4635
J . Phys. Chem. 1991,95,4635-4647 frequency and other modes have been identified, which are characteristic of particular two-dimensional aggregates adsorbed onto perylene. Different cases have been presented that show coupling of internal modes of the aromatic molecule to intermolecular modes. Cases studied include "damping" of the butterfly mode of perylene in argon clusters and the perturbation of a pair of levels in Fermi resonance, in molecular clusters. Hole-burning
studies of simple methane complexes reveal low-frequency mode structure which may be due to hindered rotational motion. Continuing work will explore details of the methane cluster spectra with deuterium substitution.
Acknowledgment. This project was supported by the Research Foundation of the University of Pennsylvania.
Femtosecond ReaCTlme Probing of Reactions. 6. A Joint Experimental and Theoretical Study of Blp Dissociation
R. M. Bowman, J. J. Cerdy,' G. Roberts, and A. H. Zewail* Arthur Amos Noyes Loboratory of Chemical Physics,$ California Institute of Technology, Pasadena, California 91I25 (Received: December 19, 1990)
The dynamics of the ultraviolet photofragmentation of bismuth dimer are studied experimentally and theoretically in the time domain. Employing the technique of femtosecond transition-state spectroscopy,the evolution of the dissociative process along two reaction channels leading to the 6p3(%03/2)+ 6p3(2D03/2)and 6p3(4Soy2)+ 6p3(2D05/2) levels of the atomic products is investigated following initial excitation of Bi2at X = 308 nm. The broad spectral width of the ultrashort probe laser pulse coupled with the closely spaced excited energy levels of Bi enables fluorescence via some 14 atomic transitions to be monitored in real time, rendering possible the detection of dissociating molecules at different internuclear separations on the controlling potential surfaces. Long-time detection of the D ' O312 spin-orbit level permits clocking of the reaction along the lower energy exit channel, for which we report a dissociation time rl12 of approximately 1 ps, at which time the product Bi atoms are separated by some 10.7 A. Analogous measurements for the reaction giving rise to the higher-lying J = level of the 2D, term yield a value of r112= 1.5 ps, corresponding to an interfragment distance of 7.5 A. From the dissociation times so obtained, values for the length parameters that characterize noninteracting model potential curves Vl(r)and V&) for dissociation via both exit channels may also be determined. Early time detection of [Bi--Bi]** reflects dynamical behavior Over transition-state regions of the potential surfaces and allows various aspects of the nature of the force field governing fragmentation to be deduced. Finally, model quantum and classical calculations of the dissociation process are presented, which reproduce many of the salient features of the observed reaction dynamics.
-
I. Introduction of femtosecond transition-state ~pectroscopy.'J~,*~' On-resonance (longtime) detection of CN(X2Z+) via the B2Z+ X2Z+band Experimental efforts to study molecular reaction dynamics in real time' have been directed toward the following hierarchy of problems: ( I ) the internal motions executed by molecules on (1) Khundkar, L. R.; Zewail, A. H. Annu. Rev. Phys. Chem. 1990,41,15. bound potential energy surfaces (PESs); (2) direct dissociation (2) Williams, S.0.;Imre, D. G. J . Phys. Chem. 1988, 92, 6648. (3) Heather, R.; Metiu, H. Chem. Phys. Lett. 1989, 157, 505. Over a repulsive PES;(3) predissociation involving surface hopping (4) Lee, SPY.;Pollard, W. T.; Mathia, R. A. Chem. Phys. Len. 1989,160, between two intersecting diabatic PESs; (4) dissociation over 531. multidimensional PESs involving several exit channels leading to (5) Krause, J. L.; Shapiro, M.; Bersohn, R. J . Chem. Phys., submitted for product formation: ( 5 ) multiphoton excitation, ionization, and publication. (6) Engel, V.; Metiu, H.; Almeida, R.; Marcus, R. A.; Zewail, A. H. fragmentation processes. Such studies have served to initiate a Chem. Phys. Lett. 1988, 152, 1. number of theoretical investigations of these processes that aim (7) Engel. V.; Metiu, H. J . Chem. Phys. 1989, 90, 6116. to calculate the temporal dynamics as revealed by experiment. (8) Choi, S.E.; Light, J. C. J . Chem. Phys. 1989, 90,2593. Most quantum dynamical calculations2-12 based upon such an (9) Engel, V.; Metiu, H. J . Chem. Phys. 1989, 91, 1596. (IO) Lin, S. H.; Fain, B. Chem. Phys. Letr. 1989, 155, 216. approach have involved propagation of wave packets on approLetokhov, V. S.; Tyakht, V. V. Isr. J . Chem. 1990,30, 189. priately chosen PESs, while c l a ~ s i c a l ' ~and - ~ ~s e m i ~ l a s s i c a l ~ ~ (11) (12) Gruebele, M.; Roberts, G.; Zewail, A. H. Philos. Tram. R. Soc. A treatments have also been successful in describing the time evo(London) 1990, 332, 223. lution of the dissociating system. One reaction that has been (13) Dantus, M.; Rosker, M. J.; Zewail, A. H. J . Chem. Phys. 1988.89, examined in detail in the time domain, both t h e ~ r e t i c a l l y ~ - ~ J ~ 6128. J~~~ (14) Rose, T. S.;Rosker, M. J.; Zewail, A. H. J . Chem. Phys. 1989, 91, and e ~ p e r i m e n t a l l y , ' ~is ~the ~ ~dissociation ~' of ICN: 7415. ICN(X'Z+)
+ hu
+
[I-..CN]'*
+
CN(X22+) + I(2P3/2,1/2) (1)
which evolves over interacting PESs that are essentially repulsive at all interfragment separationsa (category 2 above). Following excitation of ICN in the A continuum at X = 306 and 285 nm, corresponding to excess energies for fragment separation of 6550 and 8960 cm-I, electronically excited transition-state configurations ([I.*.CN] **) of the parent molecule undergoing spatial separation to form products have been monitored in real time by the technique N S F Predoctoral Fellow. *Contribution Number 8373.
0022-3654/91/2095-4635$02.50/0
(15) Dantus, M.; Bowman, R. M.; Gruebele, M.; Zewail. A. H. J . Chem. Phys. 1989, 91, 7437. (16) Benohn, R.; Zewail, A. H. Ber. Bunsen-Ges. Phys. Chem. 1988,92, 373. (17) Bernstein, R. B.; Zewail, A. H. J . Chem. Phys. 1989, 90, 829. (18) Benjamin, I.; Wilson, K. R. J . Chem. Phys. 1989, 90, 4176. (19) Lee,S.-Y.; Pollard, W. T.; Mathies, R. A. J . Chem. Phys. 1989, 90, 6146. (20) Yan, Y. J.; Fried, L. E.; Mukamel, S.J . Phys. Chem. 1989,93,8149. (21) Fried, L. E.; Mukamel, S. J . Chem. Phys. 1990, 93, 3063. (22) Mukamel. S.Annu. Rev. Phys. Chem. 1990,41, 647. (23) Marcus, R. A. Chem. Phys. Leu. 1988, 152, 8. (24) Scherer, N. F.; Knee, J. L.; Smith, D. D.; Zewail, A. H. J . Phys. Chem. 1985,89, 5141. (25) Dantus, M.; Rosker, M. J.; Zewail, A. H. J . Chem. Phys. 1987,87, 2395.
0 1991 American Chemical Society
4636 The Journal of Physical Chemistry, Vol. 95, No. 12, 1991 system permitted the time taken for the C N radical to separate from the force-field of the I atom to be determined as T ~ =/ 205 ~ f 3013*26 and 160 f 30 fs,13 respectively, for these pump wavelengths. From these data, Dantus et al. derived a "length" or "range" parameter of 0.8 A characterizing a (simplified) exponential PES for dissociation along a single translational reaction coordinate." Off-resonant (short-time) measurements at wavelengths to the red of the CN(B2Z+ X2Z+) band indicated that [I-CN]'* transition states lead an evanescent existence, persisting only for some 20-50 fs.I3 By detecting C N product in different rotational levels and by carrying out measurements with polarized laser p u I s e ~ , the ~ ~time-development *~~ of angular momentumz9 and coherence'O of reaction 1 have also been investigated and related to the angular properties of the excited-state PESs governing reaction.29 On a reactive PES that is wholly repulsive in nature, a wave packet is expected to spread and evolve with time to a wave function that characterizes product species. As pointed out clearly by Bawick and Jortner," these two processes involve distinct time constants: one that describes the spreading of the initial packet, which depends on its preparation and the local gradient of the PES; and a second that is characteristic of the recoil dynamics, which is determined by the nature of the chemical bond potential. The latter we have previously termed the clocking timel3Jsn and naturally depends on the detection "windowwprojected onto the reactive PES by the probe laser pulse as discussed by Bernstein and Zewail;I7 thus the effect of the laser pulse width on the ultrafast dynamics on a repulsive potential is (For b o ~ n d ~and~ -q u~a~s i - b o ~ n d ~ ~ *systems ~ ~ - ' " the effect is straightforward to understand.) To test some of these ideas for repulsive PESs,we have carried out FTS on a dissociation process that exhibits kinematic and potential features dissimilar to those of reaction 1, in that both the length parameter of the potential curve governing reaction and the masses of separating fragments are different. Here we report our first experimental and theoretical results on the direct dissociation of diatomic bismuth following absorption of an ultraviolet femtosecond laser pulse at X = 308 nm:
-
+
Bi2(X1Z+& hu
-
-
-
[Bi...Bi]** Bi(6p3 4S03/2)+ Bi(6p3 'D03/2) (2a)
Bi(6p3 4S03,2)
+ Bi(6p3 2D0s/z)
(2b)
Subpicosecond kinetic spectroscopy on reaction 2 has been carried out first by Sorokin and ~ o - w o r k e r stheir ; ~ ~ study, ~ ~ ~ which utilizes (26) (27) 6113. (28) 3519. (29) (30)
Rosker, M. J.; Dantus, M.;Zewail, A. H. Science 1988,241, 1200. Rosker, M. J.; Dantus, M.;Zewail, A. H. J. Chem. fhys. 1988,89, Black, J. F.; Waldeck, J. R.; a r e , R. N. J . Chem. fhys. 1990. 92, Zewail, A. H. J . Chem. Soc.. Furuduy Truns. 2 1989, 85, 1221. Dantus, M.;Bowman, R. M.; Baskin, J. S.; Zewail, A. H. Chem.
fhys. Lett. 1989,159,406. (31) Bawick, J. A.; Jortner, J. Chem. fhys. Lett. 1990, 168, 246. (32) Bowman, R. M.;Dantus, M.;Zcwail, A. H. Chem. fhys. Lett. 1989,
161. 291. ( 3 3 ) Dantus, M.; Bowman, R. M.; Zewail, A. H. Nature (London) 1990, -343 .- , 111 .- .. (34) Scherer, N. F.; Ruggiero, A. J.; Du, M.;Fleming, G. R. J . Chem.
fhys. 1990, 93. 856. 0 5 ) Gerd~.J. J.; Dantus, M.;Bowman, R. M.;W a i l , A. H. Chem. fhys. Lett. 1990, 171, 1. (36) Jamsen, M.H. M.;Bowman, R. M.;Zewail. A. H. Chem. fhys. Lett.
