Storage time dependent photodissociation action spectroscopy of polycyclic aromatic hydrocarbon cations in the cryogenic electrostatic storage ring DESIREE.

The multi-photon photodissociation action spectrum of the coronene cation (C24H12+) has been measured in the cryogenic electrostatic storage ring DESIREE (Double ElectroStatic Ion Ring ExpEriment) as a function of storage time. These measurements reveal not only the intrinsic absorption profile of isolated coronene cations, but also the rate at which hot-band absorptions are quenched by radiative cooling. Just after injection, the action spectrum is severely reddened by hot-band absorptions. These hot bands fade with a time constant of 200 ms, which is consistent with radiative cooling via infrared emission from vibrational transitions. A comparison of the present results to those obtained in cryogenic ion trap experiments is discussed at length.


Introduction
The spectroscopy and photophysics of gas-phase Polycyclic Aromatic Hydrocarbon (PAH) ions such as coronene C 12 H 24 + is motivated by their ubiquity in the Interstellar Medium (ISM). 1 While it has become widely accepted that PAHs are responsible for the infrared emission observed throughout the ISM, 1 other attributions of astronomical phenomena to PAHs remain unconrmed or disputed.These include the ubiquitous Diffuse Interstellar Bands (DIBs), 2 the blue luminescence seen from the Red Rectangle nebula, 3 and the elevated abundance of H 2 (purported to be catalytically formed by PAHs [4][5][6] ) in photodissociation regions. 7or direct comparison to astronomical observations, various experimental techniques (e.g.supersonic expansion, 8 buffer gas cooling, 9 and noble gas tagging 10 ) have been employed to cool gas-phase PAH ions to internal temperatures similar to those predominant in the ISM i.e. <100 K. Despite its status at the prototypical PAH, only two previous action spectroscopy experiments have been reported for the coronene cation.The rst, by Joblin and co-workers, recorded multi-photon photodissociation (MPD) action spectra of coronene ions inside a cryogenically cooled (35 K) Fourier Transform Ion Cyclotron Resonance (FTICR) mass spectrometer. 11More recently, Maier and coworkers reported the photodissociation action spectrum of C 12 H 24 + -He complexes at approximately 10 K. 12 In the present experiments, which also employ MPD, isolated PAH ions relax at their intrinsic rates via infrared (IR) radiative cooling in the cryogenic ($13 K), collision free environment of the Double ElectroStatic Ion Ring ExpEriment (DESIREE). 13he purpose of this contribution is to compare the results of these three very different implementations of cold ion action spectroscopy.

Experimental methods
Coronene powder (97%) was purchased from Sigma Aldrich.Hot coronene cations were produced using a Nielsen-type plasma ion source equipped with a temperature-controlled oven.The ions were accelerated to 15 keV and those with mass-to-charge ratio m/z ¼ 300 were selected using a bending magnet.These ions were injected into the so-called "symmetric ring" (one of the two DESIREE storage rings 13 ) and stored for up to one minute.The experiment is shown schematically in Fig. 1.Stored ions were excited at a 10 Hz repetition rate in one of the straight sections of the ring in a crossed-beam geometry using a tunable wavelength OPO laser system (EKSPLA).Neutral fragments (presumed to be H atoms) formed in this section are unaffected by the electrostatic steering elds and y straight into a micro-channel plate (MCP) detector, labeled 'Imaging Detector' in Fig. 1.The detector signal is gated with a 1 ms width and a delay aer the laser ring time corresponding to the ight time from the interaction region to the detector.This eliminates the counting of scattered laser light and strongly suppresses the counting of detector dark noise and background fragmentation events due to collisions between stored ions and residual gas in the ring.The excitation wavelength is stepped in between ion injections, creating a twodimensional photodissociation action spectrum time series.Photo-excited ions may in principle undergo delayed fragmentation up to several tens of milliseconds aer irradiation, corresponding to several hundred revolutions around the storage ring (the revolution time is about 88 ms).Delayed fragmentation occurring in the same straight section as photo-excitation will be witnessed by the same MCP as the main prompt signal, while neutrals formed in the opposite straight section will y to a different MCP equipped with a secondary electron emissive glass plate.In the present experiments, very little delayed fragmentation was observed, amounting to less than 1% of the prompt signal.Only the prompt signal is analyzed here.
Although the data presented here were recorded using injection cycles of up to 60 s, the actual beam storage lifetime (limited by collisions with residual background gas) is considerably longer. 14,15Measurements performed at the end of the cycle, when the beam was dumped into a Faraday cup, found a C 24 H 12 + storage lifetime of about 400 s.
3 Results and discussion

