Ultrafast Spectroscopy

ULTRAFAST SPECTROSCOPY

MARCOS DANTUS AND PETER GROSS, Department of Chemistry, Michigan State University, East Lansing, Michigan, U.S.A.

PhysicalIntroduction Framework and .431 4.1 Unimolecular

I. Photodissociation along a

ApplicationsExamplesIllustrative Example , 432 Single Reaction Coordinate. . 445

1.1 435 4.2 Unimolecular

1.2 436 Photodissociation along

2. Experimental Techniques Multiple Reaction

and Methods , 439 CoordinatesOther Unimolecular 445

2.1 UltrafastDetection Laserin UltrafastSystems. 439 4.3

2.2 ReactionsBimolecularOther Applications Reactions of 446 Spectroscopy: The Pump- 4.4 448

UltrafastProbe Method Spectroscopy of 440 5. 3. WorksBiologicalGlossaryFurtherUltrafastLiquidsSolids Cited ReadingSpectroscopy. 449 MoleculesUltrafast Rotational 440 5.1 450 5.2 453 441 UltrafastSpectroscopy Vibrational 5.3 453 3.2 454 ChemicalSpectroscopyCoherence Reactionsand Dephasing 443 3.3 444 455 4. 445 456

INTRODUCTION time-resolved kinetic information about pro- Spectroscopy in general is the study of cesses that are statistical in nature. "ultra- the interaction between light and matter. It fast" spectroscopy, on the other hand, in- is the major tool used for the determination volves temporally short (and therefore of quantum energy levels in atoms, mole- spectrally broad) light pulses, which are used cules, semiconductors, etc. For example, in to probe directly the dynamics of the system addition to their internal electronic motion, rather than the energy levels themselves. molecules possessvibrational and rotational Rapid advances in laser technology over the degrees of freedom. Such motion is quan- past decade have resulted in the ability to tized, i.e., only motion corresponding to dis- produce pulses as short as 6 fs (I fs = 10-15 crete rotational or vibrational energies is s), and pulses of width 60 fs are now pro- allowed. Spectroscopy, which excites transi- duced routinely in many laboratories around tions between these quantized states, is the the world (see ULTRASHORTPULSE PHENOM- primary tool in elucidating the energy-level ENA). spacing. These, in turn, are useful in deter- The advantage of using ultrashort pulses mining bond strengths and overall molecular is that they open the door to investigating structure. the dynamics of the system directly, i.e., the "Traditional" spectroscopy can be de- movement of individual particles such as scribed as energy or frequency resolved be- electrons or atoms. From the perspective of cause measurements associated with this classical mechanics, a short pulse whose du- type of spectroscopy involve spectrally nar- ration is on the same time scale as the mo- row light that is tuned across discrete energy tion of a particle in a confined system could levels. These measurements can be carried be used to probe the dynamics of the parti- out with pulsed light sources to provide cle directly. For typical atomic speeds of the

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431 432 Ultrafast Spectroscopy order of 10000 m/s ( = 0.1 A/fs), laser pulses The rest of the article is as follows. Sec- 10 fs in duration achieve l-A spatial resolution 1 covers the physical basis for ultrafast tion, a range that is of great scientific inter- spectroscopyand contrasts it with frequency- est in physics and chemistry. Ultrafast spec- resolved spectroscopy. In Sec. 2 the experi- troscopic techniques have been used to mental setup required for ultrafast spectros- observe rotational and vibrational dynamics copy is described along with a discussion of in molecules. Electronic motion has been ex- the pump-probe technique. Results from an plored in semiconductor systems.The key is experiment on iodine are shown in Sec. 3, that the duration of the laser pulses must be where both the vibrational and rotational dy- shorter than the time scale of the dynamics namics are obtained. In Sec. 4 studies of var- that one wants to observe. Time scales of ious different chemical reactions in the gas some physical and chemical processes are phase are presented. Additional applications displayed in Fig. 1. of ultrafast spectroscopy to condensed In summary, ultrafast laser spectroscopy phasesand biological systemsare outlined in has become a very useful tool in the study of Sec.5. the dynamics of atoms and molecules in a range of environments from gas phase to solid state. Results from these types of ultra- I. PHYSICAL FRAMEWORK AND fast studies have been loosely classified as EXAMPLES femtochemistry, when chemical reactions are involved, and femtophysics, when the inter- Ultrafast spectroscopy is based on the use action between ultrashort laser pulses and of light pulses that have very short temporal matter is being studied. duration to interrogate matter. These pulses,

r Atomic Resolution Single Molecule Motion

( Transition ~t lReaction Intermediates)

IVR & Reactianpr~~~

-;;-v' I I I. II, I I ~

10-3 10-8 10-9 10-10 10-11 10-12 10-13 10-14 10-15 Mllli Nana Pica Femto

IRadiativeDecayll RotationalMotion II Vibrational Motion I IFundamentals

, . ~ ibrational ~ OlliSiOnS in Internal Conversion & Intersystem Crossing R e axa tion Li qUi ds I ' Iphysical

I Predissociation II Harpoon II Norrish IIDissociationl I Reactions II Reactions I I Reactions II Reactions I

§ roton Abstraction, Exchange I Diels-Alder I Transfer & Elimination I ,,--- D--~-h I I Cage Recomb, I

Photosynthesis (ET) Protein Motions Vision (isom,) IBiOlO91Cal

FIG. 1. Time scales and scope of ultrafast phenomena in physical, chemical, and biological changes. On the upper side of the arrow of time, we display the fundamental elements for the dynamics of the chemical bond, defining the scales for intramolecular vibrational relaxation (IVR), transition states, and single-molecule motion in femtochemistry. The time scales for the vibrational and rotational motions are shown. Below the arrow of time, examples of studies of physical, chemical, and biological changes are given (Zewail, 1996.) Ultrafast Spectroscopy 433

being very fast compared to the underlying an = C('PnIXo) J-~ exp[ -i(En -Eo)t/li] dynamics of the system, are capable of taking "snapshots" of the atomic motion. A col- x exp( -f/a~) cos(oJt)dt, (2) lection of snapshots taken at subsequent times can be thought of as a "movie" of the where c is a constant including such factors dynamics as a function of time. Each snap- as the field amplitude of the pulse and the shot implies a degree of localization of the electronic transition dipole moment, and a is system in space that must be consistent with a constant equal to 21il/ln(2). The term Heisenberg's uncertainty principle. To illus- «({)nIXo)is called the "Franck-Condon" factor trate the advantagesof ultrafast spectroscopy and is just the overlap integral between the and explore some of its implications, a quan- initial and final states. Evaluating the inte- tum-mechanical formalism is required (for a gral in Eq. (2) gives review see QUANTUMMECHANICS). Quantum mechanically speaking, the fact an = C(lpnIXo) exp[ -(Wn -UI)2ar/4], that short pulses probe dynamics and long (3) pulses probe energy levels is indicative of the where Wn = (En -Eo)lh is defined as the uncertainty principle, that time and energy Bohr frequency. Note that in evaluating the resolution are related to each other through coefficients an all we have done is evaluate the Fourier transform. For example, a very the Fourier transfol1ll of a Gaussianfunction short pulse (on the order of 10-15 s) pos- (the importance of the Fourier transfol1ll sesses a broad energy bandwidth, which and its relevance to the distinction between spans the whole visible spectrum. In con- energy- and time-resolved spectroscopy is trast, a longer pulse (on the order of 10-9 s) made clear below). possessesa much narrower spectrum. This In the limit of an ultrashort pulse ( 7 -+ 0) relationship can be illustrated in a com- the coefficients in Eq. (3) become pletely general manner by showing the effect of the laser-pulse width (time duration) on an = C(fPnIXo). the transition probability from one state Xo (4) of a system with energyEo to other states tPo, tPl' tP2'etc. with corresponding energies Eo, Note that the newly created wave function El, Eb etc. First-order perturbation theory can then be written from Eq. (I) as can be used to describe the transition prob- 1/1= c L (rPnIXo)rPn° (5) ability from the initial state Xo to each state n=O in the upper potential induced by the laser pulse that is nearly resonant with the transi- Note also that the initial wave function can tion (i.e., the photon energy hal is roughly be expressedin terms of the excited eigen- the same as the energy difference En -Eo functions ~n' between the energy levels). The laser pulse is assumed to be a Gaussian, ~o exp{-r2/a,.2} Xo = ~ ('PnIXO)'Pn' (6) x cos(UIt),with a temporal full width at half n=O maximum (FWHM) 'T. The resulting wave function after excitation can be written as a Thus we see that a very short (delta function superposition of the eigenstates of the sys- in time) pulse creates a wave packet 1/1on the tem: upper potential that possesses exactly the same shape as the initial wave function (to 1/1= ~ anfPn' (I) within an overall constant). Of course, this n=O wave packet is not an eigenstate of the system but rather a coherent superposition of where an are the coefficients (or amplitudes) excited eigenstates. Over time, these states of the eigenstates 'Pw These coefficients, dephase with respect to one another, since whose moduli squared represent the popula- the time dependence of the wave function is tions or occupation probabilities of the indi- given by vidual eigenstatesafter the pulse is applied, can be determined from the following first- IIJ(t) = L an exp( -iEnt/h)

