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ULTRAFAST SPECTROSCOPY MARCOS DANTUS AND PETER GROSS, Department of Chemistry, Michigan State University, East Lansing, Michigan, U.S.A. .431 4.1 I. 432 435 436 445 1.1 1.2 2. 4.2 Introduction Physical Framework and Examples Illustrative Example Applications , Experimental Techniques and Methods , Ultrafast Laser Systems. Detection in Ultrafast Spectroscopy: The Pump- Probe Method Ultrafast Spectroscopy of Molecules Ultrafast Rotational Spectroscopy Ultrafast Vibrational Spectroscopy Coherence and Dephasing Chemical Reactions 439 439 445 2.1 2.2 4.3 446 448 4.4 5. 440 3. 449 450 453 453 454 455 456 440 5.1 5.2 5.3 441 3.2 443 444 445 3.3 4. Unimolecular Photodissociation along a Single Reaction Coordinate. . Unimolecular Photodissociation along Multiple Reaction Coordinates Other Unimolecular Reactions Bimolecular Reactions Other Applications of Ultrafast Spectroscopy. Liquids Solids Biological Glossary Works Cited Further Reading time-resolved kinetic information about pro- cesses that are statistical in nature. "ultra- fast" spectroscopy, on the other hand, in- volves temporally short (and therefore spectrally broad) light pulses, which are used to probe directly the dynamics of the system rather than the energy levels themselves. Rapid advances in laser technology over the past decade have resulted in the ability to produce pulses as short as 6 fs (I fs = 10-15 s), and pulses of width 60 fs are now pro- duced routinely in many laboratories around the world (see ULTRASHORT PULSE PHENOM- ENA). The advantage of using ultrashort pulses is that they open the door to investigating the dynamics of the system directly, i.e., the movement of individual particles such as electrons or atoms. From the perspective of classical mechanics, a short pulse whose du- ration is on the same time scale as the mo- tion of a particle in a confined system could be used to probe the dynamics of the parti- cle directly. For typical atomic speeds of the INTRODUCTION Spectroscopy in general is the study of the interaction between light and matter. It is the major tool used for the determination of quantum energy levels in atoms, mole- cules, semiconductors, etc. For example, in addition to their internal electronic motion, molecules possess vibrational and rotational degrees of freedom. Such motion is quan- tized, i.e., only motion corresponding to dis- crete rotational or vibrational energies is allowed. Spectroscopy,which excites transi- tions between these quantized states, is the primary tool in elucidating the energy-level spacing. These, in turn, are useful in deter- mining bond strengths and overall molecular structure. "Traditional" spectroscopy can be de- scribed as energy or frequency resolved be- cause measurements associated with this type of spectroscopy involve spectrally nar- row light that is tuned across discrete energy levels. These measurements can be carried out with pulsed light sources to provide Encyclopedia of Applied Physics. Vol. 22 @ 1998 WILEY-VCH Verlag GmbH 3-527-29475-9/98/$5.00 + .50 431

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Page 1: ULTRAFAST SPECTROSCOPY - Chemistry · ULTRAFAST SPECTROSCOPY MARCOS DANTUS AND PETER GROSS, Department of Chemistry, Michigan State University, East Lansing, Michigan, U.S.A..431

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

.431 4.1I.

432435436

4451.1

1.2

2.

4.2

Introduction Physical Framework and

Examples Illustrative Example Applications ,

Experimental Techniques

and Methods ,

Ultrafast Laser Systems. Detection in Ultrafast

Spectroscopy: The Pump-

Probe Method Ultrafast Spectroscopy of

Molecules Ultrafast Rotational

Spectroscopy Ultrafast Vibrational

Spectroscopy Coherence and Dephasing Chemical Reactions

439439

4452.1

2.2

4.34464484.4

5.440

3. 449450453453

454

455

456

440 5.1

5.2

5.3441

3.2

443444445

3.3

4.

Unimolecular

Photodissociation along a

Single Reaction Coordinate. .

