Ultrafast electronic relaxation pathways of the molecular photoswitch quadricyclane

The light-induced ultrafast switching between molecular isomers norbornadiene and quadricyclane can reversibly store and release a substantial amount of chemical energy. Prior work observed signatures of ultrafast molecular dynamics in both isomers upon ultraviolet excitation but could not follow the electronic relaxation all the way back to the ground state experimentally. Here we study the electronic relaxation of quadricyclane after exciting in the ultraviolet (201 nanometres) using time-resolved gas-phase extreme ultraviolet photoelectron spectroscopy combined with non-adiabatic molecular dynamics simulations. We identify two competing pathways by which electronically excited quadricyclane molecules relax to the electronic ground state. The fast pathway (<100 femtoseconds) is distinguished by effective coupling to valence electronic states, while the slow pathway involves initial motions across Rydberg states and takes several hundred femtoseconds. Both pathways facilitate interconversion between the two isomers, albeit on different timescales, and we predict that the branching ratio of norbornadiene/quadricyclane products immediately after returning to the electronic ground state is approximately 3:2.


FEL and UV Beam Parameters
The experiment was conducted at the Low Density Matter (LDM) beamline (Svetina et al., 2015) at the Free-Electron laser Radiation for Multidisciplinary Investigations (FERMI) at the Elettra Synchrotron facility in Trieste, Italy (Allaria et al., 2012).This seeded FEL provides bright XUV and soft X-ray photons at sub-100 fs pulse durations.The FEL pulses are emitted at harmonics of an input seed laser (itself the 3 rd harmonic of the fundamental infrared laser source) that pre-bunches the electron beam in a downstream undulator, triggering coherent emission of XUV light rather than relying on shot-noise to initiate the emission process, as is the case in FELs relying on self-amplified spontaneous emission (SASE).Seeded FELs thus deliver high-intensity narrow-bandwidth XUV pulses.The same laser system that generates the seed laser beam is also used to generate the (UV) pump pulses used in the experiment, thus minimizing shot-to-shot timing jitter between the UV and XUV pulses (Cinquegrana et al., 2021).This setup therefore provides good temporal and spectral resolution that have proven effective in studying the UV-induced ultrafast dynamics of gas-phase molecules via valence photoelectron spectroscopy (Pathak et al., 2020;Squibb et al., 2018;Travnikova et al., 2022).For the experiment reported here, the XUV photon energy was 18.97 eV with a bandwidth of 24 meV (FWHM), selected to be below the ionization energy of the helium carrier gas used for the molecular beam.The UV-pump pulse had a central wavelength of 200.6 nm with a bandwidth of 0.6 nm.The 4th harmonic generation setup for obtaining these pulses was based on an original common-path scheme (Susnjar et al., 2023), providing a very high stability.The beam diameter of the UV and XUV in the interaction region was 80 µm (FWHM) and 40 µm (FWHM), respectively.Both the FEL and the UV laser operated at 50 Hz, with the UV laser being blocked every other shot by inhibiting the trigger of the Ti:Sapphire amplifier to allow for interleaved recording of the "unpumped" spectra for subtraction (see SI Section 1.4).
A Sn filter and a gas attenuator, filled with Ne at 9.2 x 10 -2 mbar, in the beamline were used to suppress any higher harmonics of the FEL.For the data shown here, the average FEL pulse energy behind the filter and attenuator was »70 µJ, as monitored on a single-shot basis via a nitrogen gas-monitor that converts the measured nitrogen ion yield to pulse energy (Zangrando et al., 2015).This yields an estimated XUV pulse energy on target of approximately 15 µJ when accounting for the beamline transmission, which is approximately 22% at a photon energy of 20 eV (Svetina et al., 2015).The XUV pulse intensity was chosen such that it provided the highest possible count rate while minimizing multiphoton ionization, broadening of the photoelectron spectra due to space charge, and saturation of the photoelectron detector.
The XUV beam was focused into the LDM end-station by a custom Kirkpatrick-Baez (KB) active-optic focusing system (Raimondi et al., 2013).The system consists of two grazing-incidence mirrors, the first one focusing the beam in the vertical direction, while the second mirror focuses in the horizontal direction.The curvature of both mirrors is fully tunable since their substrate bending is fully assisted by piezo actuators (Manfredda et al., 2022), such that the focal spot size can be tailored to the experimental requirements by monitoring the spot profile on a (removable) Ce:YAG scintillator mounted inside the LDM end-station.Before the two grazing-incidence mirrors, a pair of (horizontal and vertical) slits spatially filters out spurious tails surrounding the main spot of the incoming beam and to select the desired working areas of the downstream focusing optics.
The pulse energy of the UV pulses was controlled via a /2 waveplate and monitored on a shot-by-shot basis with an energy meter.It was recorded in the shot-by-shot data stream along with the XUV pulse energy and the single-shot electron spectra.To determine the optimal UV pulse energy, photoelectron spectra were measured at a delay of 0.5 ps as a function of UV pulse energy, as shown in Supplementary Figs.1A and 1B.The resulting electron yield as a function of UV pulse energy for several regions of interest is shown in Supplementary Figs.1C and 1D.For the data shown in this manuscript, a pulse energy of 10 µJ was chosen to yield a reasonably high excitation fraction while safely remaining in the single-photon excitation regime, as demonstrated by the linearity of the excited-state electron yield as a function of UV pulse energy.For comparison, the scans were repeated with a UV pulse energy of 2 µJ, which resulted in the same observations as reported in the main text but with lower statistical significance (see Supplementary Fig. 1).
The FEL-UV temporal instrument response function was determined by recording the time-dependent ion yield from UV-ionization of electronically excited helium atoms produced by resonant 1s → 4p excitation with the FEL undulator set to the 5 th harmonic of the seed, 23.72 eV.The ion yield and fit to the data are shown in Supplementary Fig. 3, yielding a Gaussian instrument response with  = 79  (186 fs FWHM).We note that since this cross-correlation measurement was done at the very beginning of the beamtime, more than 24 hours before the data shown in the main text were recorded, the time zero (corresponding to temporal overlap of the UV and XUV pulses) for the QC scan was determined from the fit of the depletion signal shown in Supplementary Fig. 10.Applying that same time zero to the He scan yields a temporal offset of 83 fs between the two, which we attribute to a temporal drift in the time between the two measurements.We carefully analyzed the QC scan data recorded over several "loops" but did not observe any temporal drifts over the time period of those scans.
Supplementary Figure 2: Fluence-dependence of the pump-probe signal.(A) Photoelectron spectra of QC in the excited-state region (without subtraction of the "UV-off" signal) at different UV pulse energies at a delay of 0.5 ps.(B) Same as (A) but shown for the entire binding energy range that was recorded (i.e., including the ground-state region) and with subtraction of the "UV-off" signal.(C), (D) Integrated electron yield in the indicated binding energy regions as a function of UV pulse energy.The data in the main text were acquired with 10 µJ UV pulse energy.The red data points in (D) were scaled by a factor of -0.2 to fit on the same scale as the blue data points.The data and error bands in (A), (B) and error bars in (C), (D) represent the mean value and the 68% confidence interval obtained from a bootstrapping analysis (see Methods).

Supplementary Figure 3: Characterization of the pump-probe instrument response function.
To estimate the temporal resolution () and determine the delay-stage position corresponding to time overlap (t0), a supersonic beam of helium atoms was excited at 23.72 eV photon energy (generated by the fifth harmonic of the FEL seed laser) to the 1s → 4p resonance and subsequently ionized by the UV pulse at 200.6 nm.The resulting ion yield was plotted as a function of pump-probe delay.To model the process, a two-component fit was applied to the He + signal (see Eq. 1).One component models the (1+1') resonant ionization described above via the convolution of a step function with a Gaussian (i.e., a Gaussian error function), the other models the contribution from a non-resonant (1+1') ionization via a pure Gaussian:

Magnetic Bottle Spectrometer
The photoelectron spectra were measured using a magnetic bottle electron spectrometer (MBES) with a »2-meter flight tube.At the end of the flight tube, electrons were detected by a 40-mm-diameter MCP detector operated at 2200 V bias voltage and with 2400 V applied to the detector anode.The MBES configuration was identical to the one described in Squibb et al. (Squibb et al., 2018), but differs from the one used by Pathak et al. (Pathak et al., 2020), which had a hollow magnet to allow for simultaneous ion detection.The solid-magnet configuration was chosen for the present experiment since it has slightly better (nominal) kinetic energy resolution.
For the data presented here, the solenoid current was set at 0.9 A, and a nominal retardation voltage of 11 V was applied to the drift tube to increase the kinetic energy resolution of the photoelectrons of interest.Combined with a small (1 V) bias voltage on the magnet, this resulted in an effective retardation potential of 9.7 V, according to our kinetic energy calibration.Additional data were also taken at lower and higher retardation voltages, and one example of a spectrum taken without retardation is shown in Supplementary Fig. 4. From this, a kinetic energy resolution of '( ( ~ 0.03 was estimated for electrons with »10 eV kinetic energy.This was estimated by comparing the photoelectron spectrum of QC measured without retardation voltage to a high-resolution spectrum from the literature recorded with synchrotron radiation at a photon energy of 95 eV (Palmer et al., 2020).

Supplementary Figure 4: Comparison of the measured photoelectron spectra with literature & energy resolution estimate.
To estimate the energy resolution of our experiment, the measured QC photoelectron spectrum at 19 eV photon energy without retardation applied to the magnetic bottle spectrometer (blue) is compared to a high-resolution photoelectron spectrum (Palmer et al., 2020) at 95 eV photon energy (thin grey line).In order to estimate the energy resolution of the MBES spectrometer, the reference spectrum is convolved with a Gaussian such that it resembles the MBES spectrum.A convolution with a Gaussian of width '( ( ~ 0.03 yields a satisfactory resemblance (thick black line).
During the experiment, the liquid QC sample was kept in a stainless-steel reservoir and introduced into the ultrahigh vacuum chamber as a pulsed molecular beam using an Evan-Lavie valve with a 26 µs opening time and using helium at a backing pressure of 6 bar as carrier gas.
Supplementary Figure 5: 1 H NMR of the quadricyclane sample with color coding of QC and NBD signals.

Experimental data analysis
As described in the main text, photoelectron spectra were recorded on a single-shot basis.The analog signals from the MCP detector were saved by a 1-GHZ digitizer (CAEN, model VX1751) with 1-ns time bins.FEL pulses are tagged, and their index ("bunch number") is recorded in the data stream for unambiguous event sorting, such as separating the shots where the UV pump was blocked (all odd indices).After sorting events by the delay, the shot-integrated waveforms for a given delay were normalized by the corresponding shot-integrated pulse energies, and the normalized signal from shots without the UV pump pulse was subtracted.To account for any instability beyond pulse energy fluctuations, these values were divided by the total electron yield in the unpumped shots at each delay: Here,  ) () is the processed data at digitizer bin b and delay .Qbi and Pi are the analogue signal (in arbitrary analog-to-digital units) and pulse energy (in units of ) corresponding to shot  .The pumpprobe delay was scanned between -0.5 to 1.0 picoseconds with varying step sizes.Near pump-probe overlap (-0.25 to 0.25 ps), steps of 25 fs were taken, while steps of 50 fs were taken outside of this range.At each delay value, 3000 shots were acquired.This scan range was repeated four times for the data presented in this paper.
Supplementary Figure 6: Time-dependent photoelectron spectra of QC with and without pump pulse.During the pump-probe scans, the UV laser was present only for every second FEL shot, such that data with and without pump pulse were recorded in parallel.All data presented in the main text are shown as a difference signal of all the accumulated "pump on" (A) minus "pump off" (B) spectra at each delay point.Note the log scale for the color map in the above spectra to show the weak pump-probe signal in the nonsubtracted spectra.This figure is the same as Extended Data Fig. 1.
At delay values where the XUV probe precedes the UV pump pulse, subtle features in the difference maps attributed to space-charge broadening and shifting (Zhou et al., 2005) are observed.We assign this to additional space-charge when the UV pulses are present since they create additional photoelectrons by multiphoton ionization.This effect results in a constant difference feature in the region of the groundstate photolines, as shown in Supplementary Fig. 7. Since the space-charge lifetime is on the order of nanoseconds (Zhou et al., 2005), the spurious difference signal due to space charge was removed from the two-dimensional photoelectron spectra by subtracting the difference spectra averaged over the first 5 delay bins (i.e., before time-zero) from each individual delay bin in the 2D map.
Supplementary Figure 7: Space charge effects.2-D difference spectrum as shown in Fig. 2A of the main text but without the space-charge correction.The small, persistent difference feature around 8-9 eV BE is attributed to a line broadening and shifting due to space charge.
Supplementary Figure 8: Time-dependent photoelectron difference spectra of QC in the excited-state region at different pump-probe delays.This figure is the same as Extended Data Fig. 2.

Fitting of the time-dependent electron yields
A variety of fit models were applied to describe the time-dependent electron yields, shown, e.g., in Fig. 2(D) and 2(E) of the main text and Supplementary Fig. 9 below, including global fitting routines and various kinetic models.Since the resulting fit parameters depended strongly on the fit model, we opted to show below the results of the most basic model, namely the independent fit of each line-out in the excitedstate region with an exponential decay convolved with a Gaussian:   16) 66 (4) -7 ( 7) The time-dependent electron yield in the ground-state region, shown in Supplementary Fig. 11, displays an enhancement at low BE, which is also fitted by Eq. ( 3), and a depletion and recovery at higher BE, which is modelled with two contributing terms given in Eq. ( 4): a prompt decay and an exponential rise, both convolved with the instrument response.

Electronic Structure
QC presents a challenge to electronic structure methods due to the variety of states and the large configuration space explored in the reaction.Supplementary Fig. 12 shows the three molecular geometries discussed in the main text (QC to MECI to NBD).The mean carbon separation rcc, identified as the 'wing-flapping' (opening) motion, increases uniformly from QC to the MECI and then onwards to NBD.
QC (rcc=1.51Å) MECI (rcc=1.98Å) NBD (rcc=2.47Å) Supplementary Figure 12: Optimized geometries.The molecular geometries for QC, NBD, and the MECI, optimized using RMS(9)-CASPT2(2,6)/6-31G*+D level theory.The geometries are shown looking down the z-axis (as shown in Figure 1 in the main manuscript).Note the rhombic nature of the MECI geometry, which does not lie on the totally symmetric displacement between the two equilibrium geometries of QC and NBD.This figure is the same as Extended Data Fig. 3.
For the dynamics simulations, a viable electronic structure model was devised which captures the key features of the molecular system while remaining computationally feasible.The method chosen is rotated multi-state (RMS-CASPT2), a multi-state perturbative correction to the CASSCF method recently developed by Battaglia and Lindh (Battaglia & Lindh, 2021).This constitutes an effective compromise between the well-known multi-state (MS-CASPT2) and extended multi-state (XMS-CASPT2) variants.The method accounts for the multiconfigurational character of the excited states and recovers a sizeable amount of the dynamic correlation in the system.The key aspects to consider are the basis and the active space, discussed in the following.
We also point out that the Sn numbering of the adiabatic electronic states is linked to the electronic structure model used.For example, the V/3px state in QC (at 7.53 eV) is not the true experimental S5which is likely a 3d state -but is needed within the confines of our model.The model includes all electronic states relevant to the dynamics, but excludes states high in energy that are not seen in the dynamics, for example the 3d Rydberg states and some valence states in NBD (see later discussion).

Character of states
To justify the electronic structure model, we make comparisons of potential energy curves (PECs) along the same set of linear interpolation in internal coordinates (LIICs) as shown in Fig. 3 in the main text.The PECs join QC to the MECI, and then onwards to the NBD, using the geometries shown in Supplementary Fig. 12 which have been optimized at the RMS-CASPT2(2,6) level of theory.We use the same coordinates in all PEC comparisons.Firstly, we explore the character of the states across the LIIC.The method used calculated 9 roots, only 6 of which are seen with significant population in the dynamics.The primary reason for this is the inclusion of a state with double excitation character, the inclusion of which is important for a correct description of the conical intersection.Supplementary Fig. 13 shows the PECs with the dominant state characters indicated along the LIIC for all 9 roots.As the energies plotted come from adiabatic states, the exact nature of the states changes as a function of the geometry, and so we have indicated only the approximate character.Previous studies (Valentini et al., 2020) have used a (4,8) active space to describe this system, containing four valence orbitals plus the 3s and three 3p Rydberg orbitals.To achieve better stability in the simulations and improve computational efficiency, we moved to a (2,6) active space, removing the highest and lowest energy valence orbitals.Pictures of these active space orbitals are shown in Supplementary The RMS-CASPT2 PECs for both of these active spaces are shown in Supplementary Fig. 16.The agreement is good for most states, but the highest state, S6, is described qualitatively differently by the (4,8) and (2,6) active spaces.This state is mostly of doubly-excited character and is only important for Rydberg dynamics on the NBD side of the dynamics, lying higher in energy in QC-like geometries.As the Rydberg dynamics is mostly constrained to the QC side, this state does not significantly affect the dynamics.

Supplementary
Supplementary Table 5: Basis sets primitives and contraction coefficients for the additional S and P basis functions (Lorentzon et al., 1994).This basis gives an acceptable level of agreement compared to standard basis sets for Rydberg calculations, e.g.aug-cc-pVDZ (see Supplementary Fig. 17).This provides a significant computational saving, allowing the calculations to use the dynamically correlated RMS-CASPT2 method.The comparison between 6-31G*+D and aug-cc-pVDZ is shown in Supplementary Fig. 17.There is an acceptable level of agreement between the two sets of PECs.The greatest difference is seen in terms of the relative description of the valence states and Rydberg manifold.This could contribute to the difference in Rydberg lifetimes observed in the paper and relates to the effective strength of Rydberg/valence coupling.
of the photoelectron spectra in the excited-state region.Panel (A) shows the photoelectron spectrum integrated over all delays.The integrated photoelectron yield in the regions marked in panel (A) is fitted with an exponential decay convolved with a Gaussian, see Eq. (3), as shown in panels (B).The data and error bars in (B) represent the mean value of approximately 40,000 single-shot digitizer traces and the 68% confidence interval obtained from a bootstrapping analysis (see Methods).The resulting fit parameters are summarized in Supplementary 4)Supplementary Figure11: Fitting of the photoelectron spectra in the ground-state region.(A) Photoelectron difference spectrum in the BE region 7.0 -9.5 eV integrated over all delays.(B) The integrated photoelectron yield in the region corresponding to the photoproducts, marked in red in panel (A), is fitted with Eq. (3).(C) The depletion and recovery of the region corresponding to the (cold) QC ground-state, marked in blue in panel (A), is modelled with two contributions given in Eq. (4): a prompt decay (dashed light blue) and an exponential rise (solid blue line), both convolved with the instrument response.The data and error bars in (B), (C) represent the mean value of approximately 40,000 singleshot digitizer traces and the 68% confidence interval obtained from a bootstrapping analysis (see Methods).The resulting fit parameters are summarized in Supplementary

Figure 13 :
State characters.LIIC for all states considered in the RMS(9)-CASPT2(2,6)/6-31G*+D model, with approximate character labelled (color coded).Each state is labelled by its principal character (e.g., 3py indicates a state of mostly HOMO →3py character).DE indicates a doubly excited state, with the character of the orbital(s) excited into in parentheses.In all comparisons that follow hereafter, we show only the lowest 7 adiabatic states (6 which are important to the dynamics and one additional state for reference).This figure is the same as Extended Data Fig.4.The comparison between CASSCF and RMS-CASPT2 PECs is shown in Supplementary Fig.14.The dashed CASSCF curves are clearly quite different to the solid RMS-CASPT2 curves, especially in the Rydberg manifold.This is because diffuse Rydberg orbitals require less dynamic correlation than valence orbitals, and so in CASSCF, which has little dynamic correlation, the valence states are artificially raised in comparison to Rydberg states.RMS-CASPT2, which includes more correlation than CASSCF, therefore provides more balanced and thus accurate energies of the Rydberg states in relation to the valence states.Supplementary Figure14: Comparison of CASSCF and CASPT2.LIIC plot of RMS(9)-CASPT2(2,6) (solid lines) and SA(9)-CASSCF(2,6) (dashed lines) potential energy curves (PECs).The lowest seven states are shown, including the six states that participate in the dynamics and one additional state for comparison.The highest-energy state shown (S6, maroon color) is of double excited character.It can be clearly seen that the Rydberg manifold, i.e., the comparatively 'flat' PECs between in the energy range 4 £ E £ 6 eV, is systematically lower in energy when using CASSCF compared to RMS-CASPT2.

Fig
space orbitals calculated at QC.The active space consists of 2 electrons in a space of 2 valence and 4 Rydberg orbitals.Extending the active space to include one additional pair of virtual and occupied orbitals creates the (4,8) active space of Valentini et al.(Valentini et al., 2020).The two orbitals that extend the (2,6) active space are identified by a (4,8) in their caption.The isosurface cutoff value has been adjusted such that 80% of the total density is shown for each orbital, and Rydberg orbitals are shown zoomed out to fully render their spatial extent.A rendering of the molecule is included in each frame.This figure is the same as Extended Data Fig.5.