Pulse energy dependence
The dependence of the photodissociation signal rate on the OPO laser pulse energy is shown in Fig. 2. The laser power was varied using neutral density lters.
The photodissociation yield G is well represented by a power law G ¼ E 3 .The dependence on the third power of the pulse energy E indicates that the absorption of three photons is required to induce the observed signal.There is no sign of saturation of the process at high pulse energies.The lowest adiabatic dissociation energies of C 24 H 12 + are about 5 eV for H-loss and 7 eV for C 2 H 2 -loss. 16,17The energy deposited by three 450 nm photons is 8.3 eV.Neutral fragments contributing to the measured prompt signal are formed within the rst few ms aer excitation.9][20] Bearing in mind that the ions retain some internal energy prior to excitation, it seems most probable that H-loss is the dominant dissociation channel observed here.This is also the same channel observed by Joblin and coworkers. 11he pulse energy dependence in the present experiment is rather straightforward to interpret, which may be regarded as an advantage relative to ion trap experiments.In Joblin's experiments, for example, the photodissociation yield is highly saturated, and is modeled with a Monte Carlo simulation which requires quantitative details of the photophysics of coronene as inputs.Complexities in modeling those experiments include the strongly varying spatial distribution of photon ux (due to the Gaussian laser beam prole) and the high shot-to-shot variation in the overlap between the laser beam and the ion cloud.The OPO laser system used in the present experiments has a relatively at "top-hat" prole, and the stored ion beam lls the acceptance of the storage ring (at least aer the rst few ms) providing a more consistent target.Furthermore, only prompt dissociation occurring while the excited ions are still in the straight section of the storage ring (<5 ms aer irradiation) is recorded here.This reduces the contribution of ions dissociating aer the absorption of fewer than three photons, which would occur on much longer time scales (although for coronene such ions would probably not dissociate at all).