Unimolecular

Photodissociation along

Multiple Reaction

Coordinates Other Unimolecular

Reactions Bimolecular Reactions Other Applications of

Ultrafast Spectroscopy. Liquids Solids Biological Glossary Works Cited Further Reading

time-resolved kinetic information about pro-cesses that are statistical in nature. "ultra-fast" spectroscopy, on the other hand, in-volves temporally short (and thereforespectrally broad) light pulses, which are usedto probe directly the dynamics of the systemrather than the energy levels themselves.Rapid advances in laser technology over thepast decade have resulted in the ability toproduce pulses as short as 6 fs (I fs = 10-15s), and pulses of width 60 fs are now pro-duced routinely in many laboratories aroundthe world (see ULTRASHORT PULSE PHENOM-ENA).

The advantage of using ultrashort pulsesis that they open the door to investigatingthe dynamics of the system directly, i.e., themovement of individual particles such aselectrons or atoms. From the perspective ofclassical mechanics, a short pulse whose du-ration is on the same time scale as the mo-tion of a particle in a confined system couldbe used to probe the dynamics of the parti-cle directly. For typical atomic speeds of the

INTRODUCTION

Spectroscopy in general is the study ofthe interaction between light and matter. Itis the major tool used for the determinationof quantum energy levels in atoms, mole-cules, semiconductors, etc. For example, inaddition to their internal electronic motion,molecules possess vibrational and rotationaldegrees of freedom. Such motion is quan-tized, i.e., only motion corresponding to dis-crete rotational or vibrational energies isallowed. Spectroscopy, which excites transi-tions between these quantized states, is theprimary tool in elucidating the energy-levelspacing. These, in turn, are useful in deter-mining bond strengths and overall molecularstructure.

"Traditional" spectroscopy can be de-scribed as energy or frequency resolved be-cause measurements associated with thistype of spectroscopy involve spectrally nar-row light that is tuned across discrete energylevels. These measurements can be carriedout with pulsed light sources to provide

Encyclopedia of Applied Physics. Vol. 22 @ 1998 WILEY-VCH Verlag GmbH

3-527-29475-9/98/$5.00 + .50

431

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432 Ultrafast Spectroscopy

The rest of the article is as follows. Sec-tion 1 covers the physical basis for ultrafastspectroscopy and contrasts it with frequency-resolved spectroscopy. In Sec. 2 the experi-mental setup required for ultrafast spectros-copy is described along with a discussion ofthe pump-probe technique. Results from anexperiment on iodine are shown in Sec. 3 ,where both the vibrational and rotational dy-namics are obtained. In Sec. 4 studies of var-ious different chemical reactions in the gasphase are presented. Additional applicationsof ultrafast spectroscopy to condensedphases and biological systems are outlined inSec.5.

order of 10000 m/s ( = 0.1 A/fs), laser pulses10 fs in duration achieve l-A spatial resolu-tion, a range that is of great scientific inter-est in physics and chemistry. Ultrafast spec-troscopic techniques have been used toobserve rotational and vibrational dynamicsin molecules. Electronic motion has been ex-plored in semiconductor systems. The key isthat the duration of the laser pulses must beshorter than the time scale of the dynamicsthat one wants to observe. Time scales ofsome physical and chemical processes aredisplayed in Fig. 1.

In summary, ultrafast laser spectroscopyhas become a very useful tool in the study ofthe dynamics of atoms and molecules in arange of environments from gas phase tosolid state. Results from these types of ultra-fast studies have been loosely classified asfemtochemistry , when chemical reactions areinvolved, and femtophysics, when the inter-action between ultrashort laser pulses andmatter is being studied.

I. PHYSICAL FRAMEWORK ANDEXAMPLES

Ultrafast spectroscopy is based on the useof light pulses that have very short temporalduration to interrogate matter. These pulses,

r Atomic ResolutionSingle Molecule

Motion

( Transition ~t

lReaction Intermediates)

IVR & Reactianpr~~~

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

10-3 10-8 10-9 10-10 10-11 10-12

Mllli Nana Pica

~

10-15Femto

I I

10-13 10-14

IRadiative Decayll Rotational Motion II Vibrational Motion I

, . ~ ibrational ~ OlliSiOnS in

Internal Conversion & Intersystem Crossing R I ti Li 'de axa on qUi s

I Predissociation II Harpoon II Norrish IIDissociationlI Reactions II Reactions I I Reactions II Reactions I

§ roton Abstraction, Exchange I Diels-Alder I

Transfer & Elimination I ,,--- D--~-h II Cage Recomb, I

Photosynthesis (ET)

Protein Motions Vision (isom,)

IFundamentals

Iphysical

IBiOlO91Cal

FIG. 1. Time scales and scope of ultrafast phenomena in physical, chemical, and biological changes. On theupper 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 infemtochemistry. 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.)