1990, 172,99. (37) Rose. T. S.: Rosker. M.J.: Zewail. A. H. J . Chem. fhvs. 1988.88. 66i2. . (38) Rosker, M.J.; Rose, T. S.; Zewail, A. H. Chem. fhys. Leu.1988, 146, 175. (39) Cong, P.; Mokhtari, A.; Zewail, A. H. Chem. fhys. Lett. 1990, 172,
Bowman et al.
50
40t I I I
-lot-\ t
2
I/ W
I
I
1
I
I
1
I
I
I
I
I
1
I
1
8
4
1
1
I1 10
r?A
Figure 1. Potential energy diagram for Bi,. Potential energy curves for Bi2 relevant to this work with dissociation limits below 50 X lo3 cm-l relative to the electronic ground state of atomic Bi,6w and an illustration of the concept of the FTS experiment. For clarity of presentation, several ~ below ~ ~ 43 X~ lo3~cm-'~ have ~ been ~ ~ molecular ~ t a t e slying omitted. The vertical line labelled by wavelength XI represents the pump transition of the FTS experiment to the Franck-Condon region of Vl(r) and/or Vlt(r),resulting in preparation of a wave packet that consists of a distribution of continuum eigenstatcs determined by the spectral profile of the laser pulse. Several probe transitions connecting Vl(r)and Vl,(r) to various states V2(r)at different wavelengths X2 are likewise displayed and illustrate the possibilities for detection of transition states and final products evolving over the dissociative surfaces (see text for details).
absorption measurements, indicates that processes 2a and 2b both proceed over what are believed to be essentially repulsive PESs. The reaction falls within the second category of half-collisions listed above, resulting in formation of the ground 4S03/2and fust-excited 2Do, states within the ground electronic configuration of atomic Bi. The work reported in this paper therefore extends and complements earlier real-time measurements of ICN fragmentation and affords us an opportunity to compare both experimental and theoretical results for the heavier Biz system ( p = 104.490 au) with analogous investigation^^^.^',^^^"^^ on the dissociation of the lighter ICN molecule ( p = 21.591 au). The remainder of this paper is constructed as follows. In section I1 model PESs appropriate to investigation of reaction 2 in real time are briefly described and related to the overall FTS methodology. Details of the experimental procedure are given in section 111, and section IV comprises an outline of the theoretical methods employed in this work to model the observed reaction dynamics. Experimental and theoretical results are presented and discussed in section V. Finally, we offer in section VI some concluding remarks together with a short comparison of our results with previous relevant work. Prospects for future FTS investigations of the dissociation of Biz are also delineated. 11. PESs and FlS Methodology Figure 1 displays a schematic diagram of the
PESs for Biz appropriate to our studies. The lowest lying curve labeled Vo(r) corresponds to the ground electronic state designated X(lZ+,) in Hund's case (b) symmetry and correlates with separated Bi atoms in the 6p3(4S03/2)ground ~ t a t e V . l~( r ~ ) and ~ ~Vlt(r) are independent unbound curves, previously'1 designated M and M', that lead to the 6f'('S03/2) + 6p3(2D"3/2)and 6p3('SoY2) 6$(2D"5 2) levels of atomic Bi, respectively; the parameters describing t i e
+
109.
(40)Mokhtari, A.; Cong, P.; Herek, J. L.; Zewail, A. H. Notum (London) 1990.318, 225. (41) Glownia, J. H.; Misewich, J. A.; Sorokin, P. P. J . Chem. f h y s . 1990, 92, 3335.
(42) Misewich, J. A.; Glownia. J. H.; Walkup, R. E.; Sorokin, P. P. In Ultrafast fhenomenu VI& Hams, C. B., Ippen, E. P., Mourou, G. A., &wail, Eds.; Springer Series in Chemical Physics; Springer-Verlag, Berlin. 1990; VOI 53, pp 426-428.
A. H.,
~
.
~
Femtosecond Real-Time Probing of Reactions
The Journal of Physical Chemistry, Vol. 95, NO. 12, 1991 4637
exponential form of these PESs are those proposed recently by Figure 1 also illustrates the concepts underlying our experiSorokin and co-workers4' (see section IVC). The higher lying mental investigation of reaction 2 using the FTS technique. The curve V&) was chosen by these authors to cross VI@)at the Bi2 approach essentially follows that undertaken to study the dissoround-state equilibrium internuclear distance (r,(XlZ+,) = 2.66 ciation of ICN13J4-26 and is described in detail elsewhere.n Unlike f9,thus providing a straightforward mechanism by which their that earlier investigation, however, we have further taken adexperimental observation4' of production of the J = 3 / 2 and s/2 vantage of the facilities afforded by the broad spectral bandwidth spin-orbit components of the 2DoJ term via reaction 2 in apof the temporally short laser pulses and dispersed fluorescence proximately equal abundance was explained. For simplicity of detection both to separate the contributions to the observed dypresentation, we omit from Figure 1 all other PESs lying at namics arising from the exit channels (2a) and (2b) and to monitor energies between -12 X 103 and 43 X 103 cm-l relative to the 'S03/2 the transformation of reagent into products at different spatial atomic ground ~ t a t e , ) ~though ~ ~ it* is~possible ~ ~ that ~ , one ~ ~ ~ regions of the reactive PESs (see Section 111). Using the dissoor more of these states may be involved in the dissociation process ciation process itself as an "internal clock", we also obtain the zero (see section IVB). A detailed discussion of the numbers and types of time for the reaction by means of early time detection of of lower lying electronic states of Biz dimer has been given by [Bi. .Bi] ** species within the Franck-Condon region of the exEffantin et aLs4 cited-state potential(s). Reaction 2 is triggered by application of a (pump) femtosecond To the best of our knowledge, little spectroscopic information laser pulse at a wavelength XI = 308 nm to a sample of Biz is currently available for the seven highest lying PESs shown in molecules in equilibrium at temperature of approximately 1100 Figure 1, labeled globally as V2(r),with asymptotic limits in the K. Absorption of a photon at this wavelength excites Bi2 via the range (60-67) X lo3cm-' above the electronic minimum of the ultraviolet M (M') X band system, resulting in preparation X ' F g state?"' Damany et al. have investigated several tranof a coherent superposition of continuum eigenstates that constitute sitions involving highly excited Rydberg states of Bi2by absorption a wave packet located on the dissociative electronic states VI@) spectroscopy in the vacuum ultraviolet region;62of the molecular and VI@) with an energy of about 5100 and 1080 cm-' in excess PESs studied by these workers whose dissociation products lie at of the respective dissociation thresholds. After a variable time energies within the above range, values of 0, a,, and re for states delay T , the evolving wave packet is irradiated by a second (probe) ~ * ~have ~ been labeled Q and S and the previously ~ b s e r v e dF~state femtosecond laser pulse centered at wavelength X2 = 298.9 or 302.5 derived?2 In general, however, it appears that the detailed tonm, which excites the system to one or more of the several higher pologies of highly excited PESs of Biz remain largely unexplored. lying PESs labeled Vz(r)in Figure 1. Fluorescence from these As a working "zero-order" approximation (elaborated upon in states is collected as a function of T at different detection wavesection IVC), the molecular potentials V2(r)are depicted here as lengths &,enabling formation of Bi atoms in their lowest being essentially independent of the dissociation coordinate at state and the J = 3/2 and 5/2 levels of the 2DoJterm to be ininteratomic separations beyond the Franck-Condon region, with vestigated. Owing to the coincidence of the probe laser frequency a repulsive feature at distances smaller than about 3 A. In order with energy separations within electronic structure of atomic Bi of increasing energy, these curves correlate6- with 6p3(4S03/2) and between perturbed levels of the [Bi..*Bi]'* moiety, it is Bi and the 6~~6d(~D3/2), 6$6d('D5/2), 2), possible to interrogate the dynamics of reactions 2a and 2b at both (symmetry label not yet unambiguously assignedh), 6$8~('P~/~), final-productand transition-state cofligurations on the dissociative 6 $ 7 ~ ( ~ P ~ and , ~ ) 6p27s(2P3/2) , levels of the excited atom at infinite PESs Vl(r) and VI@). separation. The experimental procedure outlined above contrasts fundamentally with the approach adopted by the IBM group of Sorokin and ~ 0 - ~ 0 r k e r ~ .who 4 ~ have , ~ ~ also *~~.~~ the real-time (43) Almy, G. M.;Sparks, F. M.fhys. Rev. 1933,44, 365. dynamics of reaction 2 by absorption spectroscopy using subpi(44) Nakamura. 0.;Shidei. T. Jpn. J . fhys. 1934, 10, 11. cosecond laser pulses arranged in a pumpprobe configuration. (45) Almy, G. M. J. fhys. Chem. 1937,41,47. Like the FTS method, Biz molecules are first excited to the re(46) hlund, N.;Barrow, R. F.; Richards, W. G.; Travis, D. N. Ark. Fys. 1965,30, 171. pulsive PESs Vl(r)or Vl,(r)by an ultraviolet pump pulse; unlike (47) RuJdy, S. P.; Ali, M. K. J. Mol. Spectrosc. 1970, 35, 285. FTS,however, the following probe pulse consists of a continuum (48) Gerber, G.; Sakurai, K.; Broida, H. P. J. Chem. fhys. 1976,64,3410. of wavelengths about 104 cm-' broad. In this way, these authors (49) Gerber, G.;Broida, H. P. J . Chem. fhys. 1976, 64, 3423. have recorded broadband frequency-resolved absorption spectra (SO) Huber, K. P.; Herzberg, G. Molecular Spectra and Molecular as a function of pump-probe delay time T in the vicinity of several Structure IY: Constants of Diatomic Molecules; Van Nostrand Reinhold: Bi atomic resonance lines corresponding to detection of the 2D03/2 New York, 1979; pp 92-93. and 2D05/2product states of reaction 2."*42 The time dependence (51) Bondybey,. V. E.; Schwartz, G. P.; Griffiths, J. E.; English. J. H. Chem. fhys. Lett. 1980, 76, 30. of the dynamics of the dissociation process is revealed in this (52) Bondybey, V. E.; English, J. H. J . Chem. fhys. 1980,73,42. method by the variation of the transient absorption spectra with (53) Manzel, K.; Engelhardt, U.;Abe, H.; Schultze, W.; Froben, F. W. T . At small delay times, asymmetric (derivative-like) spectra are Chem. fhys. Lett. 1981, 77, 514. obtained that change shape as a function of T , attaining asymp (54) Effantin, C.; Topouzkhanian, A.; Figuet, J.; d'lncan, J.; Barrow, R. totically a Lorentzian absorption line profile centered about a F.; Verges, J. J. fhys. B At. Molec. fhys. 1982, IS, 3829. (55) Fabre, G.;Bacci, J. P.; Athenour, C.; Stringat, R.; Bernath, P. Can. resonance wavelength of the free a t o m . 4 ' ~From ~ ~ observations J . Phys. 1982, 60, 73. of this type, these workers have determined that formation of 2D05/2 (56) Gerber, G.; Honninger, H.; J a m , J. Chem. fhys. Lett. 1982.85,415. product is delayed with respect to production of the lower lying (57) Ehret, G.;Gerber,G. Chem. fhys. 1982, 66, 27. 2D03/2spin-orbit level by some 500 fs following excitation of Bi2 (58) Christiansen, P. A. Chem. fhys. Lett. 1984, 109, 145. vapor at XI = 308 nm.41*42In addition, the time dependence of (59) Teichman 111. R. A.; Nixon, E. R. J . Chem. fhys. 1977,67,2470. absorption by Bi(2D03/2)product indicates both a rise in the atomic (60)Ahmed, F.; Nixon, E. R. J . Chem. fhys. 1981.74. 2156. population, peaking at about 1000 fs, followed by a decay ex(61) Babaky, 0.;Topourkhanian, A. Z . Naturforsch. 1982, 38a, 1270. tending approximately for a further 1400 fs!' These spectral (62) Damany, N.; Figuet, J.; Topouzkhanian, A. Chem. Phys. 1981, 63, 157. features and their time development has been treated theoretically (63) Moore. C. E. Atomic Energy -1s; Nat. Stand. Ref. Data Ser., Nat. by Walkup et al.,70971who have invoked a model based on the Bur. Stand. (US.), 35; US.Department of Commerce: Washington, D.C.,
-
-
1971; Vol. 111. pp 219-220. (64) Poulsen, 0.;Hall, J. L. fhys. Rev.A 1978, 18, 1089. (65) George, S.;Gorbett, M.J. J . Opt. Soc. Am. 1982, 72, 589. (66) George. S.;Mansce, J. H.; Verges, J. J . Opt. Soc. Am. B 1985, 2, 1258. (67) Ehret, G.; Gerber,G.In Laser Spectroscopy VI& Springer Series in Optics1 Scimcg; Harurch, T. W., Shen, Y. R., Eds.; Springer-Verlag: Berlin, 1985: pp 140-141.