Such a wave function is called nonstationary since quantum-mechanical expectation values con-esponding to physical observables such as position or momentum are not constant in time. This can be seen from the ex- pression for the time dependenceof an expectation value of some observable, say position R (i.e., the internuclear distance between the atoms in a diatomic molecule):

m-l (IfJ(t)IRllfJ(t» = ~ (fPnIRlfPn) + 2 ~ ~ a;.an n=O m=l n=O X cos[(Em -En)t/ft](fPmIRlfPn). (8)

The first term on the right-hand side of Eq. (8) gives the averageequilibrium distance of the motion and does not vary in time, but the second term does; this explicit dependence on time is responsible for the "wave- FIG. 2. Calculated expectation values for the aver- packet dynamics," in this case,the motion of age internuclear distance of a diatomic molecule the nuclei themselves. For example, in the when excited with pulses of increasingly longer tem- case of a diatomic molecule whose nuclei poral width [calculations based on Eq. (8)]. Notice that a 42-fs pulse generates a wave packet with dy- move in a harmonic potential well, the namics that are very similar to those of a classical movement of the wave packet is governed by particle in the same harmonic potential. The data the energy-Ievelspacing AB; the packet oscil- generated for the 667-fs pulse do not show the oscillates and returns to its original form after a latory motion because the wave packet formed is time h/AB, assumedhere to be 333 fs. Figure similar to an eigenstate of the potential. 2 shows the expectation value for the internuclear distance R as a function of time using Eq. (8). The dashed line shows the tra- laser photon energy h(J),only a single eigen- jectory of a particle based on classical state is excited. This is a stationary state, mechanics. Notice that when the motion is and as such, the expectation values (momen- initiated by a short-time pulse ( 7 = 42 fs), tum' position, etc.) do not change with time, the motion is very similar to that of the clas- unlike in a nonstationary state created from sical particle; however, when 7 is long (a a short pulse (see,for instance, the 667-fsex- time equivalent to two full periods of mo- ample in Fig. 2). For intermediate pulse tion, here 667 fs), the expectation value is lengths where 'I"is small enough that close to equilibrium and one is no longer able to measure the dynamics since essen- exp(-«(J)n -(J)2ar/4} ~ 0 (10) tially only a single eigenstate (a stationary state of the system) is excited. for more than one level of energy En, a non- In the limit of a very long pulse (fre- stationary state is created since more than quency-resolvedspectroscopy), i.e., 7-+ 00,we one eigenstatewill be appreciably populated. get from Eq. (2) Invoking the relationship between time and energy via the Fourier transform, it is an = C(rPnIXo)B(l1)n -l1)), (9) easily shown that the longer the pulse, the more the wave packet in the upper state re- where 8(% -w) is a delta function, which is sembles a single stationary eigenstaterather always zero except when w equals Wn.Thus, than a coherent superposition. The shorter unless the laser frequency exactly matches the pulse, the wider the frequency width, the difference in energy between states n and and the more the newly created wave packet the ground state, there is no excitation. in the upper state resemblesthe initial state When the energy difference does match the of the system. Since the initial state of the Ultrafast Spectroscopy 435 lower potential is not an eigenstate of the electrons; therefore, one can map the elec- upper potential, but rather a superposition of tronic potential energy as a function of inter- eigenstates that resemble it, it exhibits dy- nuclear distance. On these potential cUIVes, namics. the corresponding vibrational levels are drawn. The electronic states are shown as harmonic oscillators V1(R), V2(R),and V3(R), 1.1 Illustrative Example which resemble the potential energy that the nuclei experience in a molecule, neglecting A simple calculation based on the equa- anharmonic terms that are important at high tions presented in the last section nicely il- vibrational energies (see MOLECULARSPEC- lustrates this concept of time and energy res- TROSCOPY).Only the initial state Xo is as- olution in spectroscopy. For illustration, sumed to be populated before the laser pulse consider the excitation of a diatomic mole- excites the system; its wave function is also cule from its ground electronic and vibra- shown in Fig. 3. The first excited electronic tional state to its first excited electronic state (with a different electronic configura- state. The potential-energy curves associated tion) is found at a higher energy and slightly with this system are depicted in Fig. 3. These larger equilibrium bond length. These differ- curves are based on the Born-Oppenheimer ences are typical for molecules because a approximation, which recognizes that nuclei change in electronic configuration affects the in a molecule move much more slowly than interatomic interactions. Photon absorption from the ground electronic state is assumedto proceed through a vertical transition to the upper state, invoking the Franck-Condon approximation. The implication here is that changesin electronic configuration take place much faster than nuclear motion, and therefore the nuclei are essentially "frozen" in place during the electronic transition. When the light source is monochromatic, only one vibrational state in the upper electronic potential can be excited. For ultrashort pulses, having a broad spectral bandwidth, more than one state may be populated at the same time as described by Eqs. (1) and (2). For the calculations presented here the energy displacement (i.e., the energy difference between the potential-well minima) is taken to be 15770 cm-l (about 2 eV). The reduced mass and the q~anturn energy-level spacing of both potentials (w = 1.9 X 1013Hz, equivalent to a 333-fs oscillation period) roughly correspond to those of the iodine molecule (12). Figure 4 (left-hand side) shows (from top FIG. 3. Schematic of the potential-energy curves of a diatomic molecule with three distinct electronic states to bottom) the wave packet llIJ(x)12created on V,(R), V2(R), and V3(R). The electronic states pro- V2(R) after application of 42-, 167-, and 667- vide a harmonic potential that keeps the nuclei bound fs FWHM Gaussian pulses (~, i, and 2 times and gives rise to vibrational energy levels. Ultrafast the molecular oscillation period of 12,respec- spectroscopic information from this system can be tively). The shortest of these pulses createsa obtained by excitation at A, from the ground electronic state into the intermediate potential V2(R). This nearly perfect Gaussian wave packet on excitation generates a wave packet that oscillates in V2(R) as shown in the top left frame of Fig. time. Probing of the wave-packet motion is accom- 4; this wave packet is virtually identical to plished by a second pulse of wavelength A2 that pop- IXoP,the ground state of V1(R), as expected ulates the third electronic state. Signal from the third electronic state is measured as the intensity of the from Eqs. (4)-(6). If the pulse is lengthened, laser-induced fluorescence (LIF) from V3(R). the wave packet starts to look less like IXoP~ 436 Ultrafast Spectroscopy

three different laser-pulse widths are shown. The key point is that the shortest pulse (42 fs) provides the least spectral resolution, 353 cm-l FWHM. The longest pulse (667 fs) provides much sharper spectral lines, 22 cm- 1 FWHM, and each line corresponds to a particular Xo -+ 'Pn transition. Long-pulse excitation corresponds to a frequency-resolved spectrum; no dynamics can be observed because only single eigenstates are excited. In short-pulse excitation, where spectral resolution is very poor, the wave packet created on ViR) does exhibit dynamics as the laser pulse excites a superposition of eigenstates. -4 -2 0 2 , It should be emphasized again that the Interatomic Distance (A) spectrally broad pump pulse is responsible FIG. 4. (a) Calculation of wave packets pumped for the creation of the wave packet. A long from the ground to excited electronic state by 42-, pulse (in time) would excite onlya single ei- 167-, and 667-fs pulses [using Eqs. (1) and (3)]. The genstate on ViR), and therefore no dynam- packet formed by the 42-fs pulse is very similar to ics would be observedusing the probe pulse. the ground-state wave function Ixol2 shown with a Thus the normal way of thinking in tradi- dashed line. (b) Corresponding spectra for these same pulse lengths [using Eq. (11 )]. tional spectroscopy-that the more spectrally narrow the light, the better-is no longer true if one thinks about spectroscopyin the and more like a single eigenstate on V2(R) time domain. [see Eq. (9)]. The laser-pulse frequency for this example was chosen to match the en- 1.2 Applications ergy difference between the ground state of V1(R)and the Sth eigenstate 'Psof ViR). The The field of time-resolved spectroscopy wave function shown in Fig. 4 (bottom left) has grown perhaps as fast as the technology for the 667-fs pulse was produced by a suffi- itself, and some of the most important appli- ciently long pulse that the condition in Eq. cations have been realized in femtosecond (10) was satisfied for only one energy, Es; transition-state spectroscopy (FfS), a tech- therefore, the excited wave packet in this nique developedby Zewail and co-workers at case is essentially identical to the eigenstate Caltech and applied to numerous molecular systems (Zewail, 1994, 1996). The first appli- l'PsP.Unlike the wave functionsJ shown for the 42- and 167-fs pulses, which are linear cations of FfS were to gas-phasesystems of superpositions of the ViR) eigenstates,the small molecules, but these techniques have wave function produced by the 667-fs pulse now been applied to large molecules in the is essentially a stationary state and will not condensedphase. change with time. The basic scenario of these experiments, Scanning the frequency of the excitation which directly observe molecular dynamics, laser, one obtains an absorption spectrum of is as follows. A short (femtosecond) pump the system. The spectra depend on the tem- pulse excites the molecule from its (bound) poral duration of the laser pulses becauseof ground electronic state to an excited state. the time-energy uncertainty. This depen- As noted in the previous discussion of the la- dence is included in the an terms [Eq. (3)]. ser pulse inducing a transition between two The spectra can be calculated simply by the displaced harmonic oscillators, a wave sum packet is created "upstairs" by the pump pulse. The wave packet, being nonstationary, moves on the upper electronic state potential A({J),T) = 2, lan12. (II) n=O as a localized probability density. The motion of the wave packet (1I11(x,t)12) In Fig. 4 {right-hand side) spectra for the as a function of time in the upper potential Ultrafast Spectroscopy 437

'1 is illustrated in Fig. 5 where IfJ(x,t)is given general, the second pulse, of wavelength A2, by Eqs. (1) and (2). For this illustration, the induces a transition from the intermediate initial wave packets were generatedwith 42-, state V2(R), where the wave packet evolves, 167-, and 667-fs pulses, as shown in Fig. 4. to a higher electronic state that is easily Notice that for the shortest pulse one obtains detected by fluorescence or ionization (see the best localization of the wave packet, and Fig. 3). When the initial wave packet is its motion is most similar with that of a clas- highly localized, as representedhere with the sical particle (see Fig. 2). The intermediate 42-fs excitation, there are times when the (167-fs) pulse shows a more diffuse wave wave packet is inside the probing region, packet. However, long-pulse excitation leads marked by the dashed lines in Fig. 5, and to a wave packet that is essentially an eigen- other times when the wave packet is outside state of the upper potential and is therefore this region. stationary in time. Figure 5 demonstrates The signal one expectsfrom these types of how ultrafast excitation results in the crea- experiments can be simulated using second- tion of a time-evolving wave packet. The pe- order perturbation theory (see QUANTUMME- riodicity of the motion is determined by the CHANICS),which takes into account transi- energy difference among the states compos- tions V1(R) --ViR) and ViR) --V3(R) as a ing the wave packet [see Eq. (8)]. Monitoring function of the delay between the pump and the subsequent motion of the system re- probe pulses. Results based on the wave- quires an additional ultrashort pulse that is packet motion are shown in Fig. 6. The fired at different delay times as described be- shorter the pump and probe pulses, the bet- low. ter the wave-packetlocalization and the bet- To maintain the temporal and spatial res- ter the modulation depth in the oscillatory olution of the experiment, the monitoring or dynamics. For long-pulse excitation, no dy- probe pulse must be of duration equal to or namics is observed in the signal. Notice that shorter than that of the excitation pulse. In the results of the pump-probe experiment

'-'~ § .:d .a o ~

.§ E-t

FIG. 5. Calculated wave-packet motion for excitation of three different pulse widths [using Eq. (7)]. Darker shades indicate higher probability densities. Notice that the 42-fs wave packet is very localized, while the 667- fs one is spread across the well and shows no signs of dynamics. 438 Ultrafast Spectroscopy

FIG. 6. Calculated pump-probe signal for three different pulse durations. In all cases the pump and probe lasers are assumed to have the same pulse width and intensity. Notice the changes in the rise times and the changes in modulation depth as the pulses increase in duration.

are analogous to a direct measurement of with ultrafast pump-probe spectroscopy. the interatomic spacing given by (R) in Eq. However, this process is on a different time (8) and in Fig. 2. scale because rotational energy spacings Vibrational motion in the excited tran- transform into much longer times, on the or- sients has been observed in many systems. der of 100 ps. The basic premise of rota- The FTS pump-probe technique was used to tional spectroscopy is that the pump pulse observe vibrational motion in the excited B excites a coherent superposition of rotational state of iodine (Dantus et al., 1990) (see be- states, a wave packet, which initially de- low), in predissociative systems such as so- phases (since molecules possessingdifferent dium iodide (Nal) (Rose et al., 1988), and in angular momenta rotate away from their ini- purely dissociative systemssuch as cyanogen tial alignment at different rates) and later re- iodide (ICN), where the excited state ac- phases at time intervals that depend on the cessedby the pump pulse is purely repulsive rotational constants of the molecule. The ro- (Dantus et al., 1987). In all of these (one-di- tational motion is observed experimentally mensional) cases, the nuclear motion was by using linearly polarized light pulses that mapped out as a function of time using the excite only those molecules having transition aforementioned FTS technique. dipole moments aligned with the electric Beyond these simple one-dimensional sys- field of the pulse. tems, the FTS technique has been applied to The FfS technique has also found exten- more complex systems that allow for exami- sive application in condensed-phasespectros- nation of the vibrational motion of a transi- copy, including elucidation of solvent dy- tion state. With time-resolved spectroscopyit namics and solute-solvent interactions (here is now possible to learn, at least in principle, the solute is the entity that is photoexcited about the dynamics of the transition-state and probed, and the solvent provides the complex, i.e., how these atoms are moving surrounding "bath" molecules). Observation relative to one another as they are trans- of coherent dynamics in high-pressure gas- formed from reactants to products. Such in- phase systems or in liquids is inherently formation may bring us closer to under- more difficult than in gases at moderate standing the very nature of chemical pressures becausedephasing effects induced reactions themselves.For example, the pho- by collisions will "wash out" the coherent todissociation of mercuric iodide (HgI2) into motion. Still, in general, for sufficiently short I and HgI gave insight into the nature of the times after the initial preparation of the [1-Hg-I]** transition-state complex by again wave packet with the pump pulse, motion of looking at the vibrational dynamics (Dantus the vibrational and rotational transients can et al., 1989). be observedbefore complete relaxation takes Molecular rotation has also been observed place.