Action spectra -1 s storage
Fig. 3 shows a data set recorded with 1 s injection cycles presented as MPD action spectra for different laser ring times separated by the 100 ms repetition period of the laser.The rst laser shot is 0.01 s aer injection.These data are the sum of over 5500 cycles (nearly 300 per excitation wavelength).The number of counts at each wavelength-time point has been divided by the laser pulse energy (which was very nearly constant in this spectral range).The action spectrum at the earliest times (0.01 s, top of map) aer injection is nearly at, and over the course of the rst second the spectrum collapses to a band centered at around 465 nm.
The photodissociation signal at wavelengths longer than the band maximum, corresponding to hot-band absorptions, fades over the rst few hundred milliseconds.
The action spectrum appears to have converged to a steady state aer 0.51 s (dashed line in Fig. 3).The average of the last ve spectra in this series (i.e.those recorded aer 0.51 s) is plotted as the solid line in the upper panel of Fig. 4. By subtracting this 'cold spectrum' from each action spectrum in the time series, one Fig. 3 Action spectra recorded at times after injection ranging from 0.01 s (top) to 0.91 s (bottom) with 0.1 s intervals.Hot-band absorptions fade in the first few hundred ms and the spectrum converges to a steady state after 0.51 s (dashed line).
obtains the time-dependent contribution to the action spectrum of the vibrationally excited ions.The time-average of this hot-band contribution is shown as the dashed line in the upper panel of Fig. 4.This is perhaps not so interesting in itself, but the relative intensity of the hot-band contribution over time gives an indication of the timescale on which these vibrational excitations relax.Contributions from different excited vibrational states will of course relax with different rates, with this procedure giving a gross average.The normalized relative intensity of the hot-band contribution is shown in Fig. 5.These data are t with a single exponential decay giving a cooling time constant of 0.205 AE 0.018 s.This is in line with expected values for cooling rates of PAHs by infrared emission. 21,22utting the action spectrum time series in half and declaring the second half cold may seem somewhat crude and arbitrary.Inspired by Støchkel and Andersen, 23 a simple Principal Component Analysis (PCA) has also been carried out.PCA is a standard statistical procedure (here implemented using the PCA Python routine provided by the open-source scikit-learn library 24 ) typically used to reduce high-dimensionality data sets by nding the orthogonal linear combinations of the variables which best account for the variability in the data.When applied to the present action spectrum time series, an m Â n data matrix X consisting of the m time series (as row vectors) recorded at n different wavelengths, the procedure amounts to an eigenvalue decomposition of the covariance matrix X T X.The resulting vectors may be thought of as the eigenspectra which describe the variation in the action spectrum over time, with the eigenvalues indicating how much of the variation is captured by each PC.In the case of the data presented in Fig. 3, the vector with the largest eigenvalue, called the rst principal component or PC1, explains over 75% of the variation, with the remaining components containing only statistical uctuations.It is likely that a more granular data set would exhibit multiple signicant PCs, reective of the energy-dependence of the cooling rate.PC1 is shown in the lower panel of Fig. 4 (dashed line) and closely resembles the hot-band contribution obtained using the 0.51 s cut (upper panel, dashed line).The projection of the data onto PC1 gives its relative weight over time.As shown in Fig. 5, the relative weight of PC1 decays on the same time scale (0.200 AE 0.015 s) as the hot-band contribution.A cold spectrum is obtained by subtracting PC1 from each action spectrum in the time series (Fig. 3), weighted by its projection (Fig. 5), and taking an average.This is shown in the lower panel of Fig. 4 (solid line).Again, the cold spectrum obtained by arbitrarily cutting the data aer 0.51 s is well reproduced by this method.The PCA approach has the advantage that one is not required to choose a xed time cut a priori, and uses the entire data set to construct the cold spectrum, rather than just the data aer the cut.While the results of the two methods are very similar in this case, the PCA approach could be valuable in cases where the cooling time is comparable to or longer than the measurement time.

Action spectra -60 s storage
At DESIREE, very long storage and hence measurement times are available.Fig. 6 shows two slices of an action spectrum time series recorded over 60 seconds of storage time.Note that this measurement covers a narrower spectral region than those in Fig. 3.
Also shown in Fig. 6 is the MPD action spectrum recorded by Joblin and coworkers (dashed black line). 11This spectrum closely resembles that recorded in the present experiments aer the ions have relaxed for 10 s (blue line).Both spectra are presented with constant laser pulse energy, though the vertical scaling is arbitrary.
In Joblin's experiments, C 24 H 12 + ions were stored in the PIRENEA FTICR mass spectrometer cell cooled to 35 K and were cooled through collisions with He buffer gas.Evidently, the nal vibrational distribution reached by the ions is similar in the two experiments, however, the photo-fragment yield in the PIR-ENEA experiment is somewhat lower above 465 nm.Caution should be exercised when interpreting small differences in action spectra recorded using such different techniques.A variety of technical considerations, e.g.differences in background subtraction, the number of photons absorbed, kinetic shis, etc. could easily explain such a discrepancy.Temporarily suspending this skepticism, one may ask why it might be that the ions in PIRENEA appear colder than those in DESIREE, despite the fact that the nominal temperature inside DESIREE is signicantly colder (13 K).A plausible explanation is that buffer gas mediated cooling is simply more effective than spontaneous IR cooling.The former is limited by the coupling of translational motion in the trap to vibrational excitation. 11IR emission, on the other hand, slows dramatically as the degree of excitation of IR-active modes decreases. 21We can see a hint of this by examining the projection of the action spectrum time series on its rst principal component, shown in Fig. 7.This cooling curve is not well represented by a single exponential decay, with a better t obtained using a power law.6][27][28] Fig. 7 indicates that relaxation is not fully complete aer the disappearance of obvious hot-band absorptions.If the power law t to the PCA cooling curve in Fig. 7 is used to extract a cold spectrum, better agreement with the PIRENEA results is obtained as shown in Fig. 6.While the reader is again cautioned against over-interpreting small differences in action spectra, this result suggests that a principal component analysis can be used to analyze variations in action spectra occurring over timescales which are long compared to the measurement time.This is a signicant advantage over arbitrarily cutting of the action spectrum time series at a time when the variation may not yet have ended.
Comparing the two MPD experiments (DESIREE and PIRENA), the take-away is that the action spectra are essentially the same within the margin of inter-lab variability.In contrast, Maier's action spectrum of He-tagged C 24 H 12 + complexes (also included in Fig. 6) is qualitatively sharper, 12 although the band maximum at 457 nm is the same within the uncertainty of the MPD measurements.