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433Ultrafast Spectroscopy

an = C('PnIXo) J-~ exp[ -i(En -Eo)t/li]

x exp( -f/a~) cos(oJt)dt, (2)

where c is a constant including such factorsas the field amplitude of the pulse and theelectronic transition dipole moment, and a isa constant equal to 21il/ln(2). The term«({)nIXo) is called the "Franck-Condon" factorand is just the overlap integral between theinitial and final states. Evaluating the inte-gral in Eq. (2) gives

being very fast compared to the underlyingdynamics of the system, are capable of tak-ing "snapshots" of the atomic motion. A col-lection of snapshots taken at subsequenttimes can be thought of as a "movie" of thedynamics as a function of time. Each snap-shot implies a degree of localization of thesystem in space that must be consistent withHeisenberg's uncertainty principle. To illus-trate the advantages of ultrafast spectroscopyand explore some of its implications, a quan-tum-mechanical formalism is required (for areview see QUANTUM MECHANICS).

Quantum mechanically speaking, the factthat short pulses probe dynamics and longpulses probe energy levels is indicative of theuncertainty principle, that time and energyresolution are related to each other throughthe Fourier transform. For example, a veryshort pulse (on the order of 10-15 s) pos-sesses a broad energy bandwidth, whichspans the whole visible spectrum. In con-trast, a longer pulse (on the order of 10-9 s)possesses a much narrower spectrum. Thisrelationship can be illustrated in a com-pletely general manner by showing the effectof the laser-pulse width (time duration) onthe transition probability from one state Xoof a system with energy Eo to other states tPo,tPl' tP2' etc. with corresponding energies Eo,El, Eb etc. First-order perturbation theorycan be used to describe the transition prob-ability from the initial state Xo to each statein the upper potential induced by the laserpulse that is nearly resonant with the transi-tion (i.e., the photon energy hal is roughlythe same as the energy difference En -Eobetween the energy levels). The laser pulse isassumed to be a Gaussian, ~o exp{-r2/a,.2}x cos(UIt), with a temporal full width at halfmaximum (FWHM) 'T. The resulting wavefunction after excitation can be written as asuperposition of the eigenstates of the sys-tem:

an = C(lpnIXo) exp[ -(Wn -UI)2ar/4], (3)

where Wn = (En -Eo)lh is defined as theBohr frequency. Note that in evaluating thecoefficients an all we have done is evaluatethe Fourier transfol1ll of a Gaussian function(the importance of the Fourier transfol1lland its relevance to the distinction betweenenergy- and time-resolved spectroscopy ismade clear below).

In the limit of an ultrashort pulse ( 7 -+ 0)the coefficients in Eq. (3) become

an = C(fPnIXo). (4)

Note that the newly created wave functioncan then be written from Eq. (I) as

1/1 = c L (rPnIXo)rPn°n=O

(5)

Note also that the initial wave function canbe expressed in terms of the excited eigen-functions ~n'

Xo = ~ ('PnIXO)'Pn'

n=O(6)

Thus we see that a very short (delta functionin time) pulse creates a wave packet 1/1 on theupper potential that possesses exactly thesame shape as the initial wave function (towithin an overall constant). Of course, thiswave packet is not an eigenstate of the sys-tem but rather a coherent superposition ofexcited eigenstates. Over time, these statesdephase with respect to one another, sincethe time dependence of the wave function isgiven by

1/1 = ~ anfPn'n=O

(I)

where an are the coefficients (or amplitudes)of the eigenstates 'Pw These coefficients,whose moduli squared represent the popula-tions or occupation probabilities of the indi-vidual eigenstates after the pulse is applied,can be determined from the following first-order perturbation-theory formula:

