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The predissociation of highly excited states in acetylene by time-resolvedphotoelectron spectroscopy

Zamith, S; Blanchet, V; Girard, B; Andersson, J; Ristinmaa Sörensen, Stacey; Hjelte, I;Bjorneholm, O; Gauyacq, D; Norin, Johan; Mauritsson, Johan; L'Huillier, AnnePublished in:Journal of Chemical Physics

DOI:10.1063/1.1589479

2003

Link to publication

Citation for published version (APA):Zamith, S., Blanchet, V., Girard, B., Andersson, J., Ristinmaa Sörensen, S., Hjelte, I., ... L'Huillier, A. (2003). Thepredissociation of highly excited states in acetylene by time-resolved photoelectron spectroscopy. Journal ofChemical Physics, 119(7), 3763-3773. https://doi.org/10.1063/1.1589479

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https://doi.org/10.1063/1.1589479

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https://doi.org/10.1063/1.1589479

JOURNAL OF CHEMICAL PHYSICS VOLUME 119, NUMBER 7 15 AUGUST 2003

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The predissociation of highly excited states in acetylene by time-resolvedphotoelectron spectroscopy

S. Zamith, V. Blanchet,a) and B. GirardLaboratoire de Collisions, Agre´gats et Re´activite, IRSAMC-UPS-CNRS, Toulouse, France

J. Andersson and S. L. SorensenDepartment of Synchroton Radiation Research, University of Lund, Lund, S-221 00, Sweden

I. Hjelte and O. BjorneholmDepartment of Physics, Uppsala University, S-75021 Uppsala, Sweden

D. GauyacqLaboratoire de Photophysique Mole´culaire, CNRS, Orsay, France

J. Norin, J. Mauritsson, and A. L’HuillierDepartment of Physics, Lund Institute of Technology, Lund, S-221 00, Sweden

~Received 20 December 2002; accepted 14 May 2003!

We study the dynamics of highly excited states in acetylene initiated by an ultrashort vacuumultraviolet laser pulse. Electronic states lying in the 4s-3d Rydberg region are excited with onefemtosecond pulse, and the dynamic development of the states is monitored by a second short pulsewhich ionizes the system. We show that even for femtosecond pulses where the bandwidth of theexciting pulse covers several electronic states, it is possible to extract short decay lifetimes throughtime-resolved photoelectron spectroscopy by using a frequency-modulated~chirped! excitationpulse. We report decay lifetimes for theF 40

2 andE 4-502 states in acetylene, and for theE 40

2 andE 50

2 states in d-acetylene. The time evolution measured in the electron spectra is compared to decayspectra measured using ion yield and the differences in these results are discussed. ©2003American Institute of Physics.@DOI: 10.1063/1.1589479#

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I. INTRODUCTION

The formation mechanism of amino acids and polyolsthe extraterrestrial atmosphere is an important questionbiology, planetary astrophysics, and cosmology. The etence of a variety of important species can be traced toterstellar photochemistry taking place in interstellar molelar clouds.1 Molecular building blocks consisting of simplcarbon and nitrogen-based compounds form the basiscomplex organic molecules which play a key role in terrtrial biology. Ultraviolet photolysis of these simple moecules is a fundamental mechanism for this process andderstanding the steps leading to larger carbon-based sysis a challenge for interstellar chemistry. The most abundmolecules in the interstellar medium include H2, CO, andacetylene. A detailed understanding of photoinduced retions, including direct dissociation and predissociatmechanisms, is implicit to completing the photoreactive snario behind the formation of larger molecules such as sars and amino acids. In this work we focus on the dissotion induced by photoabsorption in the ultraviolet regionacetylene and its deuterated isotope. There are very stabsorption bands in the 9–12 eV region of these molecuthe bands consist of overlapping Rydberg series and vale

a!Author to whom correspondence should be addressed. [email protected]

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electronic states. The lifetimes of these states range fpicoseconds to a few femtoseconds, even for states lyvery close in energy.2,3

In the present experiment, we apply a time-resolvspectroscopic technique capable of monitoring dynamicsa femtosecond time scale to Rydberg and valence stateC2H2 and C2D2 using an ultrashort pump pulse at about 9eV. These states lie in the Rydberg (3d-4s) complex at about2 eV below the ionization threshold. TheF 1Su

1(3dpg) Ry-dberg state shows the strongest photoabsorption inregion.4 All of the Rydberg transitions exhibit vibrationabands corresponding to excitation of the symmetric streting moden2 since the C–C triple bond is lengthened compared to the ground state. A weak excitation of thetransbending moden4 is apparent in theF-X excitation,5 arisingfrom interaction with the nonlinearE valence state. Thesbands have been explored via photofragment action speccopy where lifetimes ranging from 60 up to 150 fs wereported.3,6 Here, we investigate the dynamics from theF 40

2

state and theE 4-502 state. The excitation scheme is shown

Fig. 1: the dissociation dynamics are probed by a transiton to the ionic continuum by a probe pulse.7,8 The dynamicsof the excited state are analyzed through time-resolved ptoelectron spectroscopy~PES! and ion spectrometry.9 Thereare only two dissociation channels open at the 9.4 eV puenergy.10 Both lead to C2H radical formation~in the A 2Pelectronic state or theX 2S1 ground state—with 3600 cm21

energy of separation between the electronic origins11!. Theil:

3 © 2003 American Institute of Physics

e or copyright; see http://jcp.aip.org/about/rights_and_permissions

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3764 J. Chem. Phys., Vol. 119, No. 7, 15 August 2003 Zamith et al.

