Ultraslow radiative cooling of C − n ( n=3−5 )
James N. Bull, Michael S. Scholz, Eduardo Carrascosa, Moa K. Kristiansson, Gustav Eklund, Najeeb Punnakayathil, Nathalie de Ruette, Henning Zettergren, Henning T. Schmidt, Henrik Cederquist, Mark H. Stockett
UUltraslow radiative cooling of C − n ( n = 3 − ) James N. Bull, a) Michael S. Scholz, Eduardo Carrascosa, Moa K. Kristiansson, Gustav Eklund, Najeeb Punnakayathil, Nathalie de Ruette, Henning Zettergren, Henning T. Schmidt, Henrik Cederquist, and Mark H. Stockett b) School of Chemistry, Norwich Research Park, University of East Anglia, Norwich NR4 7TJ,United Kingdom School of Chemistry, University of Melbourne, Parkville, VIC 3010, Australia Laboratoire de Chimie Physique Mol´eculaire, ´Ecole Polytechnique F´ed´erale de Lausanne, EPFL SB ISIC LCPM,Station 6, CH-1015 Lausanne, Switzerland Department of Physics, Stockholm University, SE-10691 Stockholm, Sweden
Ultraslow radiative cooling lifetimes and adiabatic detachment energies for three astrochemically relevantanions, C − n ( n = 3 − ≈ − mbar andtemperature of ≈
13 K, allowing storage of mass-selected ions for hours and providing conditions coined a“molecular cloud in a box”. Here, we construct two-dimensional (2D) photodetachment spectra for the targetanions by recording photodetachment signal as a function of irradiation wavelength and ion storage time (sec-onds to minute timescale). Ion cooling lifetimes, which are associated with infrared radiative emission, areextracted from the 2D photodetachment spectrum for each ion by tracking the disappearance of vibrationalhot-band signal with ion storage time, giving e cooling lifetimes of 3.1 ± − ), 6.8 ± − ) and 24 ± − ). Fits of the photodetachment spectra for cold ions, i.e. those stored for at least 30 s, provides adia-batic detachment energies in good agreement with values from laser photoelectron spectroscopy. Ion coolinglifetimes are simulated using a Simple Harmonic Cascade model, finding good agreement with experimentand providing a mode-by-mode understanding of the radiative cooling properties. The 2D photodetachmentstrategy and radiative cooling modeling developed in this study could be applied to investigate the ultraslowcooling dynamics of wide range of molecular anions. I. INTRODUCTION
Which molecular anions exist in space? What are theirformation mechanisms and life cycles? These are twolong-standing questions in astrochemistry.
Prior to adecade and a half ago, H − was the only anion thought toplay a prominent role in the interstellar medium (ISM).In 2006, the first molecular anion, C H − , was discoveredby comparing astronomical line spectra with gas-phaseaction spectra recorded in the laboratory. Over the nextfour years there were five further identifications: C H – , C H – , CN – , C N – , and C N – . Vibrationally excitedC H – was also detected alongside C N – . However, de-spite increasing interest in the role of molecular anionsin space, there has been a stall in new identifications.It is thought that the discovery of new molecular anionsis thwarted by a lack of understanding of the formationmechanism(s) and dynamical properties of both the an-ions known to exist in the ISM and new anions yet to beassigned.
Dynamical properties in this context includeelectron capture cross-sections, electronic internal con-version efficiencies and couplings between dipole-boundand valence-localised states, cross-sections for neutral-ization reactions with cations, and the rates of radia-tive cooling.