IIJ(t) = L an exp( -iEnt/h)<pn'

n=O(7)

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434 Ultrafast Spectroscopy

Such a wave function is called nonstationarysince quantum-mechanical expectation val-ues con-esponding to physical observablessuch as position or momentum are not con-stant in time. This can be seen from the ex-pression for the time dependence of an ex-pectation value of some observable, sayposition R (i.e., the internuclear distance be-tween 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)

FIG. 2. Calculated expectation values for the aver-age internuclear distance of a diatomic moleculewhen excited with pulses of increasingly longer tem-poral width [calculations based on Eq. (8)]. Noticethat a 42-fs pulse generates a wave packet with dy-namics that are very similar to those of a classicalparticle in the same harmonic potential. The datagenerated for the 667-fs pulse do not show the oscil-latory motion because the wave packet formed issimilar to an eigenstate of the potential.

laser photon energy h(J), only a single eigen-state is excited. This is a stationary state,and as such, the expectation values (momen-tum' position, etc.) do not change with time,unlike in a nonstationary state created froma short pulse (see, for instance, the 667-fs ex-ample in Fig. 2). For intermediate pulselengths where 'I" is small enough that

exp(-«(J)n -(J)2ar/4} ~ 0 (10)

for more than one level of energy En, a non-stationary state is created since more thanone eigenstate will be appreciably populated.

Invoking the relationship between timeand energy via the Fourier transform, it iseasily shown that the longer the pulse, themore the wave packet in the upper state re-sembles a single stationary eigenstate ratherthan a coherent superposition. The shorterthe pulse, the wider the frequency width,and the more the newly created wave packetin the upper state resembles the initial stateof the system. Since the initial state of the

The first term on the right-hand side of Eq.(8) gives the average equilibrium distance ofthe motion and does not vary in time, butthe second term does; this explicit depen-dence on time is responsible for the "wave-packet dynamics," in this case, the motion ofthe nuclei themselves. For example, in thecase of a diatomic molecule whose nucleimove in a harmonic potential well, themovement of the wave packet is governed bythe energy-Ievel spacing AB; the packet oscil-lates and returns to its original form after atime h/AB, assumed here to be 333 fs. Figure2 shows the expectation value for the inter-nuclear distance R as a function of time us-ing Eq. (8). The dashed line shows the tra-jectory of a particle based on classicalmechanics. Notice that when the motion isinitiated by a short-time pulse ( 7 = 42 fs),the motion is very similar to that of the clas-sical particle; however, when 7 is long (atime equivalent to two full periods of mo-tion, here 667 fs), the expectation value isclose to equilibrium and one is no longerable to measure the dynamics since essen-tially only a single eigenstate (a stationarystate of the system) is excited.

In the limit of a very long pulse (fre-quency-resolved spectroscopy), i.e., 7-+ 00, weget from Eq. (2)

(9)an = C(rPnIXo)B(l1)n -l1)),

where 8(% -w) is a delta function, which isalways zero except when w equals Wn. Thus,unless the laser frequency exactly matchesthe difference in energy between states n andthe ground state, there is no excitation.When the energy difference does match the

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435Ultrafast Spectroscopy

lower potential is not an eigenstate of theupper potential, but rather a superposition ofeigenstates that resemble it, it exhibits dy-namics.

1.1 Illustrative Example

A simple calculation based on the equa-tions presented in the last section nicely il-lustrates this concept of time and energy res-olution in spectroscopy. For illustration,consider the excitation of a diatomic mole-cule from its ground electronic and vibra-tional state to its first excited electronicstate. The potential-energy curves associatedwith this system are depicted in Fig. 3. Thesecurves are based on the Born-Oppenheimerapproximation, which recognizes that nucleiin a molecule move much more slowly than

electrons; therefore, one can map the elec-tronic potential energy as a function of inter-nuclear distance. On these potential cUIVes,the corresponding vibrational levels aredrawn. The electronic states are shown asharmonic oscillators V1(R), V2(R), and V3(R),which resemble the potential energy that thenuclei experience in a molecule, neglectinganharmonic terms that are important at highvibrational energies (see MOLECULAR SPEC-TROSCOPY). Only the initial state Xo is as-sumed to be populated before the laser pulseexcites the system; its wave function is alsoshown in Fig. 3. The first excited electronicstate (with a different electronic configura-tion) is found at a higher energy and slightlylarger equilibrium bond length. These differ-ences are typical for molecules because achange in electronic configuration affects theinteratomic interactions.