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CH1CH and C21H2 channels are not open at 9.4 eV bcause the dissociation threshold is at a higher energy forlatter channel, while the former channel is accompanied bhigh energy barrier.12,13

The density of states is generally high in molecuwhere close-lying electronic states have overlapping vibtional progressions. Complete selectivity in the excitationa vibrational sublevel requires narrow bandwidth pulsThese stringent requirements are not always compatibleshort pulse durations needed to time-resolve the dissociadynamics. We illustrate the situation for the case in handFig. 2. The absorption spectra for acetylene and d-acetyin the region of current interest are shown in the upper patogether with a Gaussian distribution of a pulse energy cresponding to two pump wavelengths, namelyl1

5132.2 nm (75 643 cm21) andl25132.0 nm (75 757 cm).Note that in acetylene thel1 pulse mainly excites theF 40

2

state, while thel2 pulse excites theF 402 state as well as the

quasi-degenerateE 4-502 states. We use a frequency mod

FIG. 1. Principle of the pump-probe experiment.

FIG. 2. REMPI~311! spectra of~a! C2H2 and ~b! C2D2 together with thepump spectra corresponding to the two different excitation wavelen~dotted linel15132.2 nm, solid linel25132.0 nm). The Wigner representation of the pulse centered at 132.0 nm is plotted in~c! and~d!. A positivelinear chirp off9515330 fs2 stretches the pump pulse from 50 to 300FWHM. For both contour plots, the instantaneous frequency of the pufield, vp(t), is indicated by the dashed line.


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lated ~chirped! pump pulse. The Wigner diagram of suchpulse~at the central frequencyl2) is shown as a contour ploin the lower panels of Fig. 2: the time axis shows the dution of the pulse, and the dashed slope represents the intaneous frequency of the pump field. The two states~indi-cated by the vertical lines in the figure! will be excited atdifferent times as the pulse ‘‘sweeps’’ through the frequenrange.

Each excited state will decay on an individual time scaThe interplay between the pump pulse and the molecelectronic states, analyzed by recording the pump-probenal gives a fingerprint of the system. The molecule provida time-energy benchmark: the energies and lifetimes of thexcited states. If the photoelectron bands overlap in thesulting spectra, and if geometry changes occur duringphotoionization, it is generally impossible to disentangletime evolution of each excited state separately, even usenergy-dispersive spectroscopy. To circumvent this problthe pump pulse is frequency modulated~chirped! so that themoment when the frequency is resonant with the state, ‘‘tizero,’’ is different for each excited state. The linear sweepthe pump frequency provides atime-energy scale, which canbe adjusted to match thetime-energy benchmarkof the mol-ecule.

The concept oftime-energy scalepresented here deserves a thorough explanation. Consider a molecule whcan be excited into statesA andB by absorption of photonsof the two different energiesEA andEB , as indicated in theupper panel of Fig. 3. In our experiment the overall, timaveraged photon energy distribution in the excitation pulsconsiderably broader than the energy separation betwstatesA andB, see the lower panel of Fig. 3. Both statesAand B will thus be excited by the same pulse. In a timresolved view, however, the photon energy distributionany given timetx is narrower due to the chirp. As schema

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FIG. 3. Principle of time-energy benchmark.


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3765J. Chem. Phys., Vol. 119, No. 7, 15 August 2003 Predissociation of acetylene

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cally shown in the middle panel, the ‘‘chirp’’ of the pulse cabe described as a sweeping of the photon energy throughenvelope of the time-averaged photon energy distributExcitation occurs when the photon energy matches the etation energy and over a time corresponding to the abstion band. TheA state will be excited att2 and theB statewill be excited att4 . The ‘‘chirp’’ can thus be said to providea time-energy scale, as statesA andB are excited at differentimes. Any dynamic development of statesA andB will thusbe separated by this difference in starting time, greatly factating the analysis of the spectra. This makes it possibleextract the time-dependent signature for each state fromtime-resolved PES. Deuterated acetylene provides a sligdifferent time-energy benchmark, with another response tthe chirped pump pulse because of the longer decay tiupon deuteration.

Another challenge of this experiment is the use of a fetosecond pump pulse in the vacuum ultraviolet~VUV !. Anumber of techniques are now becoming available to pduce short-pulsed, VUV radiation. Most of these techniquse nonlinear processes in a gas.14 Recent time-resolved dynamic studies have been performed in the VUV and eXUV range15 using cascade nonlinear wave mixing in a hlow fiber filled with a rare gas,16 two-photon resonandifference-frequency mixing,17 and high-order harmonicgeneration.18 Refinement of the harmonic-generation tecnique has led to greater control over the pulse shape19 andimprovement of the pulse-generation efficiency in the VUXUV wavelength range shows great promise, in particufor the study of femtosecond dynamics in polyatomic mecules. In the present article, we use the third harmonic ointense frequency-doubled titanium-sapphire laser as a ppulse while the probe is taken from the frequency-doublight.

The experimental setup is described in Sec. II. In SIII, we present the time-resolved PES for the two excitatwavelengths used and we compare our results to (311)resonant enhanced multiphoton ionization PES~REMPI-PES! using nanosecond laser pulses.5 The analysis of thephotoelectron spectra and the time-dependent ion-yield stra including the resulting dissociation lifetimes of the ecited states is presented in Sec. IV.

II. EXPERIMENTAL SETUP

The general experimental setup is depicted in Fig. 4.use the 10 Hz terawatt laser at the Lund high-power lafacility to generate infrared pulses with 100 mJ energy, 1fs duration, 792 nm central wavelength, and about 10bandwidth. The 396 nm pulse used to generate high-oharmonics and the time-delayed 396 nm probe pulse areerated through frequency doubling in 1.5-mm-thick KDcrystals in a modified Michelson interferometer~see Fig. 4!.The pulsed infrared beam is divided into two beams~66%for the pump generation and 33% for the probe! by a beamsplitter. A negative lens is inserted in one of the beam pato focus the two pulses at different distances. A 1.5-mm-thKDP crystal frequency doubles one of the pulses before tare recombined by a dichroic mirror, which transmits tinfrared radiation and reflects the blue~396 nm! light. An


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identical KDP crystal doubles the other pulse, and finallyremaining infrared light is filtered away by a second dichromirror ~not shown!. A computer controlled translation stagwith 1 mm resolution controls the position of the end mirroin one of the interferometer arms. This setup allows usproduce pairs of 396 nm pulses, and to control the debetween them. The output energies are 7 mJ for the pgenerating the harmonics and 1.5 mJ for the probe overcm diameter. A positive lens with a 2 mfocal length is thenused to focus the two beams. The first beam is focused uthe nozzle of a xenon gas jet~point A in Fig. 4! to generateharmonics and the second~probe! beam is focused about 1.m from the jet~point B in Fig. 4!. The time-resolved experiments utilize the third harmonic~132 nm! as a pump pulseand a probe 396 nm pulse. The fifth harmonic~15.8 eV! byionizing both the acetylene sample, and the rare gaseslows us to calibrate the photoelectron spectrometer enescale and resolution, as well as to optimize and alignexperimental setup. In the pump/probe experiments, thismonic is eliminated by using a 3-mm-thick lithium-fluorid~LiF! window after the gas jet. LiF absorbs radiation belo105 nm~11.8 eV!. The efficiency for third-harmonic generation in xenon gas is about 1026, leading to a pulse energy oabout 10 nJ at 9.4 eV.

The 396 nm pulse generating the VUV pump pulsestill present in the interaction area but we can disregardinfluence in the present experiment for two reasons. Firstpower density in the interaction region is too low to ioniacetylene through multiphoton ionization, and seconddispersion in the LiF window introduces a significant timdelay ~several picoseconds! between the fundamental pulsand the third harmonic. With the LiF window, the sampleionized only when the pump and probe pulses are propsynchronized. Note that the pump/probe signal can alsoobserved without the LiF window, but with a contrast of on50% due to higher harmonics.

An additional source of information is the time-resolveion-mass signal. The probe pulse is focused halfway betwthe ion and photoelectron spectrometers making the bdiameters and hence the overlap with the pump pulsesame for the two spectrometer source regions. Positiveare collected in a 70 cm field-free time-of-flight tube adetected by an electron multiplier~EMT!. The inevitableflow of xenon from the pulsed jet used for harmonic genetion into the ion spectrometer is used as a cross-correla

FIG. 4. Experimental setup.


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monitor gas: when pump and probe pulses are synchronixenon atoms are ionized through a nonresonant two phoionization process.

The photoelectron spectrometer is a truncated hespherical electrostatic analyzer with a 144 mm radius eploying a four-element retarding lens and a two-dimensiomultichannel detection system. The detector consists omatched set of microchannel plates with a phosphor scrThe analyzer may be operated in fixed lens potential mfor a given pass energy, or the potentials can be swthrough the kinetic energy region of the spectrum. Eaevent is recorded using a video camera and the integratiothe signal is made on the camera and charge-coupled dearray. This multichannel electron detection allows us tofectively compensate for the relatively low spectrometransmission. There is an aperture and a slit between thecell and the lens making an effective acceptance angle ofthan 0.05%. A second slit at the entrance to the analymakes an effective vertical acceptance angle of aboutThe gas sample is ionized in a continuously pumped gaswith a pressure of approximately 0.01 mbar. The backgropressure is 3.031028 mbar. For this experiment the spetrometer was run at a pass energy of 20 eV resulting inominal energy resolution of 50 meV. For these experimethe measured spectrometer full width at half maximu~FWHM! is approximately 100 meV. The difference betwethe optimal resolution and the measured value arises prrily from the ion cloud which builds up with each laser pulsThe space charge effects are severe in this case.

The spectral width of the 396 nm pulses is measuredbe 2.560.1 nm (170 cm21), which corresponds to a 90 fFourier-limited pulse. The temporal width of the pulselonger than its Fourier transform limit, due to group velocdispersion in different optical components~beam splitters,windows, crystals! affecting both the fundamental and frequency doubled pulses. In addition, the use of high enepulses also leads to self-phase modulation in these opcomponents, which is much more difficult to control aestimate than group velocity dispersion.20 After accountingfor these effects, we estimate the pulse duration of the prto be 260630 fs, with a positive~approximately linear!chirp. The spectral width of the pump pulse can be estimausing perturbation theory to be larger by a factor of) com-pared to the generating pulse. This produces a nominal pwidth of 290 cm21 corresponding to a Fourier limited temporal duration of 50 fs. Since the laser field generatingharmonics is positively chirped, it is reasonable to expecsimilar chirp of the harmonic pulse.21 In addition, dispersionin the LiF window leads also to positive frequency chirThe pulse duration and chirp of the pump~and probe! pulsesare extracted from a multifit procedure where photoelectand photoion pump-probe signals in C2H2 and C2D2, as wellas Xe ion cross-correlation data, are taken into account.procedure is described in detail in Sec. IV.

The experiment was performed at two fundamental lawavelengths producing slightly different harmonic energil15132.2 nm ~9.378 eV! and l25132.0 nm ~9.390 eV!.These wavelengths were verified by comparing the phoelectron kinetic energies from the ns REMPI spectra5 and the


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ones from the present fs pump-probe experiment. Referto the upper panel of Fig. 2 we note that for both isotopesl1 pulse initiates dynamics primarily from theF 40

2 Rydbergstate in C2H2 ~2 quanta in thetrans-bending modes! andfrom the E 50

2 valence state in C2D2 ~2 quanta in thecis-bending modes!. The other bands involved are excited wioptical intensities less than 15% of the maximum. Thel2

pulse, on the other hand, leads to excitation of two initstates: in C2H2 , the F 40

2 Rydberg and the quasi-degeneraE 4-50

2 valence states are excited, while theE 502 and E 40

2

valence states in C2D2 . In the case of excitation atl1 , thechirp of the pump pulse would be mainly visible through trising edge of the pump-probe signal effectively prolongithe time during which the laser frequency is resonant.22,23 Inthe case of two excited states~at l2), a chirp will also causethe two states to be excited at different times since the pufrequency is in resonance with the two states at differtimes within the pulse. The Wigner representation of thel2

pump laser field is plotted in Fig. 2~lower panel!, assuminga linear frequency chirp as discussed above. Second-odispersionf9515330 fs2 causes the temporal FWHM tincrease from 50 to 300 fs, with the lower frequencies arring first. The Wigner representation illustrates that thchirped pulse effectively excites theF 40

2 Rydberg state inC2H2 about 300 fs before theE valence state. This differencin time is not large enough to be observed in an integrasignal like the ion signal,24 especially when one optical transition is weaker than the other one. Excitation of two stawith different energies is visible in the final-state photoeletron kinetic energies and this makes it possible to deducerelaxation times separately for each excited state.

III. PHOTOELECTRON SPECTRA

In Fig. 5, contour plots of photoelectron spectra of C2H2

and C2D2 using a pump wavelength atl15132.2 nm@~a!

FIG. 5. In the upper part of the figure@~a! and~b!#, the photoelectron spectrarecorded atl15132.2 nm at different pump-probe delays are presentedcontour plots for both isotopes. The excited bands are~a! theF 40

2 Rydbergstate in C2H2 and ~b! the E 50

2 valence state in C2D2 . The intensity of theentire photoelectron spectrum varies with the pump-probe delay. Inlower part, the photoelectron spectra recorded atl25132.0 nm~c! in C2H2

and ~d! in C2D2 . For both isotopes, the PES contour plots show two mstructures in energy with a clear difference in temporal dynamics.


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and ~b!# or l25132.0 nm@~c! and ~d!#, are presented asfunction of the delay between the pump and probe pulsThe background spectra measured using only the 9.4pump pulse and using only the 3.15 eV probe were stracted from all photoelectron spectra. This background cresponds to only 10% of the signal maximum recordaround delay ‘‘0.’’

The spectra excited with thel1 pulse show essentiallyone photoelectron band whose amplitude varies withtime delay@Figs. 5~a! and 5~b!#. The spectra measured aftexcitation withl2 for both isotopes are more [email protected]~c! and 5~d!#. These spectra appear to have at leastdifferent features, which follow different temporal develoments.

In Fig. 6 we present~a! C2H2 and~b! C2D2 PES excitedat l1 . We have chosen the spectra at the time delay whresults in the maximum photoelectron signal and we copare them to PES recorded in (311) ns-REMPI plotted as asolid line.5 These ns-REMPI PES have been recorded wit30 meV total energy resolution, at resonance with~a! themaximum of theF 40

2 Rydberg state absorption bandacetylene and~b! with the maximum of theE 50

2 valencestate in C2D2 . The ns-REMPI spectra are broadened to100 meV FWHM measured on the fs-photoelectron sptrometer. We expect to see features arising from ionizatiothe same excited state in the fs and ns experiments, ethough in the ns-REMPI spectrum, differences in measument techniques result in narrower lines and a limited kineenergy region since electron kinetic energies below 0.4are not measured. Due to a similar geometry of the groelectronic states of neutral acetylene and its cation and to

FIG. 6. For~a! C2H2 and~b! C2D2 , a femtosecond photoelectron spectru~scatter plot! recorded atl1 is compared to the~311! ns-REMPI photoelec-tron spectrum~solid plot! recorded at the maximum of the absorption banin Fig. 3, corresponding to~a! a F 40

2 Rydberg state in C2H2 and~b! anE 502

valence state in C2D2 . The ~311! ns-REMPI photoelectron spectra is convoluted by a 100 meV Gaussian for comparison with the fs photoelecspectra.


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fact that dissociated molecules cannot be ionized, theREMPI spectrum contains the main features arising frzero time-delay pump-probe ionization. Therefore manythe features in the fs spectrum can be identified. The mintense peak in the spectrum~at ;0.9 eV) thus arises fromthe 2n4 Renner–Teller multiplet of the RydbergF 40

2 state.In the C2D2 spectrum the corresponding peak is assignedthe 2n5 band of theE 50

2 state.5 For both isotopes, theweaker component at 1.1 eV is the adiabatic peak ofexcited state.25 At l1 , the pump pulse populates mainly oninitial state. Since the total energy put into the systemidentical for the ns and fs experiments, it is clear thatsimilarities between the two photoelectron spectra reflectFranck–Condon factors for ionization from the excited staTheir difference at higher internal energy of the parent~i.e., lower kinetic energy of the emitted photoelectron! ismainly the imprint of the decay through the Franck–Condregion, as well as the signature of the continuum underlythis excitation range. We find no evidence for dynamical fetures in the spectra shown in Figs. 5~a! and 5~b!. The photo-ionization involved here is not sensitive to any nucleuselectronic wave-packet motion since no photoelectronnamics is visible on the contrary to Refs. 26 and 27. Tmost obvious reason for this is that the total energy (13.14 eV) is not sufficient for accessing excited states ofacetylene ion and that the resolution is not sufficient tosolve the Renner–Teller structure of the ionic ground stat28

The first rules out observation of any ionization dynamarising from a change of the electronic interaction in tneutral molecule,29 while the second prevents observationnuclear wave-packet dynamics.

Figure 7 shows the C2H2 PES recorded at the excitatiowavelengthl2 at a range of pump-probe delays. The twfeatures pointed out in Fig. 5~c! are clearly visible at 0.7 and0.9 eV kinetic energy. We compare with the ns-REMspectra5 for the same total energy, to identify the featureThe F 40

2 Rydberg band identified in Fig. 6 is still visible a290 fs pump-probe delay, while at 400 fs the photoelectspectrum is mainly characterized by a;0.7 eV peak. This iscompared to the ns-REMPI spectrum in the same way asprevious spectra and identified as ionization of the quadegenerateE 4-50

2 valence state. The difference of 200 meobserved between the main component of the two photoetron spectra, while the Franck–Condon image will lead todifference of only 25 meV observed on the excitation sptrum, is due to the combination of the nonlinear geometrythe E valence state and the Renner–Teller effect that undlies the photoionization.5 Thel2 excited fs spectrum is similar to the l1 spectrum for theF state and to the (311)ns-REMPI spectrum at the energy of theE valence state. Bydoing such a comparison, all features in the spectrumaccounted for. The relative weights of these two featuresclearly time-dependent and they decay with different litimes. In addition, the dynamic time-energy signature ofpulse interacting with the molecule will shift the dynambehavior of these two features if they arise from excitstates with different energies. This is becausethe time-energyscaleof the pump pulse and thetime-energy benchmarkofthe molecule are matched, as discussed further in Sec. I

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Figure 8 shows the time-resolved PES for C2D2 re-corded in experimental conditions identical to the C2H2 case.Comparing the two sets of spectra we note that for shpump-probe time delays the features are similar: the loenergy level, theE 50

2 valence state, is excited first. The dcay of this state is initiated while the pulse sweeps througthe next resonant excitation, namely theE 40

2 state. Thishigher-energy state dominates the photoelectron spectrumlonger pump-probe delays. The time features observedFig. 8 have been identified through the similarity of thePES and the ns-REMPI-PES for these valence states.

For both isotopes, the electronic state excited later inpump pulse is also characterized by a set of Renner–Tcomponents which decay together showing no dynamicalhavior. The photoelectron spectra can be simulated by uthe ns-REMPI spectra as model features which simply deon their respective time scales without including any dephing time that would be a signature of a nucleus or electrowave-packet motion. To summarize, from thel2 analysis ofFig. 7 ~Fig. 8!, we distinguish in C2H2 ~in C2D2) the time-dependency of the quasi-degenerateE 4-50

2 valence state(E 40

2 state! from the time-dependency of the RydbergF 402

state (E 502 state! observed also atl1 . This allows us to

deduce the~time dependent! relative weight of the excita-tions to the different states, which will be used in the teporal analysis presented below.

FIG. 7. Photoelectron spectra in C2H2 recorded atl25132.0 nm~scatterplots! for a series of delay times. The dotted lines represent the PEStained via~311! ns-REMPI from theE 4-50

2 states and convoluted by a 10meV Gaussian. The dashed lines represent the fs-PES from theF 40

2 staterecorded atl1 and shown in Fig. 6~a!. Their sum is plotted using a solid linein order to compare with the fs-PES.


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IV. TEMPORAL ANALYSIS

A. Description of the model

Keeping the basic spectral analysis in mind, we useinformation in our set of spectra to deduce the lifetimesthe excited states and the temporal characteristics ofpump and probe pulses. The time-resolved Xe ion sigprovides the cross-correlation time between the pumpprobe pulses directly. The temporal dynamics of photoeltron spectra and the ion-yield spectra also depend onlifetimes of the electronic states contributing to the specSince we have already determined that wave-packet dynics can be neglected,30 we can treat the system using a simplified model. A three-level system consisting of the groustate, the excited state, which decays exponentially, anfinal ~continuum! state is sufficient. The large spectral widof the PES averages any effect due to a chirp of the prob31

Each pump-probe signal can be written as

Sds~Dt !}U E

2`

1`

dtE0

`

dt8Ep~ t2t8!

3e2 i ~vLp2ve!~ t2t8!2 iap~ t2t8!2Es~ t2Dt !

3e2 i ~vLs2v f !~ t2D!2 ias~ t2Dt !2e2t8/2teU2

, ~1!

in which te is the decay time of the excited state with ener\ve above the ground state. The final state lies\v f abovethe excited state.Ep(t) andEs(t) are the Gaussian envelopeof the pump and the probe fields, respectively, defined

b-FIG. 8. Identical to Fig. 7 for C2D2 . The dotted lines represent the PEobtained via~311! ns-REMPI from theE 40

2 state. The dashed lines represent the fs-PES from theE 50

2 state recorded atl1 and shown in Fig. 6~b!.Their sum is plotted using a solid line in order to compare with the fs-P


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Ei(t)5exp@22 ln(2)t2/ti2#. tp and ts are the durations o

pump and probe pulses, respectively,Dt the pump-probe delay, whilet0p andt0s are the Fourier limited FWHM.ap andas are the chirp coefficients related to the quadratic dispsion f9 as follows~with i 5p or s):

a i52f i9

@t0i2 /2 ln~2!#214f i9

2 . ~2!

We introduce the resonant detuningsdp5vLp2ve and ds

5vLs2v f wherevLp andvLs are the central frequencies othe pump and probe fields. Since the final state is in a ctinuum, the pump-probe signal is obtained by integratSds

(Dt) over the probe spectral profile 2d f (d f585 cm21).The total signal takes the following expression:

Stheo~Dt !}E2d f

1d fddsSds

~Dt !}e2Dt/tee~t0p2

1t0s2

!/8te2

3E2d f

1d fddse

~dsast0s

2 ts

22dpapt0p

2 tp2!/2te

3U12FS gAbs1bp

2AbsbpD U2

, ~3!

whereg5( ibpds2 ibsdp22bpbsDt)/(bp1bs)11/2te andF is the error function. The coefficientsbp and bs charac-terize the chirps as follows~with i 5p or s):

b i54 ln 2

t i2 1 ia i . ~4!

The instantaneous frequency of the pump field,vp(t)5vLp

12apt, is represented as a dashed line in the Wigner ctour plots in Figs. 2~c! and 2~d!. The time dependence of thpump-probe signals appears in the exponential term anthe error function in Eq.~3!.

In Fig. 9, we illustrate the concept of atime-energy

FIG. 9. Simulated pump-probe signals from a~a! te5300 fs or ~b! te

5100 fs excited state for different detunings of the central frequency ofexciting pulse from the resonance frequency for the electronic state,dp . Thecontour plot follows a grayscale with the lighter shade as the maximumpump-probe signal. The chirped pump pulse duration is 300 fs and the ppulse is a 90 fs Fourier limited pulse for both simulations. The resonafrequencies encountered atl2 in C2D2 are indicated by the horizontal arrows. The pump frequency sweep is the solid line. The Lorentzian bawidths of the excited states~solid plot! are shown and may be comparedthe broad 290 cm21 pump field bandwidth~Gaussian dot plot! on the right-hand panel.


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benchmarkby simulating the pump-probe signal of a singexcited state defined by its excitation band and a varylaser wavelength~or conversely defined by a varying detuing dp at a fixed laser wavelength!. Several independensimulations have been carried on using Eq.~1! for differentvalues of detuningdp and are presented in a 2D contour pl~reversed grayscale!, in the (dp ,Dt) plane, since the evolution of the temporal profile as a function ofdp is smooth andregular. The electronic state is treated as a homogenodecaying state defined by a 1/2te Lorentzian absorption bandof ~a! te5300 fs and~b! te5100 fs. The pump pulse is linearly chirped from 50 to 300 fs while the probe pulsetransform limited to 90 fs. On the same contour plot is drathe instantaneous frequencyvp(t) ~bold solid straight line inFig. 9!. To illustrate the frequency scale of the relevant quatities, we have plotted the laser profile~dotted line! and thespectral line shape~solid line! on the right-hand panel. Twotick marks correspond to the two resonances encounterel2 in C2D2 .

Several features can be observed in Fig. 9: For a gidetuning, the maximum pump-probe signal ‘‘lags’’ after thzero time delay. Indeed, the population increases up to‘‘end’’ of the pump pulse. This time lag is reduced when texcited state lifetime is ultrashort compared to the pupulse duration~pump-probe signal equivalent to the croscorrelation! and for large positive detuning~and positivechirp!.32 This simulation can be used to understand the cof several transitions lying simultaneously within the lasbandwidth: The pump pulse excites them sequentially aspulse frequency comes into resonance. The shift betweenmaxima associated to these two resonances is clearly obable. The overall pump-probe signal consists of the incohent sum of the two contributions. Thanks to this shift, it cbe easily analyzed, even when the lifetimes are of simmagnitude.

The point illustrated in Fig. 9 is that the pump pulsedefined by itstime-energy scale: the chirp links the band-width and the duration of the pump pulse together. Tpump-probe signal ties thetime-energy scaleof the pumpand the time-energy benchmarkof the excited statetogether.32 Owing to the chirp imparted to the pump field, thpump-probe signal varies significantly as a functiondetuning.32 These are the direct result of the competition btween the coherent transients defining the building-timethe population and the decay process.32 This allows us inprinciple to fully characterize thetime-energy benchmark,i.e., position of the resonance energy and the decay tiConversely, for a fully characterized molecule, the behavof the time-dependent signal should allow us to determthe central frequency and the chirp of the pump laser. Inpresent work, neither the chirp of the pump field nor tlifetime of the excited state are known exactly. However,do know the resonance detuning. In addition, we have seral pump-probe signals which depend directly on the chof the pump pulse. Note that since the final state is incontinuum, a chirp of the probe pulse does not providetime-energy scale. It only decreases the time-resolution anhence attenuates the effect of thetime-energy scaleof thepump pulse.

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To determine the lifetimete of each excited state as weas the chirp of the pump and probe pulsesap and as , weperform a multifit operation. It involves a simplex optimiztion of the Err function defined as follows:

Err5(n

ErrnNn

,

with the indexn linked to thenth pump-probe signal~suchas photoion or photoelectron spectrum, for C2H2 and C2D2),Nn is the number of data points in the pump-probe signand Errn is the error to minimize for each delay. The inpparameters are the Fourier limited duration of the VUpump and probe pulses as well as the resonance detunindp

between the pump carrier frequency and the maximum ofabsorption band for each of the excited states.

B. Results and discussion at l1

Figure 10 shows the experimental data atl1 ~closedsquares for the C2H2 and C2D2 data, and open circles for Xe!together with the fits~solid and dotted lines! obtained fromthe multifit procedure described above. Note that the timdependency of the photoelectron is the one observed in F5~a! and 5~b!. The top curves show~a! the acetylene and~c!deuterated acetylene total electron signal and~a! the Xe ionsignal. The bottom curves present~b! the acetylene and~d!deuterated acetylene ion signal with the Xe fit only. Theare in reasonable agreement with the time-resolved signThe chirp of the pump pulse results in a pulse lengthenfrom 50 to 320 fs. We find a significant chirp of the probpulse resulting in a pulse lengthening from 90 to 340slightly longer than the 260 fs estimation. This leads tocross-correlation time of 470 fs obtained from the Xe1 sig-nal. The results from the multifit procedure are displayedTable I.

FIG. 10. Result of the multifit procedure of the PES signal@~a! : C2H2 , ~c!:C2D2] and the ion@~b! : C2H2 , ~d!: C2D2] as function of the pump-probedelay, for a central pump wavelength of 132.2 nm. The experimentalare plotted with closed squares. The result of the fitting procedure is plousing a solid line. The measured and fitted cross-correlation signals oare compared in~a! and the fit is reproduced in~b!–~d!. The values of theparameters derived by the multifit procedure are collected in Table I.


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The similarity between the cross-correlation and telectron signal in Fig. 10~a! clearly indicates that the temporal resolution is not sufficient to determine the decay timethe excited state. The time dependence of the C2H2

1 ion sig-nal @Fig. 10~b!#, however, is significantly slower than thameasured in the PES. We attribute this difference to a mselective decay channel for the measured electron speThe photoelectron spectrometer lens makes the transmishighly directionally selective. The detected electronsemitted in a narrow cone~less than 1°) in the horizontaplane, while the ion time-of-flight spectrometer has nea4p transmission. The transition to theF 1Su

1 Rydberg state isa S1-S1 transition, preferentially selecting acetylene moecules with the CC axis parallel to the polarization of tpump field. The entrance axis of the photoelectron spectreter is perpendicular to both pump and probe polarizatioWe propose two explanations for the striking difference btween the ion and electron signals. One possibility assumresonant pump-probe excitation scheme where no photoetron emission takes place in the horizontal plane whatethe transient state encountered during the dynamics. Thentime-dependence observed in the PES would followcross-correlation signature resulting from nonresonant etation and would be identical to the Xe cross correlatispectrum. However, for all time delays the PES shownFig. 5 clearly exhibits the signature of theF 40

2 state in the2n4 Renner–Teller multiplet.

A second explanation involves two dissociation prcesses, where one is monitored in the electron spectrumfast dissociation process producing electrons emitteddominantly in the horizontal plane and visible with an anglar selective photoelectron detector, and a slower procemitting electrons mainly in other planes would explain thdiscrepancy. The 4p detection ion signal contains the twdissociation channels, however, the slower one is the donant channel. This has similarly been observed by recordphotofragment action spectra of the C2H radicals for a

tade

TABLE I. Decay times and pulse durations for the fits in Figs. 10 and 1

at l15132.2 nm—one excited state

Isotope Species Lifetime~fs!Excited

state Ref. 6

C2H2 ions 219630 F 402

electrons 1266C2D2 ions 312630 E 50

2 140 fselectrons 200620

Pump duration~fs! 326630Probe duration~fs! 340630

at l25132.0 nm—two excited states

Isotope Species Lifetime~fs!Excited

state Refs. 6 and 3

C2H2 ions 171625 quasidegenerate

E 4 – 502

143 fs

electrons 147615

C2D2 ions 600620 E 402 210 fs

electrons 644645Pump duration~fs! 280630Probe duration~fs! 340630


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1Pu(3ddg) Rydberg state lying;6000 cm21 above theFstate.6,33 These spectra indicate two open dissociation chnels:~i! a very fast dissociation~femtosecond time scale! in aquasi-linear geometry leading to fast H fragments andC2H(A 2P) fragments with low vibrational excitation in thstretching modes; and~ii ! a slower dissociation~picosecondtime scale! taking place in nonlinear geometry and leadingslow H fragments and C2H(A 2P) fragments with a broadstructureless statistic-like energy and isotropic angudistributions.6,33 This broad internal energy distribution ithe C2H(A 2P) fragments corresponds to highly excitebending levels, as was recently shown by the analysis ofC2H fragment emission spectra,11 and is compatible with aslow dissociation process leaving time to the nuclei for laamplitude bending motion.

For theF Rydberg state andE state, the photofragmenaction spectra of Ref. 6 were recorded after excitation tovibrational 20

1 and 4-502 levels, respectively, leading to sim

lar conclusions.6 The angular emission patterns for the stameasured in this study might provide conclusive informatabout this matter. A study of the photoelectron spectra frthese states using an imaging detector would beadvantage,34 as recently achieved in other femtosecond timresolved experiments on photodissociation dynamics35 andintersystem crossing.36 Relevant information to understanthe difference between the ion and the photoelectron demight also be obtained by comparing the angular dependeof ns-PES and fs-PES. In reality, even for dissociation whis fast compared to the rotational period of the parent mecule, we would expect that the predissociation occurs wisignificant change of geometry.35 This would lead to dynam-ics visible in the electron kinetic energies and intensities,in the angular dependence of electron emission. Clearlyexperiment would benefit by having a higher photon enein the probe pulse where fragment states could be ionize

We can compare our value of 200 fs with the 140lifetime estimate from the spectral linewidth of D1 photof-ragmentation from theE 50

2 valence state in C2D2 ~see TableI!. The photofragment action spectra of the C2D radical doesnot show an angular dependency as strong as the oneserved in C2H, while still exhibiting two dissociationchannels.6 This is in line with the similarity that we observbetween the decay times observed for the ion and anselected photoelectron signal.

C. Results and discussion of l2

The discussion regarding the excitation of two stawith the same pulse makes it clear that the analysis ofspectra will be more complex than for the first excitatiwavelength. The analysis is done on seven different setpump-probe signals: the two temporal components inelectron spectra and the ion yield for both isotopes, thenon cross-correlation data. The time-dependencies of thspectra are presented in Fig. 10. The fit is carried out insame way as earlier; the fixed input parameters are therier limited pulse durations, the resonance detunings, anddecay behaviors found atl1 excitation for theF Rydbergstate for the electron~earliest temporal component! and ion


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signals in C2H2 and similarly the decay atl1 for the E 502

valence state in C2D2 . The lifetimes te of the quasi-degenerateE 4-50

2 valence state for C2H2 and theE 402 va-

lence state for C2D2 and the chirp of the pulsesap and as

are then deduced through the multifit procedure.The fitted values for these parameters are displayed

Table I. The lifetimes of the electronic states deduced frthe width of the action photodissociation peaks6 are includedin the table for comparison. It is worth noting that lifetimeevaluated in Ref. 6 always have to be taken as lower limsince it is assumed that observed bandwidths exclusivoriginate from predissociation broadening. This point hbeen discussed in Ref. 11~Fig. 3! where, for instance, theapparent very short lifetime of theH Rydberg state actuallyresults from two broad overlapping transitions and, therefohas to be corrected by first deconvoluting these overlappbands.

We expect the chirp to be about the same for both walengths, which is confirmed by the fitted value of 280 fs fthe pump and 340 fs for the probe pulse. The fact thatchirp on the visible light pulse deduced from the multiparaeter fits is identical for the two wavelengths studied speakfavor of our analysis method. Figure 11 shows the fits incluing separate contributions from each state. The good agment between the fits and the PES time dependence aconfirms the validity of the multifit procedure. The mocomplex fit is a more stringent test of the model since ttime-energy benchmarks with a known decay time andtuning are used to describe theF 40

2 in C2H2 and theE 502

state in C2D2 .Looking at the plots in Fig. 11 we see that before 200

in C2H2 and 300 fs in C2D2 the features discussed atl1

dominate. This is expected since the pump frequency swwill reach the state of lower absorption energy first. Trelative weights of the components should be determinedthe pulse energy distribution and by the oscillator stren

FIG. 11. Result of the fit of the PES signal as a function of the pump-prdelay for a central pump wavelength of 132.0 nm in~a! C2H2 and~c! C2D2 .The ion-yield spectra measured simultaneously are shown in~b! and ~d!.The time development of the two PES components are shown separateeach frame together with the results of the fit~solid lines!. The cross-correlation fit obtained from the Xe signal is plotted in dotted lines in~a!and ~c!.


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for the transition as well as by their respective detuningsC2H2 the stronger feature corresponds to theF state relativeto the E state confirming the weight ratio obtained by intgrating the absorption bands of the two states over the bpump bandwidth. In addition, for the same decay timepositive detuning will lead to a slightly stronger pump-prosignal than a negative detuning, and this effect increasesthe chirp of the pump pulse.32 This behavior is stronger inthe ion signal than in the photoelectron signal, possibly dto a strong angular dependence of the photoelectron emisfrom the F state compared to theE state. In C2H2 , the Evalence state lifetime is significantly longer than the Rydbstate lifetime, confirming the results deduced from spectrcopy onH photofragments.2,3,22 In the C2D2 spectra the in-tensity distribution of the exciting pulse accounts for thetensities of the two features. An interesting result issignificant difference in the decay times observed in C2D2 :the excitation of thecis mode seems to lead to a faster prdissociation dynamics than the excitation of thetrans mode.This tendency is also observed in the H photofragmspectrum.6 Finally, the ion signal can be reproduced fromincoherent sum of the two pump-probe signals. In agreemwith that already observed atl1 in C2D2 , the decay timededuced from the ion signal is of the same order of magtude as the PES decay time. No strong angular dependof the PES is expected.

V. CONCLUSIONS

Ultrashort VUV pulses allow photoinduced dynamics fhigher valence-excited states in molecules to be studHowever, in this excitation range, the electronic state denis significant making any meaningful temporal analysis dficult. In order to distinguish the electronic states exciteda pump pulse which overlaps two or more levels, we hacombined a PES analysis with a linear chirp of the pufrequency. The pump chirp supplies atime-energy scalesuchthat each electronic excited state can be identified in the PWe illustrate this method on the predissociation ofF andEstates in C2H2 and C2D2.

The simultaneous analysis of the time-dependent etron and ion-yield spectra together with the Xe crocorrelation data reveals the time-dependent evolution of eelectronic state. In acetylene we find lifetimes between ab20 and 200 fs, in d-acetylene these lifetimes are somewlonger, ranging up to about 600 fs. The difference betwthe electron and ion-yield time dependencies is interpreby the angle selectivity of our electron spectrometer, whdetects only those electrons emitted with a given symme

A VUV femtosecond pulse would also be useful asprobe, to directly photoionize the atomic photofragments,that the electron kinetic energies and angular distributicould be recorded or to reach the excited states of ion. Incase, nonadiabatic coupling via a photoionization pumprobe experiment might be elucidated by photoionizationnamics in the excited states of the ion.37 In many small poly-atomic molecules, a VUV femtosecond probe pulse wouldparticularly useful for this kind of application.


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the predissociation of highly excited states in...

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