- - ~ Ultrafast Spectroscopy 439

~ 2. EXPERIMENTAL TECHNIQUES short pulses presents great technical chal- AND METHODS lenges (see ULTRASHORTPULSE PHENOMENA). Femtosecond pulse generation is achieved The time scale for measurements using in an oscillator cavity that has a very broad ultrafast spectroscopy is determined by the gain bandwidth and contains a nonlinear op- spacing between the energy levels of the sys- tical element whose properties are highly tem under study, as discussed in the Intro- dependent on laser peak intensity. This ar- duction. Typically, ultrafast spectroscopy rangement favors the propagation of short measurements temporally resolve dynamics pulses (high peak intensity) compared to shorter than 10-12 s (1 ps). Given that most continuous-output operation. There are measurement equipment, such as oscillo- many successful oscillator designs of this scopes, have response times in the nanosec- type; while some use laser dyes, others may ond time scale, special experimental arrange- be all solid state, even imbedded in optical ments are required in order to achieve fibers. femtosecond time resolution. In this section Femtosecond oscillators are capable of di- we describe how ultrafast laser pulses are rectly producing very short pulses (down to generated and how they are used to measure 8 fs), but energies are typically less than a molecular dynamics. nanojoule per pulse. Ultrafast spectroscopic measurements require high-energy pulses, 2.1 Ultrafast Laser Systems and so the output of the oscillator needs to be amplified. The most successful technique There have been great advances recently for this uses grating pairs to lengthen. the in the generation of ultrafast laser pulses. pulses temporally (Squier and Mourou, This progress has been fueled to a large ex- 1992). These "stretched" pulses are then am- tent by the communication industry (primar- plified to millijoule levels and compressed ily work by Shank, Ippen, and their col- back to the femtosecond time scale. By this leaguesat Bell Laboratories) with the goal of method, millijoule pulses as short as 20 fs decreasing laser-pulse duration so that more have been produced (Backus et al., 1995). information can be transmitted within a Tunability of femtosecond laser systems given time interval. The evolution of these la- may be achieved by continuum generation, ser systems has been reviewed (Squier and whereby a very intense femtosecond pulse is Mourou, 1992; Fleming, 1986; ULTRASHORT focused on a transparent medium such as a PULSES).Here we concentrate on the princi- quartz window and emerges as a white light ples of these systems and the requirements pulse containing all wavelengths within the of ultrafast spectroscopy. window of transmittance of quartz. The laser One of the consequencesor manifesta- pulse induces a very rapid change in the re- tions of the uncertainty principle is a limit fractive index of the medium, causing it to imposed on the temporal pulse width of la- act as an ultrafast shutter. Because of the ser pulses such that their duration may not transform limit relationship between the be any shorter than the inverse of their fre- time and energy bandwidths, this results in a quency bandwidth. For pulses with a Gaus- large increase in the pulse bandwidth; con- sian intensity profile in time and frequency, version efficiency is very high, approaching this relationship can be simplified to 100%. Spectral selection from the continuum is achieved by filtering. If desired, more in- .1VT ~ lln(l)/'IT, (12) tense pulses can be generated by optical parametric amplification. In this process, a where Llv and 'I" are the FWHM of the laser- relatively weak (seed) pulse is mixed with a pulse frequency and time width, respectively. high-intensity pulse in a nonlinear optical The shortest pulse measured to date had a medium, resulting in a pulse having a higher pulse duration of 5 fs (Baltuska et at., 1997), intensity than the seed. The fundamental of and the record since 1987 was 6 fs (Fork et the laser can be used for the amplification at., 1987), corresponding to frequency band- pulse, and judicious selection of the fre- widths of 8.8 X 1013 Hz (2940 cm-l) and quency of the seed pulse will allow quite in- 7.3 x 1013 Hz (2450 cm-l), respectively, ac- tense pulses to be produced at a given wave- cording to Eq. (12). The generation of such length. 440 Ultrafast Spectroscopy

2.2 Detection in Ultrafast Spectroscopy; the Pump-Probe Method Ts-Iaser amplifier

In general, ultrafast spectroscopy has been associatedwith time scalesshorter than picoseconds. This makes it useful for the Ax ,It study of molecular motion (see Fig. l)-for example, rotation (picosecond) and vibration A (a) (femtosecond).The second major application ~. is to electronic signals extending to the tera- (b) Experiment hertz regime and beyond. These frequencies are considered ultrafast because one is no First case: Second case: longer able to use conventional equipment for their measurement. The state of the art path (a) = path (b) path (a) + 2t.x = path (b) in photon detectors is still, as of 1997, lag- 8t=O ~t = 2Ax/c ging by almost three orders of magnitude behind the generation of short pulses. This fact For Ax = 1 ~m; At = 6.67 fs has forced experimental groups to find techniques that depend on two or more ultra- FIG. 7. Pump-probe experimental setup showing a short pulses to initiate and monitor a pro- typical Mach-Zehnder interferometric arrangement used to control the timing between pump (path a) cess; the time resolution in the resulting and probe (path b) laser pulses. signal is then independent of the detection method. The most common of these arrangements is known as the pump-probe tech- mined by the position of a computer-con- nique. This technique, in fact, has been crit- trolled optical-delay line located in one of ical in the advancement of time-resolved the arms of the interferometer. The principle spectroscopy since 1949 when millisecond of the time delay is that the speedof light is resolution was first achieved (Porter, 1950). constant and that spatial displacementscor- In the pump-probe method, the time res- respond directly to temporal delays. For a olution is determined by the convoluted tem- typical step of 1 ILm, a pulse is delayed by poral width of the pump and probe laser 3.3 fs. Becausethe light traversesthe optical pulses, the degree of experimental control delay line twice, the corresponding delay is over the time delay between them, and their 6.67 fs (see Fig. 7). relative temporal jitter. Present systems for Notice that the time resolution of pump- ultrafast spectroscopyhave been able to pro- probe experiments depends on the time de- duce pulses as short as 5-6 fs, with jitter and lay between the pump and probe pulses and time-delay control better than a single fem- not on the temporal response time of a de- tosecond (Baltuska et at., 1997; Fork et at., tector. In fact, these experiments are inde- 1987). This outstanding level of control is pendent of the response time of photon de- achieved by the use of arrangements such as tectors or signal-processingelectronics. This the ~ach-Zehnder interferometer shown in has allowed pump-probe experiments to be Fig. 7. An intense femtosecond laser pulse carried out in conjunction with a number of emerging from the amplifier is split by a par- other spectroscopic techniques, e.g., absorp- tially reflective optic into two pulses that fol- tion, emission, laser-induced fluorescence, low different paths in the interferometer. ionization, and Raman spectroscopy. While in the interferometer, techniques based on nonlinear optics are used to change the wavelength of the laser pulses (if required by the particular experiment) while 3. ULTRAFAST SPECTROSCOPY maintaining their pulse duration and timing OF MOLECULES of each relative to the sibling pulse. The pulses are later recombined using a second Ultrafast molecular spectroscopy is the partially reflective optic before being steered time-domain analog of frequency-resolved to the sample region. The time delay be- spectroscopy (see MOLECULAR SPECTROS- tween the pump and probe lasers is deter- COPY).Electronic, vibrational, and rotational Ultrafast Spectroscopy 441

,.,. transitions are interrogated, but in ultrafast spectroscopy,coherence among the quantum states leads to time-dependent dynamics that can be directly associated with the classical mechanical motion. Among the advantages of time-domain spectroscopyis the complete separation of vibrational and rotational in- fonnation, which may be obscured in frequency-resolvedspectroscopy of molecules at room temperature. This effect is illustrated for the diatomic iodine molecule, where it is shown that one can measure rotational spacings of 0.027 cm-l with laser bandwidths four orders of magnitude larger.

3.1 Ultrafast Rotational Spectroscopy The electronic excitation of gas-phaseio- dine molecules from the ground state to the B state occurs in the 500-630-nm wavelength region. Rovibrational spectroscopic lines with a typical density of 100 lines per inverse centimeter can be resolved by excitation with narrow-bandwidth light. Even though the molecule is a simple diatomic, the interpre- tation and assignment of these spectral lines FIG. 8. Energy-Ievel diagram for ultrafast spectros- is not straightforward because of the hun- copy of molecular iodine. The first femtosecond laser dreds of rotational levels associated with pulse (A1) excites the iodine molecules to the each vibrational level. When the molecule is B 3IIo+u state, with accompanying vibrational and rotational excitation. The probing is carried out by a excited with an ultrafast laser pulse, the second femtosecond laser pulse (A2) that takes the bandwidth is orders of magnitude broader wave packet to the upper fluorescent state. The sig- than the spacing between spectroscopic nal detected (~eJ is fluorescence from the upper lines, which are therefore not observed (see electronic state. Absorption or ionization at A2 can Fig. 4 for example). However, ultrafast pulse also be used. (Dantus et al., 1990.) excitation results in a coherent superposition of rotational and vibrational quantum states. Probing of this coherencein the temporal re- ps. For these experiments, a linearly polar- gime can be used to obtain the energy-do- ized laser pulse excites only molecules that main information with the same accuracy as have their transition dipole moment p, paral- the frequency-resolvedmethods. lel or nearly parallel to the polarization In Fig. 8, the relevant electronic states of plane of the electric field of the laser pulse, iodine are presented; the arrow corresponds ~, becausethe transition amplitude is deter- to excitation of the ground-state iodine mol- mined by p,.~. Initial excitation therefore se- ecule to the excited B state. The vibrational lects an ensemble of aligned molecules. A spacing in the B state of iodine at 620 nm is second laser pulse, the probe, is then used to 110 cm -I; the spacing between rotational interrogate only previously excited mole- lines is =0.027 cm -I. To observe ultrafast cules; becausethe probe pulse is also polar- rotational spectroscopy, the laser pulses ized, it is sensitive to the initial alignment. must be shorter than the inverse of the en- As the rotation of the ensemble evolves in ergy spacing between rotational lines, (2B)-I time, the coherence decays because mole- where B is the molecule's rotational con- cules having different degrees of rotational stant, so that a coherencebetween rotational excitation will rotate at different rates. states may be achieved (Felker, 1992; Felker Becauseall rotational levels are related to and Zewail, 1987). For diatomic iodine in the same rotational constant by a factor of the B state, this time corresponds to =270 an integer quantum number J (the angular 442 Ultrafast Spectroscopy

three molecules are depicted, with angular momenta I = 1, 2, and 3. The moleculesare assumedto be aligned at time t = 0 and free to rotate for all later times. After a time (2B) -1 all molecules have executed an integer number of rotations that equals I, thereby regaining the original molecular alignment. In an experiment, the initial alignment is achieved by the absorption of the linearly polarized pump laser. The probe laser is also linearly polarized and achievesa larger signal when it encounters molecular alignment (provided its polarization matches the orientation of the transition dipole). No- FIG. 9. Molecular rotation for an ensemble of three idealized rotors with angular momenta J = l' 2, and tice that at times (4B)-1 and (2B)-I, the di- 3, showing the initial dephasing and the half and full pole moments are aligned and the signal recurrence of the alignment at later times. It should achievesa maxima. The observation of rota- be noted that a quantum-mechanical picture of rotational motion in real time is equivalently tions predicts that the half recurrence at (48)-1 is 180° out of phase (negative signal). The shaded re- manifested in rotational spectroscopywhere gion of the circles denotes the amount of rotation the spacing between rotational lines in the that the molecules have executed for each time step. spectrum is 2B. The atoms are shown as black or white for clarity. In Fig. 10, experimental results obtained (Dantus et al., 1990.) for iodine using 60-fs pulses are shown and compared to theoretical simulations (Dantus et at., 1990). The results obtained when the momentum), the original alignmentrephases pump and probe pulses are polarized parallel after a time (2B) -1 determined by the rota- to each other, III' are compared to those of tional energy constant B. Figure 9 illustrates perpendicular pump-probe polarization, I J.. the principle of ultrafast rotational spectros- It can be seen that the rotational signatures copy of a diatomic. For this illustration only are out of phase for these two cases.At early

FIG. 10. Ultrafast study of molecular iodine with polarized lasers. (a) Transients showing the initial dephasing due to molecular rotation (left) and the appearance of full recurrences at a later time (right). Parallel (~I) and perpendicular (I-L) probe orientations are shown and are 180° out of phase, as expected. The rapid oscillations are due to vibrational excitation; six levels are reached (the solid line through these on the left is a guide to the eye). Half recurrences were observed experimentally but are not shown here. Note that the time scale is discontinuous. (b) Calculated results for rotational dephasing (left) and rephasing (right) assuming excitation of vibrational levels 7 to 12 and taking into account vibrational and rotational coupling and centrifugal distortion. (Dantus et al., 1990.) Ultrafast Spectroscopy 443

~ times, there is a clear dephasing of the original alignment. At long times, there is a series of alignments corresponding to (2Bv)-I, where Bv is the corresponding rotational constant of the v vibrational level. Analysis of these data accounting for centrifugal distortion reveals the presence of vibrational levels v = 7-12. Ultrafast rotational coherence has been used by various groups to study the structure of large molecules (more than 25 atoms) (Felker, 1992). The principle behind these measurementsis the same as described here except for the contribution, in polyatomic molecules, of the other two rotational constants A and c. Because of the high degree of accuracy obtained and the complete iso- lation of rotational features, these experiments have been particularly useful in the determination of structures of weakly bound complexes such as those formed between amino acids that are hydrogen bonded with water molecules. Time Delay (fs)

FIG. 11. Ultrafast transients of 12obtained at different 3.2 Ultrafast Vibrational Spectroscopy pump laser wavelengths (A1). The time scale for the three traces is the same (200 fs/division). The pe- When femtosecond pulses excite several riods are measured peak to peak between the sec- vibrational levels, one is able to observe the ond and third oscillations in order to avoid convolu- molecular vibration of the wave packet. In tion effects. Complete analysis of these transients will Fig. 11, data are shown for excitation at dif - give better values. (Bowman et al., 1989.) ferent wavelengths (Bowman et al., 1989). Notice that excitation with shorter wavelengths forms products having longer vibrational periods. This is due to the anharmon- ponent co1Tespondsto the average time of icity of the bound state. As the vibrational vibrations, while the long-time-scale modu- energy spacing decreases, the oscillation lation co1Tespondsto the anharmonicity of time increases. This is a characteristic of the electronic state. In this case, one is able time-resolved spectroscopy and means that to determine that two vibrational states pri- the resolution of the technique improves as marily contributed to these data and that the the resolution of conventional (frequency-re- energy spacing between them co1Tespondto solved) spectroscopy deteriorates (and vice the vibrational energy spacing of the mole- versa). cule. Data such as those presented in Fig. 11 Comparing the Fourier-transformed data may be analyzed to obtain the shape of the from ultrafast spectroscopywith that of high- electronic state. To invert the time-resolved resolution spectroscopy,one can observethe data into the energy/frequencydomain, one great simplification becauseof the separation can simply take the Fourier transform of the of rotational and vibrational components.Ro- data. In Fig. 12, experimental and theoretical tational coherence occurs on a much longer plots are shown of data obtained for iodine time scale and can be discriminated against molecules, having the pump and probe laser by setting the polarization vectors of pump polarizations at the magic angle (54.7°) in and probe lasers at the magic angle. order to cancel rotational contributions to In general, for large and heavy molecules the signal. Notice that the data show rapid where spectroscopic transitions overlap, ul- oscillations modulated by a much slower os- trafast spectroscopy is clearly advantageous, cillatory envelope. The high-frequency com- allowing a complete separation between vi-

.~ 444 Ultrafast Spectroscopy

(a) 3.3 THz

-..I j 5pa ~I . 33 THz (b) Theorelk:al -Two Vibralk>naJ Motions ~ ~ 300 Is FIG. 12. (a) Ultrafast transients showing real-time vibrations of molecular iodine (left). The vertical scale represents the LlF amplitude, which is a probe of the internuclear distance. The corresponding Fourier transform is shown on the right. (b) Calculated results for excitation of a wave packet comprising the two principal vibrational frequencies and the corre- ~yf-J sponding Fourier transform. (Dantus et Time Delay (rs) Frequency(THz) al., 1990.)

brational and rotational information because order to understand the behavior of mole- of their differences in time scales. cules in solution (Zewail et al., 1992; Lienau et al., 1993; Lienau and Zewail, 1994, 1996; Matemy et al., 1996; Liu et al., 1996). 3.3 Coherence and Dephasing As an illustration, Fig. 13 shows a study of the vibrational coherenceof 12in the pres- The ultrafast data presented in the previ- ence of argon gas at various pressures. At ous section retain coherent excitation for a pressures below 10 bar, there is no colli- long time. This condition is easy to achieve sional effect on the vibrational coherencebe- in the gas phase at low pressures. When cause the averagetime between collisions is these types of experiments are carried out in much longer than the time range probed in high pressures approaching the density of this experiment. However, an increase in the liquid phase, the coherenceis lost by col- pressure to 100 bar causes a loss of vibra- lisions. Experiments have been carried out to tional coherence as well as electronic explore this transition from gas to liquid in quenching. Studies at higher pressures (not

620/390 (340) 620/390 (340) 10 bar Ar 100 bar Ar

""""- FIG. 13. Femtosecond transients of 12dissociation obtained as a function of increasing argon gas pressure. At 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 high pressures the decay of the wave packet is evident. (Zewail et Time Delay (ps) Time Delay (ps) Time Delay (ps) al., 1992.)

~ Ultrafast Spectroscopy 445

~ shown) have reproduced the dynamics ob- as the transition states of the reaction. ultra- served in the liquid phase, where vibrational fast spectroscopic data of this reaction are coherence survives for a few picoseconds shown in Fig. 14. Clocking the emergenceof (Zewail et al., 1992; Lienau and Zewail, 1994, free CN radicals yielded a bond-breaking 1996; Matemy et al., 1996; Liu et al., 1996). time of 205 fs (Rosker et al., 1988).This time may be directly related to the repulsion length scale (L) between the fragments if a potential of the form V(R) = E exp[ -(R - 4. CHEMICAL REACTIONS RJ/L] is assumed. One of the most important applications of Bond breakage is not always a direct pro- ultrafast spectroscopy has been to the study cess; in some cases, there are crossings be- of short-lived species such as transition tween two or more electronic states, causing states in chemical reactions. This type of ex- interference in the dissociation. The use of periment has allowed experimentalists to ultrafast spectroscopic techniques has al- measure for the first time how long it takes lowed researchers to observe these interfer- to break or form a chemical bond. Ultrafast ences in real time during the reaction. spectroscopy of chemical reactions, or fem- Photodissociation of alkali-metal halides tochemistry, has allowed the study of many leads to this type of crossing between the types of chemical reactions in real time. re- ionic and covalent coordinates (see Fig. 15) vealing details about the mechanisms in- (Rose et al., 1988). The study of this process volved (Manz and Woste, 1995). There have is as follows. A diatomic alkali-metal halide been numerous studies from various re- (for example, NaI) is excited by a femtosec- search groups around the world, but the dis- ond pump laser to the covalent state, form- cussion here is limited to a few model cases ing the activated complex [NaI]**. Because without attempting a thorough review (see of the crossing with the ionic state, the acti- Further Reading). vated complex resides in the well; coherent excitation of the complex results in vibrations detectable by ultrafast pump-probe 4.1 Unimolecular Photodissociation along spectroscopy (see Fig. 15). The curve cross- a Single Reaction Coordinate ing allows a percentageof the vibrating molecules to escapefrom the well, producing Na One of the simplest chemical reactions is + I. When the complex inside the well is unimolecular photodissociation. The fre- probed, an exponentially decaying amplitude quency-resolved spectrum associated with of coherent vibrations are observed. How- excitation to a repulsive electronic state lead- ever, when one monitors the free sodium at- ing to photodissociation is usually a feature- oms resulting from the reaction, the signal less continuum that gives very little infor- increases in steps, reaching a plateau when mation about the dynamics involved. all of the complex has escaped the bound Ultrafast spectroscopyof the same system al- well. lows one to observe the progress of bond breakage, giving the researchers additional information about the electronic state such 4.2 Unimolecular Photodissociation along as the potential energy as a function of inter- Multiple Reaction Coordinates atomic distance. In addition, the length of When more than one reaction coordinate time required to break a chemical bond can is available, the potential-energy surface of be determined by this method. The first such the reaction has a saddle point where pro- study was carried out on the elementary re- gress along one of the coordinates is deter- action mined. The first direct spectroscopic probing of a saddle point was achieved in the photo- ICN -+ [I CN]** -+ I + CN, (13) dissociation of Hgl2, shown in Fig. 16 (Dan- tus et al., 1989). where the [I. ..CN]** species represent ex- Time-resolved data from the reaction cited cyanogen iodide molecules (ICN*) in show vibrational motion in the nascent HgI the process of becoming products. These fragment (300-fs period) as well as rotational transient species are sometimes referred to motion (1.3-ps) caused by the torque of the

- 446 Ultrafast Spectroscopy

?: ... f " .. E -+- m " o cn

TIme delay (Is)

(a) (b)

FIG. 14. Measurement of bond dissociation in the reaction ICN + hv-+ I + CN. (a) A cartoon illustrating the experiment. A simple (slice through a) one-dimensional picture, with no angular dependence, is considered for the sake of clarity. At time t = 0 the laser pulse promotes the molecule to the upper potential energy surface. For 0 < t < T1/2' the bond stretches. By t = T1/2' the bond is essentially broken. (b) Typical experimental results. The heavy line is the measured ICN transient, and the thin line is the reference t = 0 transient. The figure at the bottom shows a magnified view near t = 0. The observed delay for transform-limited pulses is 205 :!0 30 fs. The error here is estimated from the scatter observed in several measurements. (Rosker et al., 1988.)

reaction. The large-amplitude rotational motion allows a direct assessmentof the mech- tion indicates that the activated complex has anism and dynamics of these reactions. This a bent geometry (see Fig. 16). The coherent is particularly important in more complex vibrational motion in the product (all HgI reactions where one wants to determine the fragments vibrating in concert) was unex- timing between multiple bond-breaking and pected and is the result of a prompt dissoci- bond-forming steps. Among these types of ation, which imparts an impulse perpendic- studies, the reaction of the cyclic carbonyl ular to the reaction coordinate. Coherencein compounds is a classic example of mecha- the vibrational motion of products of reac- nism determination (seeFig. 17) (Pedersenet tions initiated with ultrafast lasers has now al., 1994). been observed in more complex systems in- Concerted chemical reactions, whereby cluding proteins such as rhodopsin (Wang et more than one chemical bond is broken or at., 1994) and myoglobin (Zhu et at., 1994). formed in concert, are best studied by ultrafast spectroscopy in order to follow mechanisms and learn about the dynamics of such 4.3 Other Unimolecular Reactions processes.One such reaction has been stud- Ultrafast spectroscopic techniques have ied in which two bonds are broken and one been used to study a wide variety of chemi- is formed within a time that is much faster cal processes such as isomerization, charge than molecular vibrations ( <60 fs). The pho- transfer, and proton transfer. Time resolu- todissociation of methylene iodide, Ultrafast Spectroscopy 447

- ~-

Covalent: Na + I >- 0) w c w :"@ f c 0) a ~

Nal' ~ [Naooolr+ ~ Na+I+E..".

5 Rx=6.93A 10 15 0 20 Time O 5 10 15 20 (Is) Internuclear Separation (A) Internuclear Separation (A)

(a)

ro t= 0) Ci5

-2 -1 0 1 2 3 4 5 6 7 8

Time delay (ps)

(b)

FIG. 15. Femtosecond dynamics of the reaction Nal + hv-- Na + I. (a) Potential-energy curves (left) and the "exact" quantum calculations (right) showing the wave packet as it changes in time and space. The corresponding changes in bond character are also noted: covalent (at 160 fs), covalentlionic (at 500 fs), ionic (at 700 fs), and back to covalent (at 1.3 ps). (b) Experimental observations of wave-packet motion, made by detection of the activated complexes [Nal]** or the free Na atoms. (Zewail, 1996.)

CH212 -+ [CH212J** -+ CH2 + 12, (14) cules are vibrating in concert (see Fig. 18) (Marvet and Dantus, 1996). The mechanism undergoes such a concerted mechanism. involves the concerted breaking of the two Upon 12-eV excitation by the pump pulse, carbon-iodine boncfs as the iodine atoms iodine molecules are produced. Probing of come into close proximity and form a bond. these molecules reveals that all iodine mole- The fact that these steps occur simulta-

'I 448 Ultrafast Spectroscopy

[A]:!:

I I I I I I I I I Theoretical: Quantum wave packet motion -500 0 500 1000 1500 2000 2500 3000 3500

Time (femtoseconds) ~

°"'t., .,..1 = (t=o ps) (t=1.3ps) (!=3 ps)

(a) (b)

FIG. 16. Femtosecond dynamics of the reaction Hgl2 + hv-+ Hgi + I. (a) Potential energy surfaces, with a classical trajectory showing the coherent vibrational motion as the diatom separates from the I atom. Two snapshots of the wave-packet motion (quantum-molecular dynamics calculations) are shown for the same reaction at t = 0 and t = 600 fs. (b) Femtosecond dynamics of barrier reactions, IHgi system. Experimental observations of the vibrational (femtosecond) and rotational (picosecond) motions for the barrier (saddle-point transition state) descent, [IHgi]** -+ Hgi(vib,rot) + I, are shown. The vibrational coherence in the reaction trajectories (oscillations) is observed in both polarizations of FTS (femtosecond transition-state spectra). The rotational orientation can be seen in the decay of FTS (parallel) and buildup of FTS (perpendicular) as the Hgi rotates during bond breakage. (Zewail, 1996.)

neously leads to a synchronized, or "coher- as CO2 ...HI, which upon laser excitation ent," vibrational motion of the iodine mole- releasesthe hydrogen reactant with a known cules. kinetic energy. This technique helps establish the initial geometry, the energeticsof the encounter, and the time of initiation of the bi- 4.4 Bimolecular Reactions molecular encounter. Figure 19 shows data from this type of study for the CO2 ...HI The study of bimolecular reactions using system. The emergence of the OH product, ultrafast techniques has been limited because probed in this experiment by laser-induced of the difficulty of initiating these reactions fluorescence,is seen to occur within a pico- with a laser pulse; they depend on collisions second of the initiation of the reaction. that occur at random times. This difficulty An alternative approach for the study of has been addressed by two separate ap- bimolecular reactions in real time is to cap- proaches. One of them has been to take ad- ture the collision pairs with an ultrafast laser vantage of van der Waals complexes as pre- pulse that excites the reactants to a new cursors to the reaction (Hoffman et al., 1990; electronic state. This process is called pho- Wittig and Zewail, 19rJ6). If, for example, toassociation and has been shown to be use- one wants to study the reaction between H ful in frequency-resolved spectroscopy to and CO2,one can start with a precursor such study molecules having dissociative ground Ultrafast Spectroscopy 449 ,-

(a)

~ parent

600 {~ 0 e' t {i~

3. .. ~ FIG. 17. Femtosecond dynamics of addition/cleavage reaction of the cyclobutane- ethylene system. (a) The PES showing the =T=-:D.l .L : ... nonconcerted nature of the reaction, to- ..:: 4: 5 6 7 0 1 2 i i 3 ii i Time-of-Flight, fls gether with three snapshots of the struc- i; ii ; tures at to (initial), td (diradical), and tf (final). The parent precursor is also shown. 28 41 5556 84 Mass, amu (b) Experimental observation of the intermediate diradical by mass spectrometry. (b) (Zewail, 1996.)

states. It has also been demonstrated with seen in rotational coherence spectroscopy; ultrafast lasers (Marvet and Dantus, 1995), see Fig. 20. and the products show signs of coherence similar to those described earlier for bound molecular systems even though the initial 5. OTHER APPLICATIONS OF state is a thermal distribution of incoherent ULTRAFASTSPECTROSCOPY states. In particular , a bulb containing gase- ous mercury atoms has been shown to pro- Ultrafast spectroscopyhas also been used duce Hg2 molecules in the state labeled V1 in in the study of fast dynamics in liquids, clus- Fig. 20 under femtosecond laser excitation. ters, semiconductors, and large biochemical Probing of these newly formed molecules is systems. Observation of coherent dynamics achieved by population depletion that causes in the condensed phase is inherently more a decreasein the laser-induced fluorescence difficult since dephasing effects induced by (LIF) signal. The product molecules display surrounding atoms and molecules will "wash rotational alignment that is similar to that out" the coherent motion. Still, for short

- 450 Ultrafast Spectroscopy

times after the initial preparation of the wave packet with the pump pulse, motion of the vibrational and rotational transients can hv (i) be observedbefore complete relaxation takes place.

5.1 Liquids Over the past few years numerous theo- hv - (ii) retical and experimental studies on photoex- citation and photodissociation in the liquid phase have been performed. In the gas phase, accurate measurements of the reac- - tant and product in terms of how energy is (iii) ,~ i~J distributed among electronic, vibrational, and rotational degreesof freedom is, at least in principle, possible. However, in liquids, (a) where the solvent continuously interacts with the solute molecule in question, such detailed information is impossible. Neverthe- less, ultrafast spectroscopyhas been success- fully used to learn about dynamical and energy-transfer processes between the solute and solvent and within the solute molecules themselves (Sitzmann and Eisenthal, 1989; de Boeij et al., 1995). Wave-packetmotion has been experimentally observedin large dye molecules as well (Rosker et al., 1986; Chesnoy and Mokhtari, 1988; Walmsley and Tang, 1990; Bigot et al., 1991; Hashe et al., 1995). Also, ultrafast pump-probe techniques have been used to study the time scales of solvation and vibra- (b) tional relaxation of photoexcited dye mole- FIG. 18. Femtosecond dynamics of a concerted cules in liquids (Bingemann and Ernsting, chemical reaction, CH212 + hv ---CH2 + 12. (a) 1995). Femtosecond studies of chemical re- Schematic of the reaction mechanisms. All fragments are drawn relative to carbene-fixed coordinates. (i) actions in liquids include the photodissocia- Stepwise (sequential) dissociation; the first iodine tion of 13 -.Ii + I; here, the transient vi- atom released has time to move away from the mo- brational motion of the diatomic anion was lecular fragment before the second carbon-iodine simulated and the vibrational dephasing bond breaks. Molecular iodine is formed later by times for different solvents determined three-body collisions. (ii) Mechanism in which the first carbon-iodine bond breaks and an iodine-iodine (Banin et al., 1992). bond is formed while the second iodine is still part of Detailed femtosecondstudies of HgI2 pho- the molecule thus forming an ylide. This stage is todissociation in various solvents have also concerted; subsequent breaking of the second car- been performed; these studies should be con- bon-iodine bond completes the reaction. (iii) Con- certed bond breaking and formation process; break- trasted with the previously mentioned gas- ing of the two carbon-iodine bonds is simultaneous phase studies by Zewail and co-workers with formation of an iodine-iodine bond. This mech- (1992), Such studies are useful in learning anism would be expected to produce a molecular io- about how solvents affect the nuclear motion dine product with a large degree of vibrational coher- in the transition state and how they affect ence. (b) Experimental measurement showing the prompt appearance of oscillatory dynamics due to the coherent vibrational and rotational mo- the product 12 molecules vibrating synchronously. The tion of the fragment products, in this case line is a model of the vibrational motion and the HgI (Voth and Hochstrasser, 1996). As the phase of these oscillations and is consistent with initial and final states before and after appli- mechanism iii. (Marvet and Dantus, 1996.) cation of the laser pump pulse are sensitive Ultrafast Spectroscopy 451

~ 12 f-c 4110.. .. 1 u '6 ~ >. ~ 0) 0: FIG. 19. Femtosecond dynamics w of the abstraction reaction H + to 't"'c tf m GO2 --+ OH + GO reaction. The E potential energy along the reaction * a. olD Experimental coordinate is shown schematically. The experimentally observed rise Q3 of the OH from the breakup of the l ,1rr- t collision complex [HOGO]* is ~ " shown with a lifetime Tc ~ 1 ps. The corresponding structures are . ~~ To-1ps noted with emphasis on three Reaction Coordinate -2 -; ~ j ~ ~ ~ . snapshots to, TC' and t, (final) at 1lmede~y(jJs) the asymptote region. (Zewail, 1996.)

to the solvent dynamics, the effect of the sol- periment of the photodissociation of HgI2 in vent can be investigated with this femtosec- ethanol (Pugliano et al., 1996) are shown. ond laser technique. The oscillations in the signal are from the vi- In Fig. 21 the results of a pump-probe ex- bration of the HgI photoproduct; the probe

,~ '-' a ~ .~ ~ ~ ~ = j ~ ~ '; ; = ~ ".. Q ~

Internuclear Distance, RAB Time Delay (fs)

(a) (b)

FIG. 20. (a) General scheme for femtosecond photoassociation spectroscopy (FPAS) of a gas-phase system having a repulsive ground state Vo. Binding by the laser is followed by excitation to a higher state V2; the evolution of the wave packet along V1 is probed by varying the delay between Abind and Aprobeand monitoring the fluorescence from V2 or the depletion of the fluorescence from V1. (b) FPAS transients showing depletion D 1 u -+ xo; .Data are for the binding and probe lasers polarized parallel or perpendicular to one another. Note the immediate (within the pulse width) formation of photoassociated molecules and the rotational dephasing of the initial anisotropy. (Marvet and Dantus, 1995.)

