach and demonstrates that low-q scattering encodes electronic-state changes while high-q reflects nuclear geometry. The near geometry-independence of the 3p electronic signal suggests a simple interpretive framework for Rydberg-state dynamics: time evolution arises from nuclear motion plus an approximately constant electronic contribution. These capabilities offer a route to benchmarking electronic structure theory and to tracking coupled electronic and structural changes during photochemical reactions.

Ultrafast non-resonant x-ray scattering at an XFEL directly visualizes the initial electron-density redistribution upon optical excitation of CHD to a 3p Rydberg state. The experiment cleanly separates electronic and nuclear contributions, confirms theoretical predictions, and establishes that low-q scattering is a sensitive probe of electronic-state character. With anticipated improvements in XFEL performance and data-analysis methods, this approach is poised to yield accurate electron densities for ground and excited states and to monitor simultaneous electronic and structural dynamics during chemical reactions. Future work should extend to more complex molecules, higher time resolution, broader q-range coverage, and integration with advanced charge-density analysis.

• Minor discrepancies at large q are attributed to low photon counts at the detector edges, limiting accuracy of high-q features.
• The current time resolution and choice of a Rydberg state with minimal structural change preclude observation of coherent structural motion before ~200 fs; results rely on systems where electronic changes dominate over nuclear ones.
• Gas-phase, small, light-atom target (CHD) simplifies interpretation; generalization to larger or heavier-atom systems may require higher photon energies and improved statistics.
• The excitation fraction is small (≈6%), necessitating high-precision noise control (<0.1%) and extensive averaging.