Phys. Lett. 1988, 150. 374. (69) Glownia, J. H.; Misewich, J.; Sorokin, P. P. In The Supercontinuum Loser Source: Alfano. R. R.. Ed.;Springer-Verlan: . - Berlin. 1989: Chamer 8, pp 337-376. (70) Walkup, R. E.; Misewich, J. A.; Glownia, J. H.; Sorokin, P. P. Phys. Rev. Lert. 1990, 65, 2366.
Bowman et al.
4638 The Journal of Physical Chemistry, Vol. 95, No. 12, 1991
transient behavior of the induced polarization resulting from the interaction between the continuum laser pulse and the increasing population of product atoms whose resonance frequencies change with time. To provide a basic theoretical framework commensurate with the experimental FTS results discussed here, we further present two types of model calculationsof the dynamics of reaction 2. The first, a quantum dynamical simulation of FTS transients using second-order perturbation theory, involves computation of wave packets for the fragmenting system at various times following initial excitation of Bi2to either of the excited-statepotentials Vl(r) and V&) and indicates some interesting features of the dynamics probed by experiment that we may call to attention. Our second approach follows the classical mechanical treatment of ICN dissociation presented by Bersohn and Zewail,16 in which the evolution of a molecular system over a repulsive PES is related to the time dependence of absorption of the probe laser. The results of both quantum and classical calculations provide a means of testing the usefulness of such methods to describe adequately the real-time dynamics of the dissociation of a heavy molecular system. 111. Experimental Section Details of the experimental system have been presented elseand only a short description is given here. A collidingpulse mode-locked dye laser (CPM) was amplified in four stages by a 20-Hz Nd:YAG laser. The resulting pulses were 50-60 fs in duration with pulse energies up to 0.5 mJ and a central wavelength of 616 nm. These pulses were split into two beams: one beam was frequency doubled in a KD*P crystal to produce a pump pulse at XI = 308 nm; the other was focused into a cell of D 2 0 to generate a white-light continuum. An interference filter with a 10 nm (-450 cm-') bandpass was adjusted to pass the correct central wavelength from the continuum beam, which was subsequently reamplified in rhodamine B by 532-nmradiation from the Nd:YAG laser. The amplified continuum was then frequency doubled by using a KD*P crystal to provide the probe pulse; care was taken to double the entire band width. The pump and probe pulses were then propagated in a Michelson-type interferometer with the relative time delay between pulses controlled by an actuator. Subsequently the two pulses were recombined and focused into a sealed quartz cell containing bismuth metal (Aldrich Chemical Co. Inc., 99.999%purity), which was maintained at elevated temperatures in the range T = 1070-1 120 K by means of a conventional fire brick oven. At these temperatures, the vapor pressure of Bi2 molecules is approximately 150 mTorr, To ensure that compared to about 95 mTorr for the no bismuth metal condensed on the windows, the stem of the cell was kept at a slightly lower temperature. Laser induced fluorescence (LIF) was collected perpendicular to the copropagating laser beams and dispersed by a monochromator. All laser pulses were spectrally and temporally characterized, and the signal linearity was checked where possible. All investigations reported in this paper were carried out using a single pump wavelength of XI = 308 nm and either one of the two probe wavelengths X2 = 298.9 or 302.5 nm. As in previous p ~ b l i c a t i o n s ~the ~ * convention ~2~~ AI/&(&) is adopted to describe the wavelengths employed to obtain FTS transients. Thus, for example, a transient obtained by pumping at A, = 308 nm, probing at X2 = 298.9 nm and detecting LIF at Adet = 290 nm is labeled 308/298.9 (290). In total, 14 atomic transitions over the wave(71) Walkup, R. E.; Misewich, J. A.; Glownia. J. H.; Sorokin, P. P. In Ulrrafasr Phenomena VII; Springer Series in Chemical Physics; Harris, C. B., Ippen, E. P., Mourou, 0.A., Zewail, A. H., Eds.;Springer-Verlag: Berlin,
1990, pp 516-518. (72) Hultgren, R.; Desai. P. R.; Hawkins, D. T.; Gleiser, M.; Kelley, K. K.; Wagman. D. D. Selecred Values of rhe Thermodynamic Properties of rhe Elements; American Society for Metals: Metals Park, OH, 1973; pp 71-80. (73) Bowman, R. M.; Dantus, M.; &wail, A. H. Chem. Phys. Leu. 1989, 156, 131. (74) Corliss, C. H.; Bozman, W. R. Experimental Transition Probabiliries for Spectral Lines of Sewnry Elements; Nat. Bur.Stand. Monograph 53; U S . Department of Commerce: Washington, D.C. 1962; p 14.
length range & = 260-475 nm were observed during the course of the present work following 3081298.9 and 3081302.5 excitation of bismuth vapor. These are listed in Table I, which gives the relevant assignments for each wavelength X , at which a transition was monitored in real time. IV. Tbeoretical Section ( A ) Quantum Dynamics. To simulate the experimental results presented in sections VA and VB by time-dependent quantum dynamics, we invoke second-order perturbation theory75to calculate the nuclear wave function generated on one of the second excited states 12) by absorption of the pump and probe laser pulses: Iq2(t))= ( - i / h ) z ~ -*f d t 2-m~ f 2 T2(t dtl t2)
U21(h) Tl(t2 - t l ) UlO(tl)l*O) (3)
The total fluorescence intensity excited by the probe laser as function of pumpprobe delay time I(s;X2) is simply proportional to the probability ( \ k 2 ( t ) l q k 2 ( tof) )the system being located in the state 12) at time t immediately following interaction of the probe pulse with the system. Equation 3 contains the physics of the pump-probe excitation process: at time t l the initial ground-state wave function lq0)is optically pumped to the first excited electronic state 11) or 11') by the time-dependent perturbation Ulo(tl)due to the first laser pulse; the wave function I Q , ( t ) ) or lql,(r))so created, consisting of a superposition of continuum eigenstates, is propagated over the PESs VI@) or Vlf(r) for a duration t2 - tl by the action of the operator Tl(t2- f I ) ; at the later time t2, absorption of a probe laser photon represented by the perturbation U21(t2)induces a transition between electronic states 11) or 11') and 12); the resulting wave packet I q 2 ( t ) ) is allowed to evolve until the final time t . The propagators Ti(t) are given by T i ( t )= exp(-iH,t) (4) where Hi is the appropriate Hamiltonian operator for the ith electronic state. The form of the operators Uij(tk)is uij(tk)
= bij(r)'Ek(tk)
(5)
where k labels the laser pulses (k = 1 is the pump and k = 2 is the probe) that optically couple electronic states l i ) and b). pij(r) is the transition dipole moment operator connecting b) to li) and throughout this work is assumed to be independent of the spatial coordinate r, i.e., p,,(r) = p o k ) ( i l . Ek(tk)is the electric vector of the radiation field due to the kth laser pulse. Following earlier work,I2both Fourier transform limited laser pulses are assumed to have Gaussian temporal line shapes, which are arbitrarily curtailed at f 2 a . Wave packet propagation was carried out using the split operator method devised by Feit and c o - w ~ r k e r s . ~ Calculations ~'~ were performed by using a spatial (75) Loudon, R. The Quanrum Theory of tighr; Clarendon Press: Oxford, 1973; Chapter 1 1 , p 279. (76) Fleck Jr., J. A.; Morris, J. R.; Feit, M. D. Appl. Phys. 1976, 10, 129. (77) Feit, M. D.; Fleck Jr., J. A.; Steiger. A. J . Compur. Phys. 1982, 47, 412.
The Journal of Physical Chemistry. Vol. 95, NO. 12, 1991 4639
Femtosecond Real-Time Probing of Reactions grid of 4096 points with a propagation distance between 19.0 and 29.0 A depending upon the kinetic energy of the wave packet. Convergence was checked for in the usual manner by halving the number of discretizationsand time step. The initial wave function I%,) = exp(-io,t)ld,), comprising the nuclear eigenfunction I,$v) with a phase factor exp(-io,t), was taken to be the Gaussian form of the v = 0 level. ( B ) Classical Description. Normalized FTS signals 1(7;X2) as a function of delay time at a probe laser wavelength X2 were calculated employing the classical description of molecular dissociation in real time detailed by Bersohn and Zewail.16 In this approach, the probe laser is considered to project onto the potential V l ( r )or V,,(r)for fragment separation a detection "window*, whose position and width is determined by the central frequency and spectral line shape of the pulse, respectively. From that work, we may write the absorption of the probe laser along the dissociation coordinate r as
+ Vl(r*)]2/yZ)
A(r) = C exp{-ln 2[V2(r) - Vl(r) - V2(r*)
(6) where a Gaussian laser profile of fwhm = 2y has been invoked. Here Cis a constant and the asterisk designates that interfragment position on the potential VI@) where absorption of the probe laser is a maximum. An exactly analogous equation may of course be written for reaction over the PES Vlt(r). As pointed out previously,'6 y will exceed the natural line width by several orders of magnitude for femtosecond laser pulses; an intrinsically sharp absorption profile will thus appear to be Gaussian in shape. If it is further assumed that high-lying PES accessed by the probe laser is flat (see section IVC), then by integrating the equation of motion for a particle moving over an exponentially repulsive PES V l ( r ) we , may readily arrive at an expression for absorption of the probe pulse as a function of time of the form
A(?) = C expl-ln 2[E,,(sech2 x* - sech2 x)I2/r2) (7) where x = vt/2Ll and x* = vt*/2LI when r = r* at time t = t * . v = v'2E,,/p represents the terminal velocity of a particle of reduced mass p in the center-of-mass frame determined by the available kinetic energy E,, for fragment separation. Ll is the so-called length or range parameter of the exponential potential V l ( r )and represents the distance at which potential energy has decreased to 1 / e of its initial value at ro (see eq 8). The constant C of eqs 6 and 7 is chosen to be unity such that the calculated transients attain a maximum absorption A,,(t) = 1 at time t = t* irrespective of probe laser wavelength. Finally, the experimentally observed LIF signal I(&) is simply taken to be A ( t ) . (C) Choice of PES. Simple parametrized forms of the potential energy functions for the electronic states IO), Il), ll'), and 12) were selected as follows. The form of the ground-state potential Vo(r)was chosen to be harmonic since optical pumping of the population in the lowest vibrational level only is considered in these calculations. Appropriate parameters pertaining to the X'Z+ state were taken from the laser excitation measurements of Elfantin et For V l ( r )and Vlt(r), we invoke the simple exponential form
V,(r) = VP exp[-(r - rO)/LI1+ bi
(8)
Values of the parameters KO, L,, and ro given in the recent publication of Sorokin and co-workers4' were employed here: L1 = L l f = 2.0 A; ro = re = 2.66 A; VIo= 4260 cm-l; VIP = 241 cm-1. A correction was applied to the values of vio in order to account for thermal energy of Biz at the temperature of the experiments, yielding VIo= 5102 cm-I and VIP = 1083 cm-'. We note parenthetically that the V,O of eq 8 have been chosen" to coincide with E,, for a pump laser wavelength of XI = 308 nm. Values of = 28 1 11 cm-l and PI. = 32 130 cm-' were used as the dissociation energies Do for production of Bi(4S03/2) Bi(2D03/2) and Bi(4S032) + Bi(2D05/2)atoms via reactions 2a and 2b, respecti~ely.~ I,63-67 Clearly, the long-range parts of Vi(r)are im-
+
(78) Fcit,
M.D.;Fleck Jr., J. A. J . Chcm. Phys. 1983, 78, 301.
portant in controlling the dissociation dynamics of reaction 2, whereas the repulsive inner wall of the potential determines the shape of the absorption spectrum.I6 Until more experimental and theoretical (perhaps ab initio) work becomes available, however, we restrict our considerations here to this simple exponential representation for both V,(r). Equation 8 was also employed as a characterization of the upper PESs V2(r)accessed by the probe laser pulse. In a manner analogous to that adopted by Bersohn and Zewail in their treatment of ICN dissociation,I6 the supposition is made here that 1/L2 = A-' in all cases; thus V2(r)= & shows no explicit dependence on the reaction coordinate r. The basis for such an assumption rests primarily on the unavailability of relevant spectroscopic information concerning the various molecular potentials that connect with highly excited atomic levels at energies E > 40 X lo3 cm-' (see Figure 1). In addition, no evidence was obtained during the course of this work to suggest that bound levels of the F, Q, and S PESs (De = 13 920,14 250, and 15 100 cm-', respectively62)were populated at the probe laser wavelengths X2 employed here. The independence of V2(r)on atomic separation was invoked as an "adequate" description of the excited PESs populated by the probing process for both the quantum and classical calculations reported in section VC and was further employed as a starting point for initial interpretation of the experimental data presented in sections VA and VB; its validity will be addressed later in the paper (see section VB). Values of the dissociation energies B2 varied, of course, according to the upper state populated by absorption of a probe laser photon: appropriate data on the atomic energy level structure of Bi were taken from various sources.63db QJ
V. Results and Discussion ( A ) FTS of Biz: Methodology, Interpretation, and Clocking of Reaction. It is the purpose of the present section to describe and develop the essential methodology involved in the application of FTS to the study of the dynamics of Bi2 dissociation. To highlight the capabilities of the technique and to illustrate the essence of our interpretational framework, we limit our considerations here to a discussion of two examples of results that probe the reaction dynamics at transition-state and separated-atom configurations on the PES controlling dissociation via the lower-energy exit channel (2.a). Thus it shall be shown how FTSdata obtained at a single probe laser frequency can be used to acquire information on the reaction dynamics over a range of internuclear separations on V l ( r ) by an analysis of the transient behavior monitored at wavelengths corresponding to different transitions within the fluorescence spectrum of atomic Bi. We postpone until section VB the presentation of data obtained at a number of detection wavelengths that pertain to both reaction pathways, together with a more detailed consideration of the nature of the excited-state PESs of Biz. FTS investigations of bond-breaking processes in simple molecules are initiated by the preparation of excited reagent species on a dissociative PES (VI@)or VI@) here) by a femtosecond pump pulse. At a variable time 7 later, a probe pulse interrogates the dissociating molecules, generating an observable signal 1(7&) that permits the course of reaction to be monitored in real time. In general, the assumption is made that absorption of the probe laser occurs at those configurations of the reactive PES(s) that allow for a (vertical) transition to a single higher lying PES ( V2(r)), regardless of whether the probe frequency is on- or off-resonance with respect to a transition of one of the separated fragments.'.'' This assumption has been valid for all previous dissociation reactions studied in our laboratory by FTS,13-'5,2c26,32.33,3~,73,79 but for Bi2 it transpires that this is not the case. The accessibility of a number of closely spaced (and interacting) surfaces V2(r), coupled with the broad spectral bandwidth of the probe laser, permits the dynamics of reaction 2 at transition state and asymptotic regions of the dissociative PES(s) to be interrogated (79) Bowman, R. M.; Dantus, M.; &wail, A. H. Chem. Phys. Lctt. 1990, 174, 546.
Bowman et al.
4640 The Journal of Physical Chemistry, Vol. 95, No. 12, 1991 1.0
~{
1.0
I
Time Delay 50
I
-
b
-a
0
0
30.4
I
290
310
300
Wavelengthlnm Figure 2. Frequency-resolved spectrum of atomic Bi at different pump-
probe delay times. Spectra showing a portion of the dispersed fluorescence resulting from excitation of Bi vapor at XI = 308 nm and X2 = 298.9 nm at two pump-probe delay times: (a) T < 250 fs; (b) T > lo00 fs. The several maxima located at X rJ 290,294,299 (b only), 303, and 307 nm correspond to transitionswithin the Bi atomic spectrum. The broader peaks centered at A = 308 and 299 nm arise from scattered light due to the pump and probe lasers respectively. without having to undertake a systematic variation of the probe laser fre uency, a s has been necessary hitherto.13-1~.24-26~2.33.3S-40,73,79
Figure 2 displays a segment of the ultraviolet emission spectrum from 280 to 320 nm obtained when a sample of gaseous Bi and Bi2 is irradiated by pump and probe laser pulses at XI = 308 nm and X2 = 298.9 nm at different pump-probe time delays: (a) T < 250 fs; (b) 7 > 10oO fs. Both spectra show monochromator resolution-limited peaks corresponding to atomic fluorescence transitions and broader features arising from scattered light from the two laser pulses. The strong peak a t be,= 307 nm is due mostly to direct pumping of ground-state Bi atoms present in the cell via the 6p27s('P1/,) 6 ~ ~ ( ( 5 O , /transition, ~) together with a contribution arising from excitation of the M(M') X band system of Bi,; peaks a t other wavelengths result from the pump-probe process itself. Figure 2 constitutes a demonstration of on- and off-resonance behavior for Bi2dissociation in the spectral regime. For the limited wavelength range shown, it can be seen that several different V2(r) states are accessed by the 308/298.9 pump-probe scheme, which give rise to a number of atomic transitions. The uppermost spectrum shown in Figure 2a shows that at early times, four atomic Bi transitions are detected a t wavelengths be,near 290 (6p27s(2Py2) 6P3('Do3 2119 294 (6p27s(*P3/2) + 6p3('D05 2)). 303 (6p ~ S ( ' P ~ / ~ )6p4('DoS 2)). and 307 nm ( 6 ~ ~ 7 s ( ~ P , / J6p3('S03/2)). Comparison oithis spectrum with that taken at later times, depicted in Figure 2b, reveals a startling difference. A fifth large peak, corresponding to the 6$7s('P3 ,) 6d(2D"3/2) atomic transition, is shown on-resonance with t i e probe pulse a t Xdet = X2 = 298.9 nm, while the remaining peaks have decreased in intensity. Figure 2 therefore displays unequivocally the development of an atomic transition arising from the 2D"3 atomic level as a result of the dissociation of Bi2. At times earher than 1000 fs, while Bit has still not completely dissociated (;.e., in the transition-state region) there is no evidence of the unperturbed Bi atom transition, but several other atomic emission lines are
-
+
-
-
-
-
10
'
2.0
I
3.0
4.0
5.0
6.0
r/A
Figure 3. Experimental transients and corresponding potential energy functions appropriate to experiments that monitor formation of Bi(2@3/z) product via reaction 2a as a function of time. (a) Graphs of LIF signal intensity versus pump-probe time delay. The uppermost transient depicts off-resonance behavior at &, = 289.8 nm (6pz7s(2P~/~)6~'(~DO3/2)) and illustrates the passage of [Bi...Bi]'* species over the transition-state region of V l ( r ) . The lower transient shows characteristicon-resonance behavior at X , = 298.9 nm (6p27s(4P3,z) 6p3(2D03/z)) and corresponds to long-time detection of Bi(zD03/z)product in the asymptotic region of Vl(r). Pump and probe laser wavelengths are XI = 308 nm and X2 = 298.9 nm. (b) Schematic diagram of potential energy curves that may be invoked to explain how both on- and off-resonantdata can be obtained using a single probe laser wavelength Xz. The probe pulse energy may either be in resonance with a transition to the highest-lying Vz(r)state at E = 45916 cm-'" from the transition-stateregion of Vl(r)or with a transition to the lower Vz(r) state at E = 44865 cm-'" at large internuclear distances on VI@). In the former case early-time detection of dissociating Biz molecules gives rise to the uppermost transient shown in (a), while the latter corresponds to long-time detection of Bi(zD03/2) product as illustrated by the lower transient shown in (a).
-
-
present. When the pump-probe delay is greater than 1000 fs, the Bin -Bi separation is large enough such that interaction between the two atoms is negligible, resulting in essentially free-fragment absorption. Thus the peak monitored at be,= 298.9 nm grows in intensity as a function of time, while the peaks that are offresonance with respect to the probe laser become less pronounced. To cast Figure 2 in a more traditional light, Figure 3a displays the time dependences of two LIF signals obtained at two detection wavelengths: (1) &, = 299 nm (6$7~(~P,/,) 6p3(2D03/2)), the resonance transition; (2) he,= 290 nm ( 6 ~ ~ 7 s ( ),~ P , 6p3(2D03/2)). The time dependence of the 308/298.9(294) transient is characteristic of on-resonance behavior, while the 308/ 298.9(290) signal indicates off-resonant behavior, such as have been observed and analyzed previously for reaction 1.13*2)-26 In section VB more detailed consideration shall be given to the time dependences of the various off-resonant transients arising from 308/298.9 excitation, together with those data obtained at a probe wavelength of X2 = 302.5 nm. Here, attention is devoted to the on-resonant transient monitored at X , = 298.9 nm, which allows ' ~ l o c k i n g " ' ~ of . ~the - ~ dissociation ~~~~ reaction that proceeds over V , ( r ) to form 'DO312 + 'So3,, product atoms. Rosker et al. have previously offered a definition of the dissociation time for reaction in terms of the time taken for the observed LIF signal to attain half its limiting value at long times
- -
The Journal of Physical Chemistry, Vol. 95, No. 12, 1991 4641
Femtosecond Real-Time Probing of Reactions when probing final product ~ t a t e s . ~ ~ " J(Classically, ~ this corresponds to the time taken for the system to reach that point on an exponential PES where V,(t) = y cm-l.16f7) It is clear that any determination of T~ depends crucially on knowledge of the zero of time for the haldcollision p r o c e ~ s . ~ ~ * The ~ 3 3procedure 9 that has been adopted to ascertain t = 0 for dissociation along both reaction channels (2a) and (2b) takes advantage of early-time detection of [Bi*-*Bi]**species within the Franck-Condon regions of V l ( r )and VI,@) and is expounded upon in section VB. From the on-resonance transient shown in Figure 3a, a value of r I l 2= 1 ps for dissociation of Biz according to eq 2a may be obtained. (In view of the method employed in section VB to determine t = 0, such a result for T should be considered precise to within Within the framework of the classical an uncertainty of h0.2 descriptioni6of dissociation over an exponentially repulsive PES outlined in section IVB, we may calculate that at a time t = lo00 fs after impulsive bond cleavage the (classical) Bi...Bi fragment separation r, is 10.7 A, where a length parameter LI = 2 A describing the parametrized form of Vl(r)has been employed (see section IVC). It is straightforward to show that such a model may lead to an estimate of Li itself from the measured value of T ~ / In ~ the . limit t a,eq 7 may be solved for T ~ /yielding ~ , the expression
x?)
-
TI12
= (L,/u)
[4~,,/~1
(9)
obtained previously by Rosker et aL2? Here it is assumed that E," > y and that the distance travelled by the particle at time t is much greater than L,,Le., that ut >> 2L, (see eq 7). From the experimental estimate of T~~~ reported above, a value of L1 = 2 A can be derived for a transform-limited Gaussian probe pulse of temporal duration 100 fs, where the quoted error limit arises from the uncertainty associated with the measured value of ~ ~ 1 2 . Our empirical determination of the length parameter is in quantitative agreement with the arbitrarily chosen value of LI= 2.0 A for the parametrized form of V l ( r )proposed by Sorokin and co-workers4' (see section IVC). The origin of the different time dependences of the 308/ 298.9(299) and 308/298.9(290) transients may be explained in terms of a simple model involving two high-lying surfaces V2(r) of Biz populated by the probe laser. Figure 3b represents a potential energy diagram that may be invoked to interpret the real-time data displayed in Figure 3a and depicts V,(r)and two V2(r)potential curves correlating with the 6p3(4S031z)+ 6p27s(zPl/2)and 6p3(4So32) + 6p27s(4P3/2)atomic levels at asymptotic energies E = 45 91d and 44 865 cm-', respectively. As the wave packet prepared by the pump laser propagates over Vl(r)toward dissociation products, the probe pulse becomes resonant with respect to transitions to one of the two surfaces V2(r)at two distinct internuclear configurations: once in transition-state region; and also at larger separations, where the atomic transition occurs. Figure 3b thus depicts a simple picture of how a given probe wavelength can examine the dynamics on Vl(r)at different regions of configuration space. In previous FTS experiments on the dissociation reactions of ICN,13*2CM I 2 9 32*33*35 NaI,I4J7* and HgIzr15,73 X2 was tuned to a known transition of one of the separated products in order to probe on-resonance behavior; to monitor off-resonance dynamics, on the other hand, it was necessary to tune X2 to the red (lower energy) of the free-fragment transition. The work described here is therefore distinguished from earlier investigations of unimolecular processes by the fact that both on- and off-resonance behavior can be observed by using a single-probe wavelength due to the accessibility of more than one V2(r)molecular state. For Bi2 at least seven high-lying PESs can be populated by the probe laser when XI = 308 nm and X2 = 298.9 nm. Unfortunately, however, very little is known about the nature of these surfaces at small interfragment distances, though future FTS experiments could provide a useful method for elucidating the topologies of such high-lying molecular states (see section VI). ( B ) Dynamics and PESs of Bi2. In the previous section it was shown how both on- and off-resonance dynamics could be observed in the time domain in FTS investigations of reaction 2a when more
Time Delay Figure 4. Experimental transients obtained at pump and probe laser wavelengths of XI = 308 nm and X2 = 298.9 nm. Graphs of LIF signal intensity (arbitrary units) versus pumpprobe time delay recorded at (a) X , = 472.2 nm ( 6 ~ ~ 7 s ( ~ P , / ~6p3(2D03 ) J), (b) X , = 359.6 nm ) (6p27s(2P3/2) 6p3(2P"1/2));(c) X , = 2694 nm ( 6 ~ ~ 7 s ( ~ P s / 2 6p'('D03/2)h (4xd, = 278.1 nm ( ~ P ~ ~ S ( ~ P6p3(*D03/2)), ~/Z) (e) X , = 298.9 nm ( 6 ~ ~ 7 s ( ' P ~ / ~6p3(2D03/2)). )
-
-
-
-
-
Time Delay Figure 5. Experimental transients obtained at pump and probe laser wavelengths at A, = 308 nm and X2 = 302.5 nm. Graphs of LIF signal intensity (arbitrary units) versus pump-probe time delay recorded at (a) X , = 472.2 nm ( 6 ~ ~ 7 s ( ' P , / ~ ) 6p3(2D03/2)),(b) X , = 293.8 nm (6p27s(2P3/2) 6p3(2Dos/2)),(c) &, = 302.5 nm ( 6 ~ ~ 7 s ( ~ P 6p3~/~) (2D0s/2)),(dl h,= 278.1 nm ( ~ P ~ ~ S ( ~ P6P3(2D03/2)), ,/~) (e) X , = 298.9 nm ( 6 ~ ~ 7 s ( ~ P 3 / 2 6~~(~D'3/2)). )
-
-
-
-
-
than one high-lying PES can be populated by a probe laser pulse operating at Xz = 298.9 nm. Table I lists all atomic transitions that could be monitored in the time domain at probe wavelengths of X2 = 298.9 and 302.5 nm. Examples of FTS transients recorded at five values of be,resulting from different Vz(r) states are displayed in Figures 4 and 5 for the 3081298.9 and 308/302.5 pumpprobe schemes, respectively. For a given transient shown in Figure 4, the upper surface Vz(r)populated by the probe laser is identical with that for the corresponding data displayed in Figure 5 , though A,,ct may, of course, be different. Thus, for example, the data shown in Figure 4b were recorded at bet = 359.6 nm ( 6 $ 7 ~ ( ~2)P ~ 6p3(2p142))while Figure 5b displays data obtained at be,= $93.8 nm (6p 7S('P3/2)
-.
-
4642 The Journal of Physical Chemistry, Vol. 95, No. 12, 1991
ln c .3 c
Q C
wol 1
I
.
l
.
I
.
I
Time Delay Figure 6. Experimental transients originating from the same upper state V2(r)located at E = 49461 cm-l.M*” Graphs of LIF signal intensity (arbitraryunits) versus pumpprobe time delay illustrating the invariance of the observed signal, and hence underlying reaction dynamics, to detection wavelength: (a) bel= 359.6 nm (6p27s(’P3/2) 6p3(2P01/2)), (b) &, = 293.8 nm (6p’7~(~P3~~) 6p3(2D05/2)), (c) bel= 262.8 nm (6p27s(2P,/2) 6p3(’Do3/J). Pump and probe laser wavelengths are A, = 308 nm and A2 = 298.9 nm.
-
-
-
Each of the transients shown in Figures 4 and 5 reflects the dynamics of the dissociating system over different regions of Vl(r) and Vlc(r)depending upon the V2(r)state accessed by the probe laser (from which LIF subsequently originates). This point is further illustrated in Figure 6 for X2 = 298.9 nm, which depicts three off-resonant LIF signals originating from a single V2(r)curve located at E = 49 461 cm-l (corresponding to the excitation of 6 ~ ~ 7 s ( ~ PBi~ atoms64*66). /2) Emission from this PES terminates on potentials connecting with the 6p3(4S03/2)+ 6p3(2POI2), 6p3(zD0s/2),and 6p3(2D03/2!atomic levels at E = 21 661, 15 438, and 11 419 cm-I. In the limit of infinite Bi...Bi separation, transitions between these states give rise to fluorescence at X = 359.6, 293.8, and 262.8 nm of the free atom, respectively (see Table I). These transients are identical within the signal-to-noise ratio: Figures 4-6 together illustrate, therefore, that the dissociation dynamics monitored clearly depend upon which upper potential V2(r)gives rise to the observed LIF. Such a scheme is subtly different from earlier real-time investigations of ICN d i s s ~ c i a t i o n , ~in~that **~~ the previous work involved monitoring of resonance fluorescence only; that is to say, the two surfaces (correlating with product CN its X2X+ and B22+states) connected by the probe laser pulse were also responsible for the LIF signals. To proceed to rationalize the experimental transients obtained with X2 = 298.9- and 302.5-nm probe pulses, especially those exhibiting off-resonant behavior, the following three simplifying approximations are invoked (at the same time taking due note of their weaknesses): (1) all V2(r)PESs populated by the probe laser are assumed to be independent of the reaction coordinate from the Franck-Condon region to infinite separation (see section IVC), unless the data are absolutely inconsistent; (2) there is no curve crossing between different V2(r)potentials; (3) the parameterized forms of V l ( r )and VI,(?) are those given by Glownia et a1.41 As a starting point for consideration of the data shown in Figures 4 and 5 , we discuss experiments that we believe probe the production of ground-state Bi(4S0312)atoms via reactions 2a and 2b. Table I indicates that there is an atomic transition at A = 306.8 nm whose lower level is the 4S03/2ground state and whose upper level is lying some 32 588 cm-l higher in energy.63 LIF from this state was recorded at bet= 472.7 nm ( 6 ~ ~ 7 s ( ~ P -,.+/ 26~~(~DO3,2)) ) and is depicted in Figures 4a and 5a. These two transients thus correspond to 308/298.9(473) and 308/302.5(473) pumpprobe schemes. The fact that these transients are observed implies that the molecular state(s) V 2 ( r ) responsible for the LIF possess(es) an increasing degree of upward curvature as Bi...Bi separation decreases. This is because both probe. pulses are higher in energy than the 32588-cm-’ separation
Bowman et al.
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of the 6p3(4S0312)atomic transition by some 858 and 464 cm-l. Both transients show one strong peak and a weaker shoulder at longer times. That the first peak occurs earlier in time than any other feature present in all the transients monitored a t both probe wavelengths leads us to postulate that in this case, probe absorption takes place in, or very near, the Franck-Condon region. The second less intense peak shifts to earlier times by about 200 fs for the (less energetic) probe pulse closer to the free atomic resonance line at X = 306.8 nm. A consistent interpretation of the data obtained a t bet= 472.7 nm requires at the very least that the relative positions and intensity difference between the two peaks monitored at both probe wavelengths be accounted for satisfactorily. First, we note that the energy difference between the two probe wavelengths is 394 cm-’. Of the model dissociative curves Vl(r) and Vl.(r),the potential that could most reasonably be expected to result in a 200-fs difference in “appearance time” of the later peak for such a frequency difference is the more highly curved V l ( r ) . The secondary maxima shown in Figures 4a and Sa are thus assumed to be due to absorption from the VI@) state, though the early-time peak may arise by absorption from either surface as discussed below. The timing difference between the second peaks observed at the different probe wavelengths places restrictions on the form of the high-lying state(s) V2(r)that are populated by the probe laser pulse in both cases: the potential(s) must be such that the probe pulse is in resonance with Vl(r)twice, once a t very early times and again a t larger r. In addition, as the internuclear separation increases beyond the Franck-Condon region, the energy difference between Vi(?) and V2(r)must also h m e larger. Several shapes for Vz(r)can be invoked that satisfy these criteria, given a functional form for VI@). Taking such considerations into account, two possible explanations for the intensity differences in the 308/298.9(473) and 308/302.5(473) transients may be postulated. The first possibility is that two upper surfaces V2(r)are involved: one that correlates with 6p27s(4Pi/2) 6p3(2D03/2)atoms a t E = 44007 cm-I; and another that correlates with 6 ~ ~ 7 s ( ~ P , / , ) 6p3(2D05/z)at E = 48 026 cm-I. In this situation, the first peak would exhibit high intensity due to absorption by [Bi..-Bi]’* species located at Vl(r)and Vi@) to both of these upper potentials in the Franckcondon region. The wave packet created on Vi@) by the pump laser subsequently moves out of resonance with the probe pulse energy on leaving the Franck-Condon region; thus the less intense second peak is due to absorption from transition-states evolving over Vi(r) alone. The other possibility involves only a single upper surface, that formed from 6p3(4P1/2)+ 6p3(2D05/z)atoms. If some degree of mixing exists between V l ( r )and V&) in the Franck-Condon region, absorption could occur from either molecular surface to V2(r)since both lower PESs would possess substantial UZD0Sj2” character. At increasing interfragment separations, the coupling between the VI@) and Vi!(r) PESs decreases, resulting in less probe absorption from the [Bi...Bi]** wave packet moving along the Vl(r)potential a t later times corresponding to the position of the second peak. The LIF signal therefore decreases in intensity as the wave packet on VI@) propagates toward the asymptotic product region of configuration space because the dissociative PES possesses less “2D05/2”character. These very tentative explanations do not allow the construction of a unique set of PESs but do offer some insight into the topologies of the potentials involved. It appears reasonable to presume, however, that the first peaks of both of the 308/298.9(473) and 308/302.5(473) data arise from absorption in or very close to the Franck-Condon region. On account of the small difference between probe laser frequencies compared to the probe transition energies, we postulate as a working hypothesis that the first peak occurs at approximately the same time for both transients displayed in Figures 4a and 5a. In addition, the assumption is made that the point at which the early-time peaks of these data attain half-maximum intensity marks the zero of time (to within f 5 O fs) for the reaction. The remainder of our discussion in this section starts with this premise.
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= 359.6 ( 6 ~ ~ 7 s ( ~ P 3 / 26p') FTS transients obtained a t ( 2 P i 2)), 269.7 (6p27s('PSl2) 6p3(2D032)), and 278.1 nm (6p2ds(4Pl/2)76p3(2D03/2))for X2 = 298.6 nm are depicted in parts b-d of Figure 4 in order of decreasing V2(r)excitation energy: all demonstrate off-resonant behavior. For comparison purposes, Figure 4e displays the on-resonant transient recorded at = 298.9 nm (6p27s('P3/,) 6p3(2D03/2)) shown previously in Figure 3a. The data displayed in Figure 4b arise from the high-lying potential V2(r)situated at E = 49461 cm-i64,66which would be accessible from Vi(r) only by 298.9-nm probe light at transition-state geometries close to or within the Franck-Condon region (assuming that V2(r)is independent of reaction coordinate, as usual). It follows that in such a case, the observed LIF signal intensity at Xdcl = 359.6 nm would be expected to peak a t very early times, yet maximum intensity is achieved at a time T 800 f 50 fs, which is about as late as that of any transient shown in Figure 4. This leads us to believe that this transient reflects dissociation dynamics of the Vir(?)curve. Further evidence for such a hypothesis is given by the broad width of the off-resonant transient. Since the available kinetic energy E,, for product separation is only 1083 cm-' for dissociation over Vlt(r),compared to E," = 5102 cm-I for reaction via the lower lying exit channel (2a), the time-developing wave packet on this PES will proceed along the dissociation coordinate relatively slowly compared to motion on Vi(r). As a result, the probe pulse with its large bandwidth is resonant over a considerable range of internuclear separation on the dissociative potential Vlt(r). The late arrival and broad peak width therefore give us reason to suspect that the 308/298.9(360) transient shown in Figure 4b reflects the dynamics of [Bin .Bi] ** transition states evolving over Vi,(r). If the upper electronic surfaces V2(r)giving rise to the transitions a t = 269.7 and 278.1 nm are essentially independent of fragment separation beyond the Franck-Condon region and the probe wavelength is assumed to induce absorption from a single lower PES Vi(r) or Vit(r), then as the probe frequency becomes resonant with each V2(r)at successively lower energies, the peak of the off-resonant signal would be expected to occur at longer times. Such an effect appears to be operating for the data shown in Figure 4c,d, which originate from V2(r)surfaces that correlate with excited Bi atoms located at E = 4849Pqa and 47 373 We therefore postulate that these two transients probe dynamics on the Vi(r) potential at different internuclear separations determined by the different energy separations between the Vi(r) and higher lying V2(r)potential energy functions. If the topologies of the different V2(r)were known, such data would afford the opportunity to map out an entire repulsive potential surface over a wide range of configuration space. Comparison of the times at which these two transients exhibit maximum intensity with the early time peak position of Figure 4a reveals that the 308/ 298.9(270) and 308/298.9(278) signals are off-resonant by approximately 550 and 900 fs with respect to t = 0. These times are well outside the pulse widths of the pump and probe lasers (see section 111). The data displayed in Figure 5 were obtained by employing a probe wavelength tuned to X2 = 302.5 nm, in resonance with the 6p27s('P5/& 6p3(2Dos/2)atomic tran~ition.'~The transients recorded at bel= 472.2 ( 6 ~ ~ 7 s ( ~ P ~6p3(2D03/2)), /~) 293.8 ( 6 ~ ~ 7 s 2)( ~ P ~ and 278.1 nm ( 6 ~ ~ 8 s ( ' P ~ / ~ ) 6$(2D"3/2)$. shown in parts a, b, and d of Figure 5, are very similar to the analogous data shown in Figure 4. Figure 5a has been discussed previously in the context of the determination of the zero of time for reaction 2b. The 308/302.5(294) transient depicted in Figure 5b may be slightly broader than its counterpart shown in Figure 4b for Adel = 359.6 nm and acquires maximum intensity at a shorter delay time; we believe that these data correspond to off-resonance probing of reactive intermediates on Vlt(r)as discussed earlier. There is no significant difference in shapes of the transients recorded at X , = 278.1 nm for both probe wavelengths. At the present time, we have no satisfactory explanation for the shape and timing of the transient shown in Figure '5e, recorded at X, = 298.9 nm ( 6 ~ ~ 7 s ( ; P ~ / ~~P) ~ ( ~ D O ~but /,)), its broad width and (late) appearance time compared to the data
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displayed in Figure 5d for bel= 278.1 nm could possibly be a reflection of transition-state dynamics on the V&) potential. The transient displayed in Figure 5c, recorded at b, = 302.5 nm ( 6 ~ ~ 7 s ( ~ P , / , )6p3(2D0s/2))exhibits behavior a t long times, 11000 fs, that is indicative of on-resonance probing of 2D0s/2 product atoms resulting from reaction 2b. The dissociation time 71/2 in this case is noticeably longer than that for formation of the lower spin-orbit level of the 2Do, term shown in Figure 4e; relative to the t = 0 peak of Figure 5a (see earlier) we may estimate a value of T1/2 for reaction 2b of about ~ 1 . ps. 5 The appearance of 'D05/2 4S03/2Bi fragments arising from the dissociation of Bi, is therefore delayed with respect to formation of atomic products via the lower-lying exit channel (2a) by some 400 fs. This rppresents a direct measure of the difference in available kinetic energy for dissociation via the two reaction pathways (2a) and (2b) and is consistent with the potential energy curves postulated by Sorokin and co-workers4' displayed in Figure 1. The classical modeli6 of section IVB for fragmentation according to reaction 2b leads to an estimate of rl = 7.5 A as the distance apart of nascent Bi atoms in their 2Dos/zand ?SO312 levels after 1500 fs, assuming a length parameter of Lit = 2 A for Vi@) as before. Using eq 9, a value of Llt = 1.8 A may be determined from the experimentally measured dissociation time, making the same assumptions detailed in Section VA. We note that our estimate for LIris some 10% smaller than both that for L1 derived from Figure 4e, and the value of L1!I employed in section IVC to construct the model potential Vlt(r). The data of Figure 5c also exhibit a low-intensity feature a t early times preceding the on-resonant rise. The maximum of this off-resonance peak is achieved about 10oO fs earlier than q/z.for the on-resonance signal and is believed to monitor the early-time dynamics of 2D03/2Bi atoms evolving over the lower-energy