\ 452 Ultrafast Spectroscopy

-0.5 0 0.5 1 1.5 2 Time (ps)

560 nm Probe

0- ~ (I)

~ -0.5 0 0.5 1 1.5 2 Time (ps)

FIG. 21. Magic-angle (relative polarization at 54.71 pump-probe transients of a 10-mM solution of Hgl2 in ethanol. A pump wavelength of 320 nm was used for each data set. The probe wavelengths between 460 and 560 nm are designated in each of the panels. The open circles are the data points, the bold solid lines are the fits to the molecular response function, and the thin lines are the residuals of the fits. Compare these transients with those shown in Fig. 16 obtained in the gas phase. (Pugliano et al., 1996.)

, " '1' Ultrafast Spectroscopy 453

- pulse excites the ground electronic state of organic crystal (a-perylene). The technique HgI to the excited B state. Different probe involves a sudden (impulse) driving force ex- wavelengths access different regions of the erted by a short pulse on a Raman-activevi- HgI ground potential and therefore monitor brational mode of the crystal. The force ini- different vibrational states of the HgI popu- tiates coherent vibrational oscillations that lation. Note that all vibrational transient sig- are monitored by a delayed probe pulse; no- nals decay on account of the dephasing ef- tice the great similarity with gas- and liquid- fects of the solvent. Compare the data in the phase experiments. Using a train of femto- presence of the solvent (Fig. 21) with the second pulses with a time separation that is data obtained in the gas phase (Fig. 16). in resonancewith the oscillation of the crys- Another important issue in condensed- tal, Weiner et al. show an enhancement of phase processes is energy dissipation. The the amplitude of the motion. The data rate of vibrational energy transfer from the shown in Fig. 22 are the result of excitation excited solute into the solvent-molecule mo- with a series of short pulses [Fig. 22(a)] ap- tions can be described as frictional energy plied to a crystal along a selectedlattice co- loss, and femtosecond studies allow one to ordinate (Weiner et al., 1990). Like someone measure these relaxation rates. Frictional ef- pushing a child on a swing "on resonance fects on chemical reactions in the condensed such that the child acquires a small amount phase such as isomerization of large mole- of energy with every push," the amplitude of cules like stilbene can also be examined. In the crystal oscillation is increased.The effect particular, comparisons of ultrafast studies is shown in Fig. 22 where the femtosecond that monitor the dynamics of stilbene isom- train of pulses sequentially "push" the crystal erization both as an isolated molecule and in layers in a certain direction; acquisition of solution can help to elucidate the effect of this energy is demonstrated by the increases solvents on intramolecular vibrational redis- in the scattering signal [Fig. 22(b) and the tribution (IVR) within stilbene (Sension et simulation, Fig. 22(d)]. When the train of at., 1993).Thus, in addition to measuring the pulses is not resonant, the enhancement is rate of energy transfer from solute to sol- lost [Fig. 22(c)]. vent, FTS techniques allow one to study the Charge-carrier dynamics in nanoscale influence of solute-solvent interaction on en- semiconductor materials have also been ergy-transfer dynamics (i.e., between differ- studied with femtosecond pulses. These are ent vibrational modes) within the solute it- of interest due to their potential technologi- self. cal applications in photocatalysis. Pump- One technique to explore solute-solvent probe experiments can be performed to interactions is photon-echo spectroscopy study the primary eventsof electron trapping (Yang et at., 1995; de Boeij et at., 1995).Here in semiconductor nanoclusters (Caveleri et three sequential ultrashort pulses are used to al., 1995; Kashcke et al., 1990). Electron- distinguish between system-bath and vi- transfer mechanisms in photovoltaic cells bronic dynamics by reason of the difference can also be studied from the transient ab- in time scales.For example, upon optical ex- sorption data. Phonon dynamics, excitons in citation of a solute molecule that subse- quantum-well structures, and spin quantum quently dephases, one can separate which beats in GaAs heterostructures have also dephasing effects occur because of the sol- been studied with ultrashort laser excitation vent and which occur becauseof intramolec- (see Further Reading, esp. Chergui, 1996). ular vibrations. This technique has been ex- ploited in observing dephasing rates of dye 5.3 Biological molecules in different solvents. Femtosecond pulse technology has made inroads in biology as well. Ultrafast pro- 5.2 Solids cesses such as electron transfer in photosyn- Observation of molecular motions in the thetic systems can now be studied, including solid phase has also been achieved with fem- the dynamics of primary events in photobio- tosecond pulses. The example chosen to il- logical systems such as the conversion of so- lustrate these observations is the impulsive lar energy to chemical energy .One of the stimulated Raman scattering (ISRS) of an major goals in these studies is to learn how

"""'- 454 Ultrafast Spectroscopy

the energy is distributed, both within the molecule and in the solvent. These studies are an important complement to structural studies of photosynthetic reaction centers, and, in particular, femtosecond studies of the vibrational transients show how the process of electron transfer and vibrational nuclear dynamics are related. Another important process in biological systems is proton transfer. Again, as with electron transfer, this process is strongly dependent on the subpi- cosecond solute-solvent interactions, which can now be studied with ultrafast pulse techniques. Other applications of ultrafast spectroscopic techniques to biological molecules in- Z;- 'in clude observation of the cis-trans photoisom- c "' erization of rhodopsin, which has been £ studied by examining the transient absorption spectra of an excited wave packet created by a 35-fs pump pulse (Wang et at., 1994). Specifically, a pump-probe differential absorption technique was used whereby the 11-cis molecule in the So electronic state is pumped up to the SI state, where the wave packet can move from its original cis config- d uration to the trans configuration whence it decays back to the ground electronic state [Fig. 23(a)]. As shown in the figure, the cis- trans conformational change is inhibited by a potential barrier in the So state. However, as the pumped wave packet is a coherent superposition of vibrational states,

~ -3 a 3 6 9 12 this wave packet still oscillates coherently Time (ps) even after decaying to the trans conforma- tion in the electronic ground state. Theseos- FIG. 22. (a) Cross-correlation measurement of a se- cillations are detected at various probe wave- quence of femtosecond pulses with a repetition rate lengths as shown in Fig. 23(b), which excite of 2.39 THz (419 fs between pulses) produced the trans molecules back up to the SI state. through pulse-shaping techniques. The pulses can repetitively drive a selected vibrational mode to increase the vibrational amplitude. (b) Impulsive stimulated Raman scattering (ISRS) data from the a-perylene organic molecular crystal driven by a sequence GLOSSARY of (b-polarized) pulses spaced at 419 fs to match the vibrational period of the 80-cm-1 mode. The dif- fracted signal from the mode grows stronger with Coherent: This term describes a system each successive pulse, eventually reaching intensity having a well-defined phase relationship in levels comparable to the strongest electronic response. Selective amplification of the 80-cm -1 mode its energy states such that the dynamics can be clearly measured. is demonstrated. (c) ISRS data from a-perylene driven by a sequence of (b-polarized) pulses spaced Dephasing: The process of losing coher- at 429 fs, slightly off resonance for the 80-cm-1 ence, i.e., becoming incoherent. mode. The signal intensity is reduced relative to that Eigenfunction: In general, a mathemati- in (a), but the vibrational oscillation period is still 419 cal function that is regenerated to within a fs. (d) Simulation of data in (b), assuming a Gaus- sian temporal profile for the excitation pulse train. In constant when an operator H operates on it. (a) through (d), the zero of time is defined as the Schrodinger's equation, HI/I = E 1/1,is an ei- center of the input pulse train. (Weiner et al., 1990.) genvalue equation where H is the Hamilto- Ultrafast Spectroscopy 455

~ nian operator, "' is the eigenfunction, and E is the eigenvalue (see QUANTUMMECHANICS). Eigenstate: The wavefunction "' in Schro- dinger's equation represents a characteristic state (hence, "eigen"-state) of the system described by the hamiltonian operator H. IVR: Abbreviation of "intramolecular vibrational relaxation." A process by which energy deposited in one vibrational mode of a molecule is randomized through the rest of the vibrational modes. Pump-Probe Method: A technique used in ultrafast spectroscopy based on a pair of laser pulses. The first pulse, the pump, initi- ates the process of interest, and the second pulse, the probe, monitors the progress as a function of delay time between the pump and probe. Superposition of States: In quantum mechanics a superposition of states refers to the (a) linear sum of eigenfunctions with a well-defined phase relationship. A superposition of states is time dependent. Wave Packet: A more or less spatially re- stricted wave, formed by a superposition of states.

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