As an example of the need for reliablemeasurements of the dynamical properties of astrochemi- a) Electronic mail: [email protected] b) Electronic mail: [email protected] cally relevant anions, in a discussion on radiative electronattachment (which involves formation of a vibrationallyexcited ground state ion that must cool) Herbst re-marked “ The discovery of molecular anions [in space]has generated the need to include their formation anddestruction in chemical models ... the larger [carbona-ceous] molecular anions detected ( n = 6, 8) have higherabundances relative to their neutral precursors becausethe radiative attachment rate increases with the numberof degrees of freedom of the anion. However, their rateestimates are quite uncertain and experimental studiesare highly welcome. ” Although gas-phase action spectro-scopies can provide data on electronic transitions anddetachment energies for carbonaceous anions, their dy-namical properties such as infrared (IR) radiative coolinglifetimes are more difficult to measure because hot anionsneed to be isolated (i.e. free from collision) for periodsof milliseconds to minutes. These conditions are not at-tainable using conventional ion traps.Here, we used the Double ElectroStatic Ion Ring Ex-pEriment (DESIREE) infrastructure at Stockholm Uni-versity to characterize the radiative cooling lifetimes andadiabatic detachment energies (ADEs) of C − n ( n = 3 − − n ( n = 3 − and a r X i v : . [ phy s i c s . a t m - c l u s ] S e p neutral C and C are known interstellar molecules. Although anions are unlikely to be significant astrochem-ical species in ‘photon-dominated regions’ (PDRs, e.g.diffuse clouds) due to facile destruction by photodetach-ment with visible and ultraviolet light, the abundanceof anions in dark clouds (e.g. C − in L1527) has beenshown to reach nearly 10% of that for the correspond-ing neutral molecule, suggesting that negative charge inphoton-free regions of space is more likely in the form ofanions than free electrons. Cold dark molecular cloudshave temperatures of 10–20 K. The normal operatingtemperature of DESIREE ( ≈
13 K) is squarely within thisrange. In the absence of collisional quenching, the sponta-neous cooling dynamics of hot molecular anions such asC − n ( n = 3 −
5) can be divided into three time ( t ) regimes: • Statistical regime I ( t ≤ − s): Internal energyis high, e.g. several electron-volts above thethresholds for dissociation, thermionic emission, and recurrent/Poincar´e fluorescence. The energythreshold for thermionic emission is the ADE,which for C − n ( n = 3 −
5) is ≈ ≈ − and C − , involves in-verse internal conversion to an electronic excitedstate (situated below the ADE, e.g. ≈ • Slow regime II ( t ≈ − –1 s): Internal energy is inthe vicinity of the lowest thresholds for the coolingmechanisms important for Regime I, e.g. ∼ • Ultraslow regime III ( t > ∼ Cooling dynamics in this regime havebeen explored for only a few small anions due totechnical challenges associated with isolating ionsfor durations extending to minutes and maintain-ing low background temperatures.
While the target anions have been intensively stud-ied by several groups in recent years, all studies usedroom-temperature electrostatic ion storage rings or beamtraps and were limited to characterizing cooling dynam-ics occurring on sub-second timescales.
In thepresent study, we have used the DESIREE infrastruc-ture to investigate the cooling dynamics of the targetanions on the ultraslow, t > ∼ ≈ e ion coolinglifetimes, which are attributed to IR radiative emission,are well-described by a simple harmonic cascade modelof this process. Fits of the cold photodetachment spec-tra associated with ions stored for at least 30 s to theWigner threshold law demonstrate an alternative, cryo-genic method for obtaining ADE values. II. METHODS
DESIREE is a cryogenic dual electrostatic ion storagering facility located at the Department of Physics, Stock-holm University.
The major components constitutingthe so-called ‘symmetric’ storage ring are schematicallyillustrated in FIG. 1. The interior of the ring is cooledto ≈
13 K by compressed helium refrigerators and is iso-lated from external thermal radiation by several layersof insulation. Vacuum is maintained at a backgroundpressure of ≈ − mbar using cryopumping combinedwith turbomolecular pumps and oil-free backing pumps.These ultrahigh vacuum conditions allow storage of keVion beams for hours. In the present experiments, thetarget anions [C − n ( n = 3 − This process generates ions with a high degree of rovibra-tional excitation, i.e. source-heated ions. The nascentions were accelerated to 10 keV, selected according totheir mass-to-charge ratio using a bending magnet, andinjected into the symmetric ion storage ring. Transportfrom the source to the ring takes ≈ µ s. The e beamstorage lifetimes were measured at 540 ±
30 s for C − and570 ±
30 s for C − (see Supporting Information). Althoughthe beam storage lifetime for C − was not measured in thisstudy, we expect a similar lifetime to those for C − andC − . These beam storage lifetimes are limited by loss of Ion InjectionCrossed Photon-IonInteraction Region ImagingDetectorCollinear Photon-IonInteraction RegionMCP CW Dye Laser BeamPulsed OPO Beam NeutralsGlass Plate e_ Neutrals
FIG. 1. The symmetric ion storage ring in DESIREE. Neutralparticles formed by photodetachment in the lower straight re-gion (crossed-beam geometry with the optical parametric os-cillator, OPO) are detected in their forward directions withthe ‘Imaging Detector’. In another set of measurements onC − , light from a cw dye laser was merged colinearly with thestored ion beam in the upper straight section. The wavelengthof the cw light was tuned to be in resonance with the vibra-tional hot band of C − (620.5 nm). The ring circumference is8.6 m and each straight section has a length of 0.96 m. ions through collisions with background gas. A. One-color experiments
In the one-color experiments, stored ions were irradi-ated with tunable-wavelength light from an optical para-metric oscillator (OPO, EKSPLA NT342B, 10 Hz) usinga crossed-beam geometry through one of the straight sec-tions of the ion storage ring (see FIG. 1). Any neutralparticles formed through photodetachment or photodis-sociation are unaffected by the ring’s electrostatic steer-ing fields and impact on a micro-channel plate (MCP)detector (‘Imaging Detector’ in FIG. 1). Signal fromthe MCP detector was gated using a 1 µ s duration pulsethat was slightly delayed with respect to the OPO pulseto account for the neutral particle’s flight time fromthe interaction region to the detector. The purpose ofthe gate was to eliminate signal from scattered OPOlight striking the detector and to minimize backgroundcounts from collision-induced detachment events due tothe residual gas consisting of ∼ H molecules per cm .The OPO wavelengths were calibrated using an opticalspectrograph (Avantes AvaSpec-3648), which was itselfcalibrated against a wavemeter (HighFinesse WS-8) viaa diode laser (632.6 nm). The irradiation wavelengthwas stepped in 0.5 nm increments (2 nm for C − ) betweenion injections for a given ion storage time, providing atwo-dimensional (2D) photodetachment spectrum, i.e. aseries of photodetachment spectra as a function of wave-length and ion storage time (see Refs 19,27 for a similarprocedure applied to rotational cooling of OH − ). Fora given ion, the time evolution of the photodetachmentyield at a specific wavelength or range of wavelengths canbe obtained by taking a wavelength slice through the 2Dphotodetachment spectrum.Part of our interpretation applied Principal Compo-nent Analysis (PCA) to the 2D photodetachment spec-trum for each ion. PCA is a common statistical pro-cedure that decomposes a multi-demensional data set X into a set of orthogonal principal components (PCs)which are the eigenvectors of the covariance matrix X T X . The eigenvalues associated with each PC relateto the fraction of the variation in X that is explainedby each PC and the principal values (PVs, the projec-tion of X on its PCs) give the wieght of each PC asa function of time. In the present case, the PCs maybe thought of as the underlying spectra that describethe evolution of the photodetachment spectra with ionstorage time, with a time invariant background due tophotodetachment signal from cold ions (or nearly timeinvariant because of a finite ion beam storage lifetime). The cooling lifetimes obtained from the PVs should beconsidered wavelength-averaged values since each probewavelength provides slightly different ion cooling lifetimedue to a distribution of internal vibrational energies inthe stored ion beam.
B. Deplete-probe experiments with C − Deplete-probe experiments on source-heated C − wereperformed by adapting the procedure recently describedby Schmidt et al. , where the effect of the depletionlaser was to preferentially photodetach rotationally ex-cited ions and thus reduce the measured ion cooling life-times. Depletion involved intercepting the stored ionbeam with 620.5 nm light from a cw laser (Coherent899 ring dye laser) using a merged-beam geometry inthe straight section of the ion storage ring opposite theOPO light interaction region (see FIG. 1). The deple-tion laser wavelength (620.5 nm or 1.998 eV) was chosento be close to the ADE from the present measurements(see below) because the photodetachment cross-sectionfor vibrationally excited (hot band) C − is much largerthan that for cold ions. C. Adiabatic detachment energies
The adiabatic detachment energy (ADE) for each an-ion was extracted from cold photodetachment spectrumassuming fit with the Wigner threshold law: σ P D = ( KE ) L + , (1)where σ P D is the photodetachment cross-section, KE isthe kinetic energy of the ejected electron (energy in ex-cess of the ADE for a direct photodetachment process),and L is the angular momentum of the outgoing elec-tron. For the present systems which involves photode-tachment from π molecular orbital, we find that L = 2( d wave photoelectron) provides best fit to the exper-imental data. The ADE is taken to be the energy atwhich the Wigner threshold law fit exceeds 3 σ of thebaseline signal. We note the above expression is strictlyvalid for atomic species; best fit values of L can deviatefrom integers for molecules – see example fit for C − inthe Supporting Information. D. Radiative cooling lifetime modeling
Spontaneous cooling in the present experiments ispresumed to occur through IR radiative emission. Asimple harmonic cascade (SHC) model was developedto interpret the experimental results. The model as-sumes vibrational density of states ρ computed using theBeyer-Swinehart algorithm using anharmonic or scaledharmonic vibrational mode frequencies ν s calculated atthe ω B97X-D//aug-cc-pVTZ level of theory with Q-Chem 4.4 (see Supporting Information).
For a givenmode s , the IR radiative cooling rate coefficient, assum-ing only transitions where ∆ v s = − v being the vibrational quantum number, is k s ( E ) = A s v ≤ E/hν s (cid:88) v =1 ρ ( E − vhν s ) ρ ( E ) , (2)where E is the energy of a given vibrational state, h isPlank’s constant, and the summation is over v ( v = 0and 1 are the ground and first excited vibrational statesof mode s , respectively). The Einstein coefficients A s were calculated at the ω B97X-D//aug-cc-pVTZ withinthe harmonic approximation (see Supporting Informa-tion). Starting from an initial Boltzmann distributionof vibrational energy g ( E, t = 0) corresponding to1000 K, the population in each level was recalculatedat each simulation timestep. The model allowed fortwo treatments of intramolecular vibrational energyredistribution (IVR), i.e. statistical randomization ofvibrational energy with time, t :(i) IVR is negligible or slow compared with radia-tive cooling – the population of each mode is explicitlytracked according to the expression below: g ( E, t + dt ) = (cid:88) s g ( E, t ) e − k s ( E ) dt + (cid:88) s g ( E + hν s , t )(1 − e − k s ( E + hν s ) dt ); (3)(ii) IVR is fast compared with radiative cooling –vibrational energy is statistically redistributed eachsimulation time step and the total energy emittedradiatively at each time step is: dE tot /dt = − (cid:90) g ( E, t ) (cid:88) s hν s k s ( E ) dE, (4)where the total energy remaining in the ensemble as afunction of time E tot ( t ) = (cid:82) Eg ( E, t ) dE was taken as anindicator of the progress of cooling. Given that the vibra-tional energy quanta are small and the number of storedions is large, level occupation numbers were treated ascontinuous quantities. We expect that case (ii) shouldbe most relevant for the present source-heated anions be-cause ion cooling lifetimes are long (seconds timescale)compared with the expected timescale for IVR (nanosec-onds to millisecond timescale).The SHC modeling starts from a hot ensemble andsimulates the internal energy as a function of ion stor-age time. For case (i), the internal vibrational energyreached a non-zero asymptotic value because any pop-ulation that was portioned to IR inactive modes is notemitted radiatively. For case (ii), because the lowest fre-quency vibrational modes for each anion are IR active,all vibrational energy in excess of the zero-point energycan be liberated and thus the model goes asymptoticallyto zero vibrational energy at long times. To compareresults from the SHC model with experiment for which there is non-zero photodetachment signal at long ion stor-age times for wavelengths shorter than the ADE due tophotodetachment from cold ions, it was necessary to addan asymptote offset equal to the value extracted from anexponential fit of the experimental data. Furthermore,it was found that the initial temperature assumed in theSHC model (e.g. 500 – 5000 K) altered the cooling dy-namics only on timescales much faster than those probedin the present experiments, e.g. milliseconds.It is worth noting that we found use of the commonlycited harmonic frequencies and intensities from Szczepan-ski et al. calculated at the B3LYP/6-31G* level of the-ory within the SHC framework produced qualitativelysimilar results to that presented in this study, but re-quired scaling the A s coefficients with factor 0.5 to bestalign modeled ion cooling lifetimes with experimental val-ues. III. RESULTS AND DISCUSSIONA. Tricarbon anion, C − Photodetachment spectra for C − as a function of ionstorage time are shown in FIG. 2, upper. The spec-tra have been divided into four time bins, with the 0–3 s time bin corresponding to ions recently injected intothe storage ring and the 30–57 s time bin correspond-ing to ions that have been stored for at least 30 s. Thecomplete 2D photodetachment spectrum is shown in theSupporting Information. The time-binned photodetach-ment spectra show a broad feature over the expectedADE (1.99 ± ± due to vibrationally excited C − ions thatcool over the first <
30 s, providing a ‘cold’ photodetach-ment spectrum (30–57 s spectrum). A fit of the coldphotodetachment spectrum with the Wigner thresholdlaw gave ADE = 1.990 ± ± ± ± − suggested a single princi-pal component (PC1 in FIG. 3) can describe the hot-bandintensity with ion storage time. Nearly 80% of the vari-ance in the 2D spectrum is explained by PC1, with theremaining PCs describe only statistical fluctuations with N e u t r a l Y i e l d ( A R B ) Wavelength (nm)600 610 620 630 640Storage Time (s):0-33-66-930-57 C o un t s p e r C y c l e Storage Time (s)0 5 10 15 20 25 30610615625640595590
FIG. 2. Upper: Time-binned photodetachment spectra forC − , recorded by monitoring the yield of neutral particleswith wavelength of light. The black bar represents the ADEand uncertainty determined for ions stored at least 30 s,and the orange bar corresponds to the photoelectron spec-troscopy value from Ref. 51. Lower: Decay of photodetach-ment signal with ion storage time at selected probe wave-lengths (note the log scale). Time constants for single-exponential fits in the lower panel are 4.3 ± ± ± ± ± no secular time dependence. The principal values of PC1(denoted PV1) with ion storage time are shown in thelower panel of FIG. 3. Fit of PV1 with a bi-exponentialgave a fast lifetime of 3.1 ± >
200 s) is much longer than the measurement cycle (60 sfor C − ) and is presumably associated with the beam stor-age lifetime (540 ±
30 s for C − , see Supporting Informa-tion). The time-invariant cold spectrum (FIG. 3, lower)was obtained by subtracting PC1, weighted by PV1, fromthe 2D photodetachment spectrum. This closely resem-bles the cold spectrum in FIG. 2, but utilizes the entiredata set rather than arbitrarily time-binned data. Fit of R e l a t i v e I n t e n s i t y Wavelength600 610 620 630 640Photon Energy (eV)2.05 2.00 1.9543F1 PC1Cold P r i n c i p a l V a l u e / R e l a t i v e E n e r g y Storage Time (s)0 10 20 30 40 50 60PV1SHCSHC+IVR
FIG. 3. Principal component analysis on C − . Upper: Prin-cipal component (PC1) and cold photodetachment spectrum.Lower: Principal values for PC1 (denoted PV1) with ion stor-age time, and simple harmonic cascade (SHC) model of thecooling lifetime (note the log scale). The gradual decrease inPV1 for ion storage times longer than ≈
20 s is attributed tothe beam storage lifetime in DESIREE. the cold spectrum from PCA with the Wigner thresh-old law gave an ADE of 1.987 ± ± − from theSHC model are summarized in FIG. 3, lower. The dashedblack curve assumes the case of no IVR and the solidblack curve includes IVR. Exponential fits to the SHCcurves returned ion cooling lifetimes of 5.22 ± ± ± − is shown in FIG. 4. Comparison of cwlaser ON (black) with cw laser OFF (red) data at theprobe wavelengths of 615, 610, 595 and 590 nm show asystematic decrease of the ion cooling lifetimes by ≈ I o n C oo l i n g L i f e t i m e ( s ) Wavelength (nm)590 600 610 620 630cw Laser ONcw Laser OFFcw Laser Wavelength
FIG. 4. Cooling lifetimes for C − using the deplete-probescheme. The black circles and red squares are cooling life-times with and without irradiation using cw laser light at620.5 nm (dashed blue vertical line). length longer than that of the cw laser. These data pro-vide a proof-of-principle measurement demonstrating adeplete-probe scheme to preferentially remove hot ionsfrom the stored ion beam. The extent of depletion couldlikely be improved through better overlap of the cw beamwith the ion beam and increase of cw laser power. B. Tetracarbon anion, C − Time-binned photodetachment spectra and resultsfrom PCA for C − are summarized in FIG. 5 upper andmiddle/lower, respectively. The C − photodetachmentdata were recorded in larger wavelength increments com-pared with C − or C − due to substantially lower laser flu-ence from the OPO at the near-UV wavelengths neededto photodetach this species. The time-binned photode-tachment spectra for C − indicate that hot-band signalhas disappeared after ≈
30 s. Fit of the 30–55 s time-binned spectrum with the Wigner threshold law gavean ADE of 3.83 ± ± ± Application of PCA to the 2D photodetachment spec-trum of C − again suggested that a single principal com-ponent (PC1 in FIG. 5, middle) describes the variation inthe hot band intensity with ion storage time. The prin-cipal value of PC1 with ion storage time (PV1 in FIG. 5,lower) has a fitted lifetime of 6.8 ± − and comparable with the wavelength-binned values given above. Unfortunately, the data isof insufficient quality for a bi-exponential fit to accountfor the beam storage lifetime. As for C − , shorter wave-lengths are associated with longer ion cooling lifetimes –see Supporting Information for further details.IR radiative cooling lifetimes for C − from the SHC N e u t r a l Y i e l d ( A R B ) Wavelength (nm)310 320 330 340 350Storage Time (s):0-33-66-1230-55 R e l a t i v e I n t e n s i t y Wavelength (nm)310 320 330 340 350Photon Energy (eV)4.0 3.8 3.6PC1Cold P r i n c i p a l V a l u e / R e l a t i v e E n e r g y Storage Time (s)0 10 20 30 40 50 60PV1SHCSHC + IVR
FIG. 5. Upper: Time-binned photodetachment spectra forC − , recorded by monitoring the yield of neutral particleswith wavelength of light. The black bar represents the ADEand uncertainty determined for ions stored at least 30 s, andthe orange bar corresponds to the photoelectron spectroscopyvalue from Ref. 51. Middle: Principal component (PC1) andcold photodetachment spectrum from the 2D photodetach-ment spectrum of C − . Bottom: Principal values for PC1(denoted PV1) and simple harmonic cascade (SHC) model ofthe cooling lifetime (note the log scale). model are 6.74 ± ± ± C. Pentacarbon anion, C − Time-binned photodetachment spectra and PCA re-sults for C − are summarized in FIG. 6 upper andmiddle/lower, respectively. Fit of the 30–57 s ‘cold’time-binned spectrum with the Wigner threshold lawgave ADE = 2.82 ± ± ± Intriguingly, the cooling behaviourpresents a different situation compared with C − andC − . Whereas hot band photodetachment signal at wave-lengths longer than ≈
435 nm diminishes over the firstfew seconds of ion storage, there is an enhancementof photodetachment signal for wavelengths shorter than ≈
435 nm (i.e. above the ADE), which will be discussedsoon.Ion cooling lifetimes at selected probe wavelengthsare 22 ± ± ± − and C − , shorter wavelengths are associ-ated with longer ion cooling lifetimes.Application of PCA to the 2D photodetachment spec-trum of C − suggested that two principal components(PC1 and PC2 in FIG. 6, middle) are necessary to de-scribe the spectral variation with ion storage time. PC1has a similar wavelength dependence and also principalvalue (PV1) with ion storage time when compared withPC1 for C − or C − . PV1 was best fit with two expo-nential lifetimes of 1.7 ± ± ≈
10 s PV1+ PV2 is roughly steady state), implying that hot bandpopulation associated with PC1 eventually contributes toPC2 at longer ion storage time. We assign PC2 to pre-dominately the Σ + g ( ν (cid:48) = 0) ← Π ( ν (cid:48)(cid:48) = 0) detachingtransition, which occurs at slightly shorter wavelength( ≈ Σ + g ( ν (cid:48) = 0) ← Π ( ν (cid:48)(cid:48) =0) spin-orbit detaching transition. Assuming this as-signment is correct, it appears that as ions cool, the rel-ative population of ground vibrational state anions in-creases and consequently the apparent photodetachmentcross-section for resonant detaching transitions increases(presumably much more so than for C − and C − ). It fol-lows that the long lifetime associated with PC2 is dueto decay of population associated with the Σ + g ( ν (cid:48) =1) ← Π ( ν (cid:48)(cid:48) = 1) and Σ + g ( ν (cid:48) = 1) ← Π ( ν (cid:48)(cid:48) = 1)hot band detaching transitions (see spectroscopic assign-ment of photodetaching hot band modes in Refs. 51–53). N e u t r a l Y i e l d ( A R B ) Wavelength (nm)430 435 440 445 450 455Storage Time (s):0-33-66-930-57 R e l a t i v e I n t e n s i t y Wavelength (nm)430 435 440 445 450 455Photon Energy (eV)2.85 2.80 2.75543F13 PC1PC2Cold P r i n c i p a l V a l u e / R e l a t i v e E n e r g y Storage Time (s)0 10 20 30 40 50 60PV1PV2SHCSHC+IVR
FIG. 6. Upper: Time-binned photodetachment spectra forC − , recorded by monitoring the yield of neutral particleswith wavelength of light. The black bar represents the ADEand uncertainty determined for ions stored at least 30 s, andthe orange bar corresponds to the photoelectron spectroscopyvalue from Ref. 51. Middle: Principal components (PC1 andPC2) and cold photodetachment spectrum extracted from the2D photodetachment spectrum of C − . Bottom: Principal val-ues for PC1 and PC2 (denoted PV1 and PV2) and simpleharmonic cascade (SHC) model of the cooling lifetime (notethe log scale). Note, because ν (cid:48)(cid:48) is an IR inactive mode (see Support-ing Information), decay must be due to IVR followed byradiative emission.IR radiative cooling characteristics for C − from theSHC model are summarized in FIG. 6, lower. Neglect ofIVR resulted in a cooling curve that was best fit with twolifetimes of 4.78 ± ± ± ± − can be traced to mode-specific radiative emission processes. Specifically, thefaster lifetime is dominated by emission from the mainIR active mode ν ≈ − ( A ≈ ν , ≈ −
141 cm − ( A , ≈ −
30) – see mode-specificradiated power plots in the Supporting Information. Sim-ilar double lifetime cooling is not apparent for C − andC − because the majority of the cooling from the highfrequency mode with a large A coefficient occurs on asub-second timescale (see Supporting Information). IV. SUMMARY AND OUTLOOK
The present work has investigated the ultraslow cool-ing characteristics of three astrochemically relevant an-ions under conditions approximating a molecular cloud.Interestingly, an increase in molecular size leads to longeraverage ion cooling lifetimes: 3.1 ± − , 6.8 ± − and 24 ± − . Variation in ion cooling life-times across the hot band is attributed to a distributionof internal energies. These are the first known measure-ments on carbonaceous anions extending to the ultraslow(seconds) timescale; all previous measurements have beenperformed under room temperature conditions and wererestricted to measuring the sub-second cooling dynamics.The increase in average ion cooling lifetime with molec-ular size can be understood by considering the pointgroup symmetry (D ∞ h ) of the anions and that E1 ra-diative transitions require a change in electric dipole mo-ment. In particular, the high symmetry means that eachof present anions have only three vibrational modes with A coefficents larger than 10. Although A coefficientsfor Σ − g symmetric vibrational modes quickly increasewith molecular size beyond C − , for n = 3 − n (mostly IR inactive) and the weakly IR active Π u symmetric vibrational modes become lower in frequencyand have lower radiative emission rates (see EQN 2 andSupporting Information). The net result is an increase inion cooling lifetime with increasing n . These ion coolingdynamics would not be evident at room temperature for n > ≈
342 cm − (C − ) and ≈
587 cm − (C − ) at 298 K assuming harmonicvibrational partition functions. We are presently apply-ing the 2D photodetachment strategy with DESIREE tostudy the ultraslow cooling dynamics of larger carbona-ceous anions to further explore these trends. These re- sults will be the presented in a forthcoming paper.As part of the present study, we developed a simpleharmonic cascade model that proved capable of simu-lating IR radiative emission using input data from con-ventional electronic structure calculations. With provi-sion for IVR, the model was able to qualitatively repro-duce the experimental ion cooling lifetimes and providea mode-by-mode understanding of the cooling dynamics.The agreement between theory and experiment providesconfidence for applying this model to anions for which ex-perimental data is not available or difficult to measure.Finally, it should be noted that application of thepresent 2D photodetachment methodology to largermolecular anions may prove more complicated due tonear-threshold resonant excitations. Specifically, if thereare substantial cross-sections for photoexcitation of ππ ∗ states situated below the detachment threshold or forresonances situated in the detachment continuum, en-suing autodetachment and internal conversion dynam-ics might affect the observed ion cooling lifetimes andspectral features. For example, experiments have shownthat photoexcitation followed by internal conversion torecover the ground electronic state is efficient for C − n ( n >
4) and polycyclic aromatic hydrocarbon (PAH)anions, with photoexcitation cross-sections for op-tically allowed transitions in PAH anions generally beingmuch larger than cross-sections for direct photodetach-ment. If neutral formation through thermionic emissionor dissociation processes takes longer than the time ionsspend in the straight section of the ion storage ring af-ter irradiation ( ≈ µ s), then neutrals formed outsideof the straight section of the ion storage ring will not becounted. Fortunately, in DESIREE, the relative impor-tance of delayed neutral formation can be ascertained bysimultaneously measuring neutral yield on the detectoron the opposite straight section of the ion storage ring(Glass Plate/MCP detector in FIG. 1). ACKNOWLEDGEMENTS
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