Photon absorption from the ground elec-tronic state is assumed to proceed through avertical transition to the upper state, invok-ing the Franck-Condon approximation. Theimplication here is that changes in electronicconfiguration take place much faster thannuclear motion, and therefore the nuclei areessentially "frozen" in place during the elec-tronic transition. When the light source ismonochromatic, only one vibrational state inthe upper electronic potential can be excited.For ultrashort pulses, having a broad spec-tral bandwidth, more than one state may bepopulated at the same time as described byEqs. (1) and (2). For the calculations pre-sented here the energy displacement (i.e., theenergy difference between the potential-wellminima) is taken to be 15770 cm-l (about 2eV). The reduced mass and the q~anturn en-ergy-level spacing of both potentials (w =1.9 X 1013 Hz, equivalent to a 333-fs oscil-lation period) roughly correspond to those ofthe iodine molecule (12).

Figure 4 (left-hand side) shows (from topto bottom) the wave packet llIJ(x)12 created onV2(R) after application of 42-, 167-, and 667-fs FWHM Gaussian pulses (~, i, and 2 timesthe molecular oscillation period of 12, respec-tively). The shortest of these pulses creates anearly perfect Gaussian wave packet onV2(R) as shown in the top left frame of Fig.4; this wave packet is virtually identical toIXoP, the ground state of V1(R), as expectedfrom Eqs. (4)-(6). If the pulse is lengthened,the wave packet starts to look less like IXoP~

FIG. 3. Schematic of the potential-energy curves of adiatomic molecule with three distinct electronic statesV,(R), V2(R), and V3(R). The electronic states pro-vide a harmonic potential that keeps the nuclei boundand gives rise to vibrational energy levels. Ultrafastspectroscopic information from this system can beobtained by excitation at A, from the ground elec-tronic state into the intermediate potential V2(R). Thisexcitation generates a wave packet that oscillates intime. Probing of the wave-packet motion is accom-plished by a second pulse of wavelength A2 that pop-ulates the third electronic state. Signal from the thirdelectronic state is measured as the intensity of thelaser-induced fluorescence (LIF) from V3(R).

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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, 22cm- 1 FWHM, and each line corresponds toa particular Xo -+ 'Pn transition. Long-pulseexcitation corresponds to a frequency-re-solved spectrum; no dynamics can be ob-served because only single eigenstates areexcited. In short-pulse excitation, wherespectral resolution is very poor, the wavepacket created on V iR) does exhibit dynam-ics as the laser pulse excites a superpositionof eigenstates.

It should be emphasized again that thespectrally broad pump pulse is responsiblefor the creation of the wave packet. A longpulse (in time) would excite onlya single ei-genstate on ViR), and therefore no dynam-ics would be observed using the probe pulse.Thus the normal way of thinking in tradi-tional spectroscopy-that the more spectrallynarrow the light, the better-is no longertrue if one thinks about spectroscopy in thetime domain.

-4 -2 0 2 ,

Interatomic Distance (A)

FIG. 4. (a) Calculation of wave packets pumpedfrom the ground to excited electronic state by 42-,167-, and 667-fs pulses [using Eqs. (1) and (3)]. Thepacket formed by the 42-fs pulse is very similar tothe ground-state wave function Ixol2 shown with adashed line. (b) Corresponding spectra for thesesame pulse lengths [using Eq. (11 )].

and more like a single eigenstate on V 2(R)[see Eq. (9)]. The laser-pulse frequency forthis example was chosen to match the en-ergy difference between the ground state ofV1(R) and the Sth eigenstate 'Ps of ViR). Thewave function shown in Fig. 4 (bottom left)for the 667-fs pulse was produced by a suffi-ciently long pulse that the condition in Eq.(10) was satisfied for only one energy, Es;therefore, the excited wave packet in thiscase is essentially identical to the eigenstatel'PsP. Unlike the wave functions shown forJthