J. Phys. Chem. 1994,98, 6679-6683
6679
ARTICLES Odd-Even Alternation of Femtosecond Fragmentation Processes of Excited Naa=s10Clusters H.Kuhling, K. Kobe, S. Rutz, E. Schreiber,' and L. Wiiste Freie Universitiit Berlin, Institut Fur Experimentalphysik, Arnimallee 14, I41 95 Berlin, Germany Received: February 23, 1994; In Final Form: April 25, 1994'
Using femtosecond two-color resonant, two-photon ionization spectroscopy followed by mass-selective detection, we studied the fragmentation of small neutral sodium clusters in a supersonic cluster beam. The photofragmentation dynamics of the clusters could be investigated with the pump and probe technique. Ultrashort laser pulses of 150-fs duration were employed to excite the sodium clusters. Being predissociated, the prepared clusters tend to ultrafast fragmentation. The temporal behavior of these predissociation processes could be detected by using variably delayed probe pulses to ionize the nonbroken excited clusters. In the frame of a simple energy level model the fragmentation processes could be analyzed. Fragmentation times for the different cluster sizes could be estimated to be energy dependent in the region 220-900 fs. The temporal evolution of the ion signals exhibits-as a function of cluster size-an interesting odd-even alternation.
1. Introduction
Small clusters exhibit strongly varying chemical properties with increasing size due to drastic changes of their electronic as well as geometric structure. Numerous experiments and theoretical calculationsverify this (see, e.g., refs 1-6). Although the field of cluster physics is rather young, especially the alkali clusters are well-studied systems. This is-in comparison to other clusters-due to the relative simplicity of their experimental and theoretical treatment. Sodium clusters, for example, can be produced rather easily, because their metal starts to melt even below 100 OC. At 500-700 OC their vapor pressure is about 100 mbar, which is sufficient for formation of clusters by means of adiabatic expansion. Fundamental experimental results were obtained by laser spectroscopy (e&, Li? Na,8$9K'O) as well as mass spectroscopy (e.g., refs 1 1 and 12). Beyond this-due to their hydrogen-like electronic configuration-the alkali clusters suit most of the theoretical calculations. In the case of very small clusters ab initio configurationinteraction calculations (e.g., refs 13 and 14) are preferred, whereas for larger clusters the jellium model leads to good agreement with experimental results.15 With the availability of ultrashort laser pulses and time-resolved spectroscopic technique in the picosecond and femtosecond time domain, new far-reachinginformation about the physics of clusters can be obtained. Dynamical behaviors like fragmentation or internal energy-transferprocesses of clusters after optical excitation and ionization are fascinating examplesof this. These internal energy-transfer processes and wavepacket propagations lead to fragmentation16or at least to strong oscillation^^^ of the clusters. The ultrafast fragmentation of the clusters, although being found with quasi-stationaryspectroscopictechniques (Na,9J8Li7),could not be observed on a real-time scale for a long time. It was even thought that these rapid physical/chemical processes, such as the formation or breaking of a bond, were considered to be instantaneous and therefore unobservable by experimental methods. But with thedevelopmentof lasers with pulsedurations of less than 100 fs, these processes became accessible to experiments. As a pioneer in the field of "laser femtochemistry", 0
Abstract published in Advance ACS Abstracts, June 1, 1994.
Zewail could present fascinating results.1g-21The first results on the dynamical behavior of the sodium dimer after excitation with 50-fs pulses by GerberZ2followed. Other examples are the timeresolved pseudorotation of the B-state and fragmentation of the predissociated D-state of the sodium trimer.23 The real-time dynamics of the pseudorotating B-state could be well described the~retically.~~J~ Recent TPI experiments presented on the ISSPIC 616 using the picosecond two-color pump and probe technique allowed for the first time to directly observe the fragmentation process of larger sodium clusters. With the help of transient two-color TPI, it was possible to ionize the sodium clusters slightly above the ionization potential (IP). Since Nan+ is stable under these preparation conditions, it can therefore not break into NaWl+ and Na or NaWz+and Na2 as stated by Gerber for the case of highly excited sodium ions.27 Pump and probe experimentswith a higher temporal resolution should give even more detailed information about the fragmentation processes of the sodium clusters. 2. Experimental Section
The femtosecond pump and probe technique (with pump and probe photons of different energy) followed by mass-selective detection was applied to measure the temporal evolution of the population of excited sodium clusters. The experimental setup is shown in Figure 1. The sodium clusters are generated in a seeded molecular beam with argon as an inert carrier gas. The used oven technique is based on a high-temperature oven built to produce lithium ~lusters.2~ It consists of a -1 50-mm-long cylindrical cartridge made of titanium-zirconium-molybdenum heated by seven tungsten filaments of 1S-mm diameter and resists the very corrosive alkalivapor. By improving this technique, it was possible to increase the stability of the produced cluster beams. The specially designed skiff guaranteed a stable sodium cluster beam for up to 15 h, consuming only about 2.3 cm3 of pure sodium metal. Sodiumvapor of about 50-100 mbar (oven temperature -650 "C) was expanded adiabatically together with the carrier gas through a nozzle. This nozzle is about 0.4" long. The diameter
0022-3654/94/2098-6679$04.50/0 0 1994 American Chemical Society
Kiihling et al.
6680 The JourMl of Physical Chemistry, Vol. 98, No. 27. I994
achromatic XI2 retarder; therefore, the polarization vectors of both the pump and the probe beam were parallel. For the pump and probe experiment the (red) probe pulses (fundamental) were delayed in time with respect to the (blue) pump pulses (sccond harmonic) by aligning them through an optical delay line. This delay line consisted of a retroreflector being mounted on a demotor-driven translation stage. Its resolution being controlled by an optical encoder was better than 0.1 fim. So thetimeresolutionoftheopticaldelaylinein principle couldbeeven better than 1 fs. Therefore,thetotal!imeresolution of the pump and probe experiment is mainly determined by the pulsewidthofthelaser. On theirway totheinteractionchamber, theshortpulseswere broadcnedto=lSOfs,due togroupvelocity dispersion of lenses and other optical devices. The pumpand the probe laser beams were realignedcollinearly and sent into the interaction chamber where they crossed the cluster beam perpendicularly. In the interaction region the Na. clusters are excited by a photon of the pump laser. The probe pulse ionized the excited clusters, and the ions were detected mass selectively by a quadrupole mass spectrometer( Q M S ) w i t h a resolution m / A m of about 200-whose axis is mounted perpendiculartoboth thecluster beamand thelaser. Ifnecessary, the lock-in technique could provide an even better signal-to-noise ratio. Both the pump and probe beams produce by themselves a constant background signal which amounts to less than 10%of themaximum signal reached in the caseofexact overlap ofpump and probe beams.
Argon Ion Laser I
Pulse Campressor
TkSapphire
14
20
r w
/I I
E u I
Computer
I
3. Results 1
I I
Flgure 1. Experimental setup used for the detection of the transient evolution of the dissociating Nan*clustna. A laser pulse with frequency 2w is used to excite the clusters followed by a pulse of frequency w M n g
optically delayed (SHG= sand-harmonic generation, QMS = quadrupole mas spectrometer, LT-Detector = Langmuir-Taylor detector).
is 65 pm at the entrance and 75 pm at the exit. With these nozzles the production of small clusters (n 5 20) is favored. Using a 8000 11s diffusion pump, the pumping capacity of the oven chamber allowed the use of a gas pressure of more than IO bar. The resulting supersonic beam provided very cold clusters with vibrational and rotational temperature T ~ E s 30 K and Tm 5 8 K. respectively. The cluster beam entered the interaction chamber through a skimmer with an orifice diameter of 1 mm. The distance between skimmer and nozzle amounted to IO mm. The overall beam intensity was measured and controlled during the experiments independently of the laser beams by a homebuilt hot wire detector (Langmuir-Taylor detector). With an active area of IO mm2 a sodium ion current up to 2 pA was measured. To investigate the fragmentation dynamics of the sodium clusters on a real time scale, a regenerative modelocked titanium:sapphirelaser pumped by a 12-W CW (alllinesvisible) argonionlaserwasused. Itproducedlightpulseswitharepetition rate of 82 MHz and a pulse duration ofassuming a sech' pulse s h a p e l . 4 ps (fwhm). The average power was about 1.2 W. So the pulse power and the pulse energy were about IO kW and 15 nJ, respectively. The tuning range of the ti1anium:sapphire oscillator covered the spectral region of 70&900 nm. The picosecond pulses were compressed down to 30 fs (fwhm) in a fiber compressor with quartz prisms to compensate for the group velocity dispersion. The resulting pulse energy was about IO nJ with a spectral width of about 250 cm-I (-31 mev). We generated the second harmonic in a I-mm LBO crystal with a conversion efficiency of about 15%. The second harmonic was separated from the fundamental by means of a dichroitic mirror. The polarization of the fundamental beam was rotated with an
The temporal behavior of electronically excited states of Na, up to Nalo was investigated by means of time-resolved pump and probe experiments. For this the intensity of the TPI signal was measured as a function of the time delay Ai between the exciting pumpandtheionizingprobepulse. Duetoultrafast fragmentation of the excited clusters, the ion signal decreases rapidly with increasing Ai. So in a first approximation the intensity I of the ion signal for a given delay Af should be proportional to the number of still nonbroken excited clusters. Tbemeasurements werecarried out for threediffmnt energies of the pump pulses E$ (2.92, 2.94, and 2.97 eV) and the probe pulses E, (1.46.1.47, and 1.485 eV). Recently, density of states in this spectral region was found theoretically2* as well as experimentally? The total energy of both pulses was slightly above the ionization potential (3.954.2 eVZ9)of the clusters. This guarantees the stability of the produced cluster ions. The temporal evolution of the ion signal for different cluster sizes n at the excitation energy E. = 2.94 eV in comparison to the overall system response (shaded) is shown in Figure 2. The temporal resolution of the experiments was limited by theoverall system response to the laser. Due to pulse broadening in theused optical components, the system response had a width of about I 5Ofs (fwhm), which issmallcompared to theobservedionsignals. The recorded ion signals show a very fast decay. Especially for the even-numbered Na. clusters with n = 6, 8. and IO, the dramatic decay is f o r d by fast fragmentation within the first few hundred femtoseconds after excitation. The decay curves of the odd-numbered clusters with n = 5 , 7, and 9. however, show a little humb in the shoulder of the decay for 1 ps 5 Ai 5 3 ps. Therefore, they could not be described in the frame of a simple exponential decay. This behavior is comparable to results recently found for Na3'o and points out to the occurrence of fragments of larger clusters in the detected ion signal. For N a thesignalseems tobesimilar tothoseoftheothereven-numbered clusters, but with a much longer single decay time. In contrast to Na3,'0 for Na, to Nalo no obvious relation between the shape of the measured ion signals and the used excitation energy could
The Journal of Physical Chemistry, Vol. 98, No. 27, 1994 6681
Fragmentation Processes of Excited Nan=3-10Clusters " 1 " " l " ~ ' I " " I " ' '
Nan' n=4
8
II . Nam
NaIl
Nak
Figure 3. Energy level scheme to describe the temporal evolution of the
10
Nan+signal. For the presented experimental results, m > n > k. I L I I I I
-2.
-1
0
1 At/ps
2
3
4
I
,
I
5
&shaped excitation laser pulses leads to the following rate equations
4
Figure 2. Temporal evolution of the ion signals for Nan.kIO+ excited at Eo = 2.94 eV (At = delay time).
be found. For a more detailed interpretation a numerical analysis of the measured data based on a fragmentation model is necessary.
d
Z"'
1 =- 1 m - -n, TpoP
TI
4. Discussion
-m = Mo6(t)- -m
d
1
For the interpretation of the recorded transients from Na, to Nalo an improved fragmentation model was used. This model is similar to the model developed to describe the Na3 data.30 This improved fragmentation model includesthe "simple" twolevel energy model-as used for former data with picosecond resolution17-as a basis. Beyond that, an additionalfragmentation channel which influences the transients of Nan+is included. In Figure 3 the energy level scheme for our improved model is shown. The term ladder in the middle represents the energy levels of Nan. The excited state n~is excited by a photon of the pump pulse. The population of this state decreases by fragmentation with the timeconstant 70. Either the depopulation of the state or the increase of the population of the Na,l* can be estimated by means of the probe pulse in dependence of the delay time At. This was yet predicted by the simple fragmentation model and seemed to be proved in picosecond pump and probe measurements. To explain the temporal evolution of the measured data, the term ladder on the left side of Figure 3 had to be added: it is assumed that the pump pulse is capable of exciting clusters with a higher number of atoms (e.g., Nan+l,,,++2,..) with the population m which are also part of the cluster beam. These excited clusters are assumed to dissociate with the time into an excited state of Nan with the population nl constant spop which is not identical with the laser-excited state but may also be predissociated. Under these circumstances the cluster as well may tend to dissociate, but now with a time constant 71. From this second excited state nl Nan may also be ionized by the probe pulse so there is an additional account on the recorded ion signal. A differential equation system combining the population densities n ~ ,nl, and m of the excited electronic states with fragmentation times TO, T I , and T ~respectively, ~ , and assuming
dt
TpoP
with NOand MOindicating the number of clusters being initially excited. Radiative lifetimes being long in comparison to the observed fragmentation times are neglected.31 The solutions of the differential equation system are found to be
and m(t) = Moe-r'Tpop The detected ion signal is proportional to the temporal evolution of
Therefore, the equation
has to be compared with the experimental data. Regarding the temporal width of the laser pulses, the convolution function A t ) := l(t)*n(t)
6682 The Journal of Physical Chemistry, Vol. 98, No. 27, I994
I
I
Clustersize
n
0
-
Clustersize n
2.5
1400
b
ev
-2292
-
3 4 5 6 7 8 9 10
,
,
,
#
I
-292
eV
e - -297
eV
1300 2.0
1200 1100
7
Y)
At/ps
: 1000
-
-
9
0
Figure 4. Temporal evolution of the Na,+ signal for even-numbered clusters of Eo = 2.94 eV: dots, experimental data; lines, fitted function due to the improved model explained in the text.
1.5
xo
900
1.0
800 0.5
700 600
0.0
-
-
3 4 5 6 7 8 9 10
3 4 5 6 7 8 910 Clusterslze n
Clustersize n
Figures. Fitted valuw of the parameters TO,T I , T~ and MOfor different cluster sizes n and excitation energies Eo.
In Figure 6 the fitted values of the parameters TO, 71,
and
MOare shown for the different excitation energies E, and cluster
-
2
-
1
0 At/ps
-
1
2
3
4
s
-5. Temporal evolution of theNa,,+signal for odd-numberedclusters at E. = 2.94 eV: dots, experimental data; lines, fitted function due to the improved model explained in the text. was calculated. [ ( t ) is the overallsystem response of our measuring system being represented by the cross-correlation of the laser pulses. The functionfit) was fitted to the experimental data by means of a least-squares fit routine. In Figures 4 and 5 the measured data are presented in comparison to the calculated fits. While Figure 4 shows the data for the odd-numbered clusters Figure 5 presents those for the even-numbered clusters. The comparison between the recorded and the computed curves shows an excellent agreement. So the improved fragmentation model is able to describe the temporal evolution of all the different ion signals in a perfect manner.
sizes n. As a first important result of this evaluation, the direct fragmentation time TO 300 fs for n = 5-9 is nearly independent of cluster size n and excitation energy Ee. For Nalo the value of so decreases to 220 fs. For Na4 70 shows a strong relation to the excitation energy with increasing values from 350 fs (2.92 eV) to 900 fs (2.97 eV) with enlarged Ec. While the signals of even-numbered clusters showed just a small amount of fragments from larger clusters (0 5 MOI0.3), there is a strong amount of fragments from larger clusters (0.6 IM OI2.4)found for the odd-numbered clusters. This indicates that most of the fragments of excited clusters with 4 5 n 5 10 are odd-numbered. This odd-even alternation found for the measured ion signalscan be explained by two different dissociation channels. Na, clusters with even n dissociate into an oddnumbered cluster and one Na atom
-
Nawl*+ N a
-
+ Na,
Nan*
while odd-numbered clusters dissociate into an odd-numbered cluster, too, but one dimer
Nan*
Naw2*
So in both cases an odd-numbered daughter cluster is generated, and this effect is independent of the excitation energy. The population time T~ ranges between 0.6 and 1.O ps, which is about a factor of 3 larger than the laser-induced fragmentation time 70. Having a speed of =lo00 m/s the dissociating moieties separate with a10 A in 1 ps. Reaching this distance two independent particles, the fragments, are formed. So there seems to be a transition state, in which the dissociating cluster is not Visible" for the experiment. A potential scheme describing this
Fragmentation Processes of Excited NaPrlo Clusters Excited C h m r
Transition State
The Journal OfPhysicd Chemistry, Yo/.98. No. 27, 1994 6683 Refmafes and Notes
FragP"t8
(1)
20.
RoQdings of the ISSPIC 5, Konstans 1990; 2.PhyJ. D 1991.19,
(2) Pmmdings of the ISSPIC 6, Chicago. 1992; Z. Phys. D 1993.26,
27. (3) Benedck, G., Martin. T. P., Pacchioni. G., Edr. Elemcmtd and Molecular Clusterr; Springer-Verlag: Berlin. 1988. (4) Sugno. S.. Nishina, Y.. Ohniahi. S.. MS. M1cmlwrcrr; Springer. Vcrlag: Berlin. 1981. (5) TrKxer. F., Putlitz G., Edr.MnalCluslcrs;Springn-vcrlag:Berlin, 1986. (6) Kautcckg. J.; Fantucci. P. Chem. RN. 1986,86,539. (7) Blanc. J.; Broycr. M.; Chcvaleyrc, J.: Dugaurd. Ph.; Kahling. H.; Labastie. P.; Ulbricht. M.;Wolf, J.-P.; W&te. L. Z. Phys. D 1991, 19. 7. ( 8 ) Sclby.K.;Vallmcr. M.;Masui,J.; Kmin,V.;de Hwr, W.A.; Knieht, W. D. Phys. Rm. B 1989.40. 5417. (9) Wang. C.; Pollak. S.; Dahlacid, T.A.: Korctsky, G. M.; Kapps. M. M . 1.Chem. Phys. 1992.96, 7931. (IO) BreChignaz C.; Cahurae. Ph.; Rour, J. Ph. 1.Chem. Phys. 1988.88.
Figure 7. Energy level scheme to describe the fragmentation pmccss of thelaJer-ncitedNa.'cluster. Passingthetransitionstatethedisnociating cluster is 'invisible" to the probing laser pulscs. After the time rWthe fragment Na,. can be p r o w .
fragmentation process is shown in Figure 7. Similar transition states of dissociating molecules recently have been observed by means of femtosecond transition-state spectroscopy (e.g., refs 32 and 33). An odd-evcn effect can be noticed for the parameter TI as well (see Figure 6). but it is not understood at this time. It has to be stated that the simple fragmentation model does not explain the energy dependence of the parameters of the recorded spectra. It alsodoesnot takeintoaccount thedynamics of wavepackets prepared in the excited clusters as they were observed for example in the B state of Na3.2' To describe the observed phenomena, more detailed theoretical calculations of the dynamic on t h c n o t yet known-potential energy surfaccs of the Nan* clusters are necessary. 5. Summary
The femtosecond pump and probe technique was used to study the fragmentation of predissociated states of Na,rlo in a cold cluster beam. As a rCsumC, it can be stated that within the 'improved" model presented bere the temporal evolution of the NaPrlo+ signal can bedescribedconsistently. Within this model fragmentation times of the excited clusters were estimated to W e p e n d e n t on cluster size and excitation energy-between 200and 900 fs. A different fragmentation behavior for odd- and even-numbered clusters was found.
Acknowledgment. This work has been financially supported by the Deutsche Forschungsgemeinschaftwithin the Sonderforschungsbereich 337 (TP A8).
an?? (11) Martin, T. P.; Bergmann. T.;G3hlich. H.;Langc, T.Z . Phys. D 1991. 19. 25. (12) Bj0mholm,S.;Barggr~n,J.;~ht,O.:Ha~n.K.;R.sm-.H. D. 2.Phys. D 1991.19.47. (13) Baustani. 1.; Pcwrstorf, W.; Fantucci. P.: BonatibKoutcckf, V.; Koutcck$, I. Phys. Rm. B 1987,35,9431. (14) Andrmni. W.Z. Phys. D 1991. 19. 31. (15) dcH~r.W.A.;Knight.W.;Chou,M.Y.;Cohen.M.L.SoNdSf~tr Phys. 1981.40, 93. (16) Kahling, H.; Kobc. K.; R u t s S.: Schdber. E.; W&t%L. Z . PhyJ. D 1993, 26. 33. (17) Rutz. S.; Kobe. K.; KUhling. H.;Schrcibcr. E.; W&f+ L. Z. Phys. D 1993~ 2%276. ,....... (18) Broycr.M.:Delarrt~G.;La~tic.P.; Wolf, J.-P.; W&te.L. Phys. Rm. Ian. 1986.57.1851. (19) Zcwail. A. H.Science 1988. 242, 1645. (20) Khundkar, L. R.; Zcwail, A. H.Annu. Reo. Phys. Chem. 1990.41. ~
~~~~
.-
1 U"
(21) h a i l . A. H.Faraday Direus. Chem. Sac. 1991,19,201. (22) Baumert. T.;G m e r , M.; Thslwciscr, R.; Gerbcr, 0 .Phys. R N . Lett. 1991. 67, 3753.
(23) Schmbcr. E.; Kahling, H.; Kobe. K.; RulzS.: Wbtc, L. Be,. Bunrm-
Ges. Phvs. . . 1301. , Chem. 1992.96. (24) Gaus. J.; Kobe. K.: BanafihKoutskf, V.; KOhling. H.;Manr. J.; Reisehl.B.;Ruf~.S.:Schrcibcr.E.;W&f+L.1.Ph~~.Chrm.1993.97.12509. ( 2 5 ) Kobe. K.; KGhlmg. H.;Rum, S.:khnibcr. E.; Wolf, 1.-P.; W($tc, L.; Broyer. M.; Dugourd, Ph. Chcm. Phys. k t t . 1993,213, 554. (26) Dcladtaz, G. Thesis, Lsusaunc, 1985. (27) Bdhler. B.; Thalwciacr, R.; Gerbcr. 0.Chem. Phys. fer:. 1952 188, 247. (28) BOME~C-KOU~~~W, V.; Fantucci. P.; Fuchs, C.; Koutcckf. J.; Fittner, J. Z. Phys. D 1993, 26, 17. (29) Dugaurd. Ph.; Rayanc, D.;Labaatic. P.; Pintar, B.; Chevaleyrc. J.; Broyer. M.:W M c , L.: Wolf, J.-P. 1.Phys. Ill 1992. 0, 509. ~~~
(30) Kahling, H.;Rut& S.: Kobe, K.; Schrcikr, E.; W&te, L. 1.Phys. Chem. 1993,97, 12500. (31) Broycr,M.;Dclanttaz,G.;NiGuoqwn: Wolf,J.-P.;W&te,L. C h m . Phys. k t r . 1%. 145, 232. (32) Rcdker. M.J.; Dantus. M.; Zcvvail. A. H.1.Chem. Phys. 1968, 89, 6113. (33) Dantus, M.; Rosker. M. J.; Znvail, A. H.1.Chcm. Phys. 1968.89, 6128.