exit channel (2a). It would appear therefore, that for X2 = 302.5 nm both the 6P%4ps/z) 76P3(2y3/2)and 6$7S('ps/z) 6$('ws/2) transitions can be excited, permitting the transition-state dynarmcs on Vi@) and the longer time asymptotic behavior on Vlf(r)to be interrogated simultaneously. In a single transient it is possible to obtain in real-time two snapshots of the dissociation dynamics of Biz as the molecule fragments along the exit channels (2a) and (2b). We recognize that the discussion presented in this section is indeed qualitative in nature. The possibility of curved potentials V2(r)for Bi2and the presence and location of conical intersections between excited-state PESs have been mostly ignored. If an extensive pump and probe-wavelength-dependent study were to be performed, it could be possible to elucidate such features for Vi(r) and Vit(r)and for many of the V2(r)PESs. One fact that should be pointed out is that the existence and exponential form of Vi@) was taken to be that of the model potential of Glownia et aL4I without any further justification. An alternative explanation for the appearance of 2D0s/2atoms via reaction 2b could for instance be that a lower lying PES connects to this atomic level, though we point out that our investigations to date fail to provide conclusive evidence for either hypothesis. In this latter case, no new potential need be invoked to explain the formation of this product, but rather a conical intersection between the lower lying PES with Vi(r) at some region on the reaction coordinate may be postulated. The weakly bound V(O+,)state analyzed by Effantin et aLS4or the states labeled D and E by Gerber and Br~ida:~for example, may connect with 6p3(?S03/2) ~P~(~DO,/,) atoms at infinite separation. (0Theoretical Analyses. ( i ) Quantum Dynamics: Figure 7 shows snapshots of l*l(t)) as a function of time following M X excitation of Bi2 by a pump laser pulse centered at time t = 0. It can be seen that I*i(t)) initially spreads during the laser pulse as more population is transferred to the upper-state potential Vl(r)but thereafter remains highly localized for times as long as 2400 fs (with only a small degree of spreading), at which time the wave packet samples regions of the PES corresponding to an average Bi. .Bi fragment separation of (r) = 26.0 A (nearly 10 times longer than re = 2.66 AM). After some 1200 fs, the wave packet may be considered to have reached the asymptotic region
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transient monitored at X, = 359.6 nm ( 6 ~ ~ 7 s ( ~ P 3 / 2 )6p3(2F"'~,2)), displayed in Figure 4b, reflected the early-time dynamics of Biz dissociation along the higher lying reaction pathway (2b). t=Ofs Comparison of Figure 4b with the calculated FI'S signal shown in Figure 8d reveals that the observed intensity maximum occurs at r i= 800 f 50 fs, somewhat later than the computed maximum given above. The calculated off-resonant transient for formation of 2D03/z 4S03/2product atoms via exit channel (2a), displayed .6 in Figure 8c, may likewise be compared with the experimental A results obtained at & = 269.7 nm (6~~7s(~P5/2)6p'('D03/2)) t I i v shown in Figure 4c. In this case the experimental LIF signal attains maximum intensity at a delay time 7 = 500 f 50 fs, again larger than the calculated peak position. We consider that the difference between experimental and theoretical results is m a t likely a reflection of the inadequacy of the simple exponential forms of Vl(r) and VI?(?)used in the quantum calculations (see section IVC) to model successfully the early-time dynamics with quantitative accuracy. However, given the degree of broad qualitative agreement between the experimental results of Figure 4b,c and the computed signals shown in Figure 8c,d, we feel that the calculations of off-resonance behavior reported here lend 0 5 10 20 25 30 support to the general thrust of the discussion presented in section VB and in particular to the proposal that Figure 4b,c monitors Figure 7. [Bi.-.Bi]** wave packets. Graph of p , ( r ) ) versus r / A dethe early-time dynamics of dissociation Over the VI,@) and Vl(r) picting the time evolution of the wave function prepared on V,(r) by potentials. excitation at XI = 308 nm with a Gaussian-shaped laser pulse of fwhm Finally we note, as has been observed in revious calculations = 100 fs centered at t = 0 fs. of ICN wave packets on a repulsive PES?-Pthat the peak signal intensity of detuned transients is less than the asymptotic intensity of the PES,where VI@) is only some 50 cm-I above the dissoof the on-resonance signal. The maximum LIF intensity is related ciation limit. Similar behavior was calculated for 191t(t)),though to the temporal duration of the pump and probe laser pulses, the in this case the group velocity of the time-evolving wave packet amount by which the probe wavelength is detuned off resonance, is much smaller. 191,(t)) arrives of the asymptotic region of VI@) and the spreading of the wave packet as it evolves over the PES after approximately 890 fs and then proceeds to larger r as a arising from the forces acting on it during the dissociation process localized wave packet. The expectation value ( r ) for 19,,(t)) is (which reflects the shape of the controlling PES). 12.9 A after 2400 fs and about 15.1 A at t = 3000 fs. ( i i ) Classical Treatment: Displayed in Figure 9 is the time Graphs of ( 9 2 ( t ) 1 9 2 ( t )versus ) delay time 7, representing FTS dependence of probe pulse absorption calculated from eq 7 for spectra, are displayed in Figure 8 for dissociation according to the same probe laser wavelengths as employed in the quantum eqs 2a and 2b. Pump and probe laser frequencies were chosen dynamics calculations. No attempt has been made to convolve to match those employed in the experimental measurements rethe calculated FTS signals with either the pump or probe laser ported in sections VA and VB. Figure 8a,b, depicts on-resonance response functions or their cross correlation, which would both behavior, corres nding to detection of Bi atoms in their 6p3broaden the transients and cause a decrease in peak intensity as (2D0312) .ande6pE(D 05/2) spin-orbit levels at long times. For a function of detuning of the probe laser frequency from the dissociation ma exit channels 2a and 2b, Figure 8a,b indicates that on-resonance value. A more detailed consideration of such conthe dissociation times calculated by quantum dynamics for the volution effects13-2s-27 will be given in a forthcoming publicationVs0 model potentials Vl(r) and Vl,(r)described in section IVC are The on-resonance transients, depicted in Figure 9a,b for reactions = 990 and 1480 fs, respectively. It may be considered that 2a and 2b, respectively, are characterized by dissociation times these times are in reasonable quantitative accord with the corof rI12 1040 and 1590 fs. We note the reasonable agreement responding experimental estimates of rI/?= 1 and 1.5 ps reported between these values and those obtained from the perturbation in sections VA and VB; we note the particularly close agreement theory calculations reported above, as may be anticipated for a between computed and experimentaldissociation times for reaction particle as heavy as Bi2. That the classically derived values of 2b, even though the value of LIt used to construct the model rI12are larger than those computed from quantum dynamics by potential V&) (section IVC) is 0.2 A larger than the value derived some 50-100 fs may be a reflection of the finite and time-defrom experiment (section VB). At delay times r = IO00 and 1500 pendent width of the dissociating wave packet in the latter calfs, the expectation values ( r ) of the wave ckets on the two PESs culations, though we also note that parts a and b of Figure 8 are VI@) and Vlt(r)are ( r ) = 10.7 and 7.5 ccorresponding closely constructed from only 10 points, whereas parts a and b of Figure to the classically determined values of r, given in sections VA and 9 involve 2000 and 3000 points, respectively. VB as might be expected. The off-resonance signals shown in Figure 9c,d were constructed Figure 8c.d displays off-resonant transients for the two exit so as to attain maximum absorption at times r* = 223 and 671 channels leading to the 2DoJterm. Thesc transients were calculated fs, equivalent to the times taken by a classical trajectory on VI(?) for a probe laser wavelength of X2 = 298.9 nm detuned by 3625 or VI@) to reach that point on the PES corresponding to the center and 577 cm-', respectively, from the appropriate resonance wavelengths for separated atoms (A2 = 269.7 ( 6 ~ ~ 7 s ( ~ P ~ / ~ )of the detection window viewed by the probe laser (that at a given frequency connects to the upper surface V2(r) from which LIF 6p3(2D03/2))and 293.8 nm ( 6 ~ ~ 7 s ( ~2) P , 6p3(2D05/2)))and indicative of off-resonance behavior is observed experimentally). correspond to early-time detection of di, wave packets at transition-state regions of configuration space. Both transients show, VI. Concluding Remarks as expected, a rise and decay in signal intensity, as the wave In this paper, we have reported on the use of FI'S to probe the packets pass through the absorption-resonant region viewed by dynamics of Bi2 fragmentation in real-time following ultraviolet the probe laser, with maxima located at delay times 7 = 220 and excitation of the parent molecule at XI = 308 nm. The presence 670 fs. At these times, the Bi2 wave packets are located at ( r ) of two exit channels (reactions 2a and 2b) leading to atomic = 3.4 and 3.9 A on V , ( r ) and V&), respectively. The results products in the 4S03/2+ *Do3/, and 4S03/2+ 2D05/2levels of the of these calculations may be compared with the appropriate experimental data obtained by using a probe wavelength of X2 = 298.9 nm. In section VB it was argued that the broad off-resonant (80) Roberts. G.; Zewail, A. H.J . Phys. Chem., accepted for publication. l
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T/fS Figure 8. Transient behavior calculated by quantum dynamics (eq 3). Graphs of the norm of the wavefunction 1q2(r)) created on V2(r)by the probe laser, representing the observed time-dependent LIF signal, as a function of pumpprobe time delay. Values of (qz(r)lqz(t)) are normalized with respect to the long-timeasymptote of Figure 8b. XI = 308 nm in all caw, and both pump and probe laser pulses arc assumed to have Gaussian temporal profiles of fwhm = I 0 0 fs. (a) On-resonance (long-time) signal indicating the growth of Bi(2D01/2)product from dissociation over Vi(r): X2 = 298.9 nm [6p27s('P1 2) 6p1(2Ll$)]. (b) On-resonance (long-time) signal indicating the growth of Bi(2Doy2)product from dissociation over Vit(r): X2 = 302.5 nm [ 6 ~ ' 7 s ( ~ P ~ /6p1(2y5/z)]. ~) (c) Off-resonance (early-time) probing of [Bi--.Bi]** transition states proceeding over Vi(r): X2 = 298.9 nm; V2(r)corresponds to the excitation energy of Bi(6p27s'P5,J. (d) Off-resonance (early-time) probing of [Bi. .Bi]** transition states proceeding over Vit(r): X2 = 298.9 nm; Vz(r)corresponds to the excitation energy of Bi(6p27s2Pl/2).
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6p3 ground electronic configuration has been established. Dissociation times of 71/2 1 and 1.5 ps have been measured for available energies of 5102 and 1083 cm-' above the dissociation thresholds for the two reaction pathways. The possibility of accessing several high-lying PESs by the probe laser energies employed has provided an opportunity to examine the dynamics of the dissociation process over a range of interfragment separations on the governing PES(s) from near the Franck-Condon region to separated-atom configurations. The overall shapes of the off- and on-resonant transients obtained in this series of experiments are qualitativelysimilar in form to analogous data re rted hitherto for dissociation of ICN via the A continuumi3* EO(reaction 1). which is controlled by at least three unbound P E S S . ~This suggests that the fragmentation of Biz via the two reaction channels giving rise to the ground term and fD03/z or 2D05(2products proceeds over PESs that are predominantly repulsive in character at all distances greater than the Franck-Condon region. We note that the experimentally
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observed values of r1 determined for reactions 2a and 2b are approximately some 4-7 times longer than those for ICN dissociation and that the off-resonance signals are correspondingly broader in the former case. These effects may be readily anticipated a priori, assuming a small degree of internal excitation of the I and CN products of reaction 1, simply on the basis of the large reduced mass of the Bi2 molecule and the lower available kinetic energy for product separation. Complementary quantum and classical calculations of reaction 2 confirm our experimental findings, yielding on-resonant FTS signals with dissociation times ri in reasonable quantitative agreement with observed values, and off-resonant transients whose shapes are in qualitative accord with the empirical data. These calculations could be brought into closer agreement with experiment by judicious refinement of the parameters describing the model dissociative potentials Vl(r)and Vit(r). By utilizing the density matrix approach to nonlinear spectroscopy to derive classical formulas for the time-dependent probe absorption
Bowman et a].
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t/fs Figure 9. Transient behavior calculated by classical mechanics (eq 7). Graphs of probe laser absorption A(f)/arbitrary units as a function of time, representing the time dependence of the deconvolved LIF signal. In all cases a spectral width of fwhm = 2y = 148 cm-l is assumed for transform-limited Gaussian laser pulses. Times I* are calculated on the basis of the distance travelled by a classical particle on VI@) or V&) so as to achieve maximum absorption at probe wavelengths X2 connecting the V2(r)levels indicated; commensurate with experimental observations of on- and off-resonance behavior. (a) On-resonance (long-time)signal indicating the growth of Bi(2Do,/2)product from dissociation over Vl(r): I* = 2000 fs; A2 = 298.9 nm; Vz(r) corresponds to the Bi(6p27s4P3/z)energy level. (b) On-resonance (long-time) signal indicating the growth of BI(~D~,/,)product from dissociation over V&): I* = 3000 fs; X2 = 302.5 nm; V2(r)cormponds to the Bi(6$7s 4P5/2)energy level. (c) Off-resonance (early-time) probing of [Bi...Bi]'* transition states proceeding over Vl(r):I* = 223 fs; A2 = 298.9 nm; V2(r)corresponds to the Bi(6$7s 4P5,2)energy level. (d) Off-resonance (early-time) probing of [Bi...Bi]'* transition states proceeding over V,,(r): I* = 671 fs; A2 = 298.9 nm; V2(r)corresponds to the Bi(6p27s2P,/2)energy level.
monitored in femtosecondpump-probe experiments,sa Mukamel and co-workers have succeeded in identifying those situations where classical predictions of the temporal dynamics are in good agreement with exact quantum mechanical as a protypical example, the conditions for classical absorption behavior have been illustrated explicitly for the dissociation of ICN.Z1 For reaction 2, where the laser pulse durations are short in comparison to the time scale of the nuclear dynamics, the results of the quantum and classical treatments presented in this paper exhibit the expected2'*22close correspondence. Our results further offer general support to the proposed exponential forms for Vl(r)and Vlt(r) put forward by Sorokin and co-workers" to model Biz dissociation trajectories along the reaction pathways 2a and 2b, leading to different spin-orbit levels of the DJterm. An estimate of the length parameter of LI = 2 A derived from the measured value of 7 for reaction 2a is in agreement with the values LI = L I ,= 2.0% arbitrarily chosen
by these workers4' for one-dimensional potential curves, while the value LI, = 1.8 A determined from analogous experimental data for reaction 2b is 10% lower. The difference between our measured dissociation times for formation of 2D03 and D ' O512 products of ~ 4 0 fs 0 is in overall accord with the =hO-fs delay observed by Glownia et for the onset of absorption by 2D05/2atoms with respect to that arising from the D ' O312 level. At the present time, however, we are unable to provide a satisfactory explanation of the decrease in absorption near the 6p27s('P3/2) 6p3(2D032) resonance line at A = 298.9 nm monitored by these workers /or pump-probe delay times greater than about 1100 fs!I In our FTS experiments, following an induction period of about 800-fs duration, a monotonic increase in the LIF signal intensity monitoring 'D03/2 atoms at A2 = hoc = 298.9 nm at long times is observed which reaches an asymptotic limit after about I600 fs and which does not subsequently decay on the picosecond time scale (the radiative lifetime of the 6p3(2D03/2) level has been determined to +
J. Phys. Chem. 1991,95, 4647-4651 be T~ = 44 f 3 mssl). This and off-resonance observations are consistent with the detection of “free” Bi atoms and [Bi...Bi]** transition-state configurations, respectively. Determination of the topologies of the dissociative PESs” and their absolute location in configuration space relative to the ground-state molecular geometry await the outcome of future experiments in which the excess energy above dissociation threshold is varied by means of tuning the pump laser wavelength XI. Such data should further reveal the possible existence and location of conical intersections between the reactive PESs and allow the appropriate interaction matrix element to be elucidated, as has been carried out in the case of predissociation of NaI.I4 A range of experiments involving systematicvariation of XI would be of considerable assistance in carrying out a direct characterization of the topology of the PES(s) involved in which use would be made of an inversion method such as that developed by LeRoy et for determining potential energy functions from boundcontinuum spectra. In this vein, a procedure has recently been adopted to derive the potential energy curves for the bound electronically excited B 3 h Ustate of molecular 123233,83*84 and the A 3 n l state of I C P from real-time measurements, in which the appropriate potential functions were obtained by Fourier transformation of the FTS data followed by application of the wellknown RKR integrals. In a similar manner, for a known functional form of the reactive PES(s), measurements over a range of prohe laser wavelengths X2 at a fixed XI would provide an (81) Patel, D.; Pritt Jr., A. T.; Coombe, R. D. J . Chem. Phys. 1982, 76, 6449. (82) LeRoy, R. J.; Keogh, W. J.; Child, M. S.J . Chem. Phys. 1988,89, 4564. (83) Gruebele, M.; Roberts, G.; Dantus, M.; Bowman, R. M.; &wail, A. H. Chem. Phys. Lett. 1990, 166,459. (84) Bernstein, R. B.; Zewail, A. H. Chem. Phys. Lett. 1990, 170, 321.
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invaluable aid to determining the shapes of the high-lying molecular states V2(r)populated by the probe laser and the nature of interactions between them. Clearly, the assumptions regarding the exponentiality of the PESs V2(r)and the nature of the long-range regions of Vl(r)and Vl,(r) need to be strengthened, and we hope that future experiments will provide a better description of the PESs.
Acknowledgment. This work was supported by the Air Force Office of Scientific Research under grant number AFOSR 900014. We are grateful to Drs. P. P. Sorokin and R. E. Walkup for sending us a preprint of ref 70 and for their thoughtful and careful reading of this paper. G.R. thanks SERC for the award of a NATO Postdoctoral Fellowship. Note Added in Proof. A recent theoretical treatment of time-resolved absorption spectra (Walkup, R. E.; Misewich, J. A.; Glownia, J. H.; Sorokin, P. P. J. Chem. Phys. 1991,94, 3389) has been applied to the dissociation of Bi2 (Walkup, R. E., private communication): good agreement was obtained with the results of Figures 4 and 5 by using a repulsive length parameter L, = 0.3 A and a van der Waals difference potential with a coefficient of 2 X lo* cm-’ A6. As discussed here and previously,16 the long-range region of the potential is important in governing the dissociation dynamics, and the value L,= 2 A of Sorokin and c o - w ~ r k e r sused ~ ~ in this work is only an indication of the less repulsive nature of the reactive potentials Vxr)at large internuclear separations. When further experiments (involving tuning of XI and A,) are completed and ab initio calculations (Morokuma, K., private communication) become available, it should be possible to deduce the key features of the PESs that contribute to the interesting dynamics of Bi2 fragmentation.
Low-Frequency Raman-Active Modes In a-Methyl,o-hydroxyollgo(oxyethy1ene)s Carl Campbell,+Kyriakos Viraq*J Andrew J. Masters, John R. Craven,%Zhrng Hao,I Stephen G. Yeates,ll and Coiin Booth Manchester Polymer Centre and Department of Chemistry, University of Manchester, Manchester, MI 3 9PL, UK (Received: August 14, 1990; In Final Form: November 29, 1990) Low-frequency Raman spectra were recorded for a-methy1,w-hydroxyoligo(oxyethylene)s,CIEmOHwith m in the range 4-16, Le., 14-50 chain atoms. Longitudinal acoustical mode (LAM) frequencies were identified and compared with those determined previously for a-hydro,whydroxyoligo(oxyethylene)s and a-methy1,o-methoxyoligo(oxyethy1ene)s. On the basis of the linear crystal model of Minoni and Zerbi, the two most prominent bands in the low-frequency spectra were assigned to the LAM-1 and LAM-3 modes of the H-bonded dimer crystallized in a bilayer structure.
Introduction of low-frequency Raman spectra of crystalline oligo(oxyethy1ene)s have yielded information on the longitudinal vibrations of helical chains, particularly on the large effect of end forces on the frequency of the longitudinal mode. A recent study’ by Raman spectroscopy of a series of uniform oligo(oxyethy1ene) dimethyl ethers, CIEmCI,with oxyethylene chain lengths in the range m = 2-25, has served to reinforce conclusions that ‘ h n t addrm: European Vinyls Corp. (UK) Ltd., Research and Technology, The Heath, Runcorn, Cheahire, WA7 4QD. UK. Present address: Physical Chemistry Laboratory, University of Athens, 13A Navarinou Street, Athens 106 80, Greece. ‘Present address: Albright and Wilson Ltd., Petroleum Additives Group, Whitehaven. Cumbria CA28 9QQ, UK. Present address: Institute of Applied Chemistry, Academia Sinica, Changchun, PRC. ‘Present address: IC1 Chemicals and Polymers Ltd., Research and Technology, The Heath. Runcorn, Cheshire, WA7 4QD, UK.
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van der Waals end forces significantly increase the frequency of the single-node longitudinal acoustical mode (LAM-]) of oligo(oxyethy1ene)s. The effect is greatly enhanced by strong hydrogen bonds at the chain ends of oligo(oxyethy1ene) diols, HE,,,OH: in this case, the observed LAM-1 frequency approaches twice that anticipated for an oligo(oxyethy1ene) chain with free ends.’V2 Direct comparison of the Raman spectra of a short uniform oligo(oxyethy1ene) dimethyl ether with that of its corresponding diol is not straightforward, since the chain ends of the short oligomers are very restricted by hydrogen bonding in the end-group planes of their layer crystals’J and the longitudinal mode may (1) Campbell. C.; Viras. K.; Booth, C. J . Polym. Scl., Polym. Phys. Ed., in press. (2) Viras, K.; Teo, H. H.; Marshall. A.; Domszy, R. C.; King, T. A,; Booth, C. J. Polym. Sei., Polym. Phys. Ed. 1983, 21, 919. (3) Viras, K.; King, T. A.; Booth, C. J. Polym. Sei.,Polym. Phys. Ed. 1985, 23, 41 1.
0 1991 American Chemical Society