Multi-photon effects
In comparing their action spectra of He-tagged C 24 H 12 + to the earlier MPD results, Maier and co-workers offer two different explanations for the broadness of the bands in the latter.They write that the MPD "process leads to broadening effects of the bands due to the heating of the ion ensemble" and later that "widths of the bands in the MPD experiment are broader owing to the higher internal temperature of the ion". 12The rst issue is a common critique of photodissociation action spectroscopy generally: that such spectra do not accurately reect the ion's true absorption cross section.The second explanation, that the He-tagged ions are colder, is indisputable.The question addressed in this section is whether the broadness of the MPD spectra is due only to the higher initial temperature, or if additional broadening is induced by the MPD process.
In MPD experiments using nanosecond pulsed lasers, it is generally assumed that the ions absorb photons sequentially, i.e. returning to a hot ground electronic state via ultrafast internal conversion and intramolecular vibrational redistribution in between absorption events.In this case, the photodissociation yield G PD at a wavelength l is proportional to the probability of absorbing the number of photons N required to induce photodissociation on the time scale sampled by the experiment: where s i is the photo-absorption cross section for the i th photon and 3 is the laser ux.Two different approximations are commonly made at this point.The rst is that the cross section for absorbing subsequent photons is the same as for the rst i.e. s i>1 (l) ¼ s 1 (l) for all l.The other extreme is to assume that the absorption cross section of the laser-heated ions is so severely broadened that it is effectively constant i.e. s i>1 (l) ¼ const.Note that in neither case does the absorption of multiple photons lead to an action spectrum G PD (l) that is broader than the "true" absorption cross section of the initial cold ion s 1 (l).Indeed, in the rst approximation, where the cross section is unchanged, absorption bands would appear narrower in the action spectrum.This was demonstrated by Wellman and Jockusch, who found the photodissociation action spectrum of (room temperature) rhodamine 110 cations to be narrower than their uorescence excitation spectrum. 29easurements of rhodamine ions by the Roithová group, which have higher spectral resolution, show a clear blue-shi in the MPD action spectrum with decreasing trap temperature as hot-band absorptions become inactive. 30This conrms that at least some information about the initial low temperature absorption cross section is preserved in the MPD action spectrum.Roithová also gives action spectra of He-tagged rhodamine ions. 30,31Compared to these data, the MPD spectrum recorded at a 50 K trap temperature (the lowest reported by Roithová) is slightly ($2 nm) redshied and broadening is observed to both sides of the band maximum.The widths of the bands in the He-tagging spectra however are limited by the bandwidth of the excitation source, making it difficult to quantitatively compare them with the MPD spectra.Rhodamine dye cations are of course highly uorescent, and the number of photons required to dissociate them is notably high. 29,30If most of the excitation energy is re-emitted optically, it may be reasoned that s i>1 (l) does not differ signicantly from s 1 (l).It should also be noted that both Jockusch and Roithová use quasi-cw laser excitation sources, meaning that signicant time (up to tens of milliseconds) may elapse in between excitation events during which the hot ions may relax by IR emission or collisions with trapping gas.
PAH cations are generally non-uorescent and are instead characterized by very short excited state lifetimes.Maier estimates the excited state lifetime of C 24 H 12 + to be 50 fs. 12Thus the full excitation energy (around 2.7 eV at 465 nm) is converted into vibrations.Reddening of s i>1 (l) relative to s 1 (l) might be expected due to enhancement of hot-band absorptions.This, however, would lead to a red-shi of the multi-photon spectra relative to Maier's 1-photon spectrum, while instead a more symmetric broadening is seen in Fig. 6.Looking back at Fig. 3, we see that 10 ms aer injection the action spectrum is nearly at.Recall that this is itself a multi-photon action spectrum, and that the internal energy at 10 ms may be much higher than 2.7 eV, which corresponds roughly to room temperature.Still, the symmetric broadening of the MPD spectrum is consistent with s i>1 (l) ¼ const.This is further supported by the similarity of the present 3-photon action spectrum to that from PIRENEA, which was modeled as arising from the absorption of more than 4 photons. 11The width of the MPD spectra can thus reasonably be assumed to be broadened relative to the He-tagged spectrum only by the higher initial temperature of the ions without invoking any additional broadening from the MPD process itself.

Conclusions
Multi-photon photodissociation action spectra of coronene cations have been recorded as a function of storage time in the cryogenic electrostatic ion storage ring DESIREE.Contributions from hot-band absorptions dissipate on a timescale consistent with IR radiative cooling from vibrational transitions.Spectra recorded more than 10 s aer injection closely resemble those recorded in an ion trap mass spectrometer cooled to 35 K. Extrapolation of the cooling characteristic obtained by principal component analysis further increases this agreement.Considering the rather different experimental conditions, it has been argued that the MPD action spectra are proportional to the absorption cross section of the initial cold ion.Due to the higher internal temperature prior to excitation, the MPD spectra are symmetrically broadened relative to the one-photon photodissociation spectrum of C 24 H 12 + -He complexes, with no signicant difference in the band maximum.
In the present experiments, isolated C 24 H 12 + ions cool via their intrinsic radiative transitions, exactly as they would in the ISM where collisional cooling is slow.Such a preparation might be considered to be a more realistic reproduction of interstellar conditions than cooling by interactions with buffer or carrier gases.Action spectra of He-tagged complexes provide accurate center wavelengths useful for the identication of interstellar absorption bands. 32The internal temperature of He-tagged complexes, however, is considerably lower than the prevailing conditions in interstellar clouds, where temperatures of non-polar molecules range from 30-80 K. 33,34 Temperature controlled ion trap measurements, such as those carried out by the Joblin and Roithová groups, as well as time-dependent measurements on isolated, freely radiating ions possible in cryogenic electrostatic storage devices, are thus needed to asses the widths of optical transitions of purported interstellar ions.For example, a species whose He-tagged action spectrum shows a transition coincident with a diffuse interstellar band, but with an incommensurate band width at the temperature of interstellar clouds, is unlikely to be the carrier of that DIB.Further development of single-photon action spectroscopies of bare ions such as laser-induced uorescence 29,35,36 or laser-induced vibrational emission 37 is needed to reduce any ambiguity associated with multi-photon processes like photodissociation.

Fig. 1
Fig.1The DESIREE symmetric storage ring.Stored C 12 H 12 + ions are irradiated in a crossed-beam geometry in the lower straight section.

Fig. 4
Fig. 4 Upper panel: The solid line is the average of the action spectra recorded from 0.51-0.91s.The dashed line is the average hot-band contribution found by subtracting the cold spectrum from the raw data.Lower panel: The dashed line is the first principal component (PC1) of the data from Fig. 3.The solid line is the cold spectrum found by subtracting PC1 from the raw data, with appropriate weighting (see text).

Fig. 5
Fig. 5 Time dependence of the relative intensity of the hot-band contribution to the action spectra from Fig. 3, and of the projection of the data on PC1.

Fig. 6
Fig. 6 Action spectra recorded over different time intervals after injection into DESIREE, and extracted using PCA. a FTICR data from Joblin and coworkers. 11b Action spectrum of He-C 24 H 12+ complexes from Maier and coworkers.12

Fig. 7
Fig. 7 Normalized projection (or weight) of the first principal component of the 60 s action spectrum time series of coronene cations in DESIREE.A power-law fit better represents the cooling curve than a single exponential decay.