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Ultrafast Photo‐ion Probing of the Ring‐Opening Process in Trans‐Stilbene Oxide

Abstract The ultrafast photo‐induced ring opening of the oxirane derivative trans‐stilbene oxide has been studied through the use of ultrafast UV/UV pump‐probe spectroscopy by using photo‐ion detection. Single‐ and multiphoton probe paths and final states were identified through comparisons between UV power studies and synchrotron‐based vacuum ultraviolet (VUV) single‐photon ionization studies. Three major time‐dependent features of the parent ion (sub‐450 fs decay, (1.5±0.2) ps, and >100 ps) were observed. These decays are discussed in conjunction with the primary ring‐opening mechanism of stilbene oxide, which occurs through C−C dissociation in the oxirane ring. The appearance of fragments relating to the masses of dehydrogenated diphenylmethane (167 amu) and dehydrogenated methylbenzene (90 amu) were also investigated. The appearance of the 167 amu fragment could suggest an alternative ultrafast ring‐opening pathway via the dissociation of one of the C−O bonds within the oxirane ring.


Simulations of under-sampled ultrafast decays
Pump-probe photoelectron investigations by Kotsina et al. have shown that when probing molecules with states that possess a lifetime shorter than the duration of the laser pulse used to investigate it, one can still observe a signal from this state, but it will be significantly undersampled compared to longer-lived states within the same system. [1,2] This led us to believe that the sharp narrow peak observed in the time-dependent signal of the parent ion ( Figure  4c), and, to a lesser extent, the 90 and 167 amu ions (Figure 4a and b, respectively), could be due to under sampling a very short-lived state in stilbene oxide.
To investigate the possibility that this feature was an artefact of under sampling a fast decay, a number of calculations were performed to simulate this possibility. This work started with the calculation of the second-order coherence function of two identical pulses, [3,4] which is analogous to a two-photon non-resonant auto-correlation signal, taking into account the bandwidth and non-negligible chirp of the laser pulses. When calculated, the second-order coherence function produces a fringe-resolved signal, like that in Figure S1, where the interference fringes in the center sit on top of a broader smooth background as expected for chirped pulses. [3,5] A low-pass fit can then be applied to the to the fringe-resolved signal to obtain the gaussian-like signal, which is similar to the signal that one would expect from an auto-correlation experiment. When a Gaussian curve is fitted to this low-pass signal, one can obtain the FWHM of the auto-correlation signal. Figure S1: Simulated signal from the second-order coherence function of a chirped pulse, showing the finge-resolved signal (blue) as well as the low-pass filter fit to the fringe-resolved signal (red). The insert shows the same signal zoomed-in over the -3 to 3 fs region to highlight the fringes of the signal. The example here is based on a 266 nm pulse, chirped enough that the low-pass filter fit of the auto-correlation is stretched to a FWHM of 430 fs.
For the simulation in question, the model laser pulse was based on a 266 nm pulse with an initial duration of ~35 fs. A chirp was then applied to the simulated pulse until the FWHM of the low-pass / auto-correlation signal was stretched to 430 fs, suggesting a pulse duration of 300 fs. This is equivalent to the auto-correlation signal seen in our dioxane experiment (see Experimental Section for details), and is the one explicitly depicted in Figure S1.
The fringe-resolved signal obtained in the simulation described above is what one would expect to see from a perfectly stable interferometer. However, whilst we expect the interferometer in our experiment is stable over the short time scale (i.e. the minutes/seconds needed to collect a single data point), we expect that there are small changes in the in the interferometer that occur over the course of the hours needed to collect the full data set. This is most likely due to either temperature changes or air movements within the lab, and this will ultimately affect the phase between the two pulses over the course of the experiment (N.B. There should be no pointing changes in the interferometer due to our virtual-focus feedback system). This ultimately would mean that whilst the specific fringes would eventually blur out, the individual data points that are collected throughout the experiment will still fall within the "interference envelope" that is loosely defined by the extremes of the peaks and troughs of the fringes that sit above and below of the low-pass signal. Given enough samples, the average of these individual data points from this quasi-stable interferometer will still tend to the low-pass signal.
To simulate this quasi-stable interferometer, a set of Gaussians were loosely fit to the peak and trough values of the fringe-resolved signal seen in Figure S1 to obtain the general shape of the time-dependent interference envelope. With this envelope described, we then looked to simulate an auto-correlation pulse overlap experiment using a set of pump-probe delays similar to what was used in our actual experiments. At each of these delays a random intensity value was chosen that fell within the time-dependent interference envelope. This random selection was repeated multiple times over the same set of delays, in a sense simulating what one would expect from the data collection of a pump-probe experiment that is repeated over the course of N samples (/runs) for the same set of delays. This random selection was weighted in such a way, so that as the number of samples tended to infinity (i.e. N > 100,000), the mean signal of all samples tended to the low-pass fit of the original second-order fringeresolved signal. From here on we will use the term "SACI" to describe the "Simulated Auto-Correlation Interaction" that we have created here.
With a suitable simulation of the auto-correlation signal form a quasi-stable interferometer established, the simulation was extended to simulate the interaction of the laser pulses with a system that possess non-zero decay (i.e. the molecular sample). This was achieved in a similar fashion to how we fit the time-dependent data in our experiment; by convoluting the auto-correlation signal with a series of decaying exponentials (each with a fixed decay constant, τi). [6,7] More exactly, for a set of N samples, each individual SACI was convoluted with the same set of decaying exponential functions, before averaging all N of the convoluted samples together. Overall, we tested a range of τi values extending from the few-femtosecond to few-picosecond length, for different sample numbers in the range of N = 1  100,000.
As a check we compared these SACI simulations to a simpler simulation, in which a Simple Gaussian (SG) was convoluted with the same decaying exponential functions. The FWHM of the SG was set to match the FWHM of the low-pass filtered signal of the second-order coherence function used to create the SACI (and hence also matching the SACI as N Infinity).
In Figures S2 to S19 we show the results of the example simulations in which the SACI (and SG) are convoluted with two decays. In the first set of simulations (Figures S2 to S10) the decays τ1 and τ2 are 25 fs and 1,000 fs, respectively, where τ1 is significantly shorter than both the expected pulse duration (~300 fs) and the auto-correlation signal (~430 fs), whilst τ2 is longer than both. In the second simulation (Figures S11 to S19), τ1 and τ2 are set to 500 and 1,000 fs, respectively, and hence are both longer than the pulse duration and auto-correlation signal.
From these simulations, the following trends are observed: 1) When the number of samples, N, is large, no matter what the decay constants are (i.e. larger or smaller than the auto-correlation signal) the SACI signal tended towards the same shape as the SG convoluted with the same decays (i.e. proof of concept).
2) When the SACI signal is convoluted with long decays (i.e. τi > auto-correlation FWHM), even at small N values the signal observed is similar to that of the SG convoluted with the same decays. Essentially, it appears that the coherent interference only adds noise to the signal.
3) When the SACI is convoluted with short decays (i.e. τi < auto-correlation FWHM) one can identify a profound artefact around the pump-probe temporal overlap at low N numbers. Instead of matching the signal seen when the SG is convoluted with the same decaying exponential functions, in a large number of instances the SACIconvoluted signal generally showed a tall and narrow feature sitting on top of the wider low-pass auto-correlation signal.
Ultimately, trend 3), and the strong similarity between the experimental data observed for the parent ion of Stilbene oxide with the low-N value simulation (especially with some of the plots seen in Figure S2), leads us to conclude that the tall, narrow feature of stilbene oxide is due to an under-sampling of a fast decay in the system.
We can also see that despite the tall narrow feature being present around time zero in the under-sampled signals, the rest of the decay signal still resembles the well-sampled signals. This means that any fits that are made outside of tall narrow spike around time zero should still be somewhat representative of well-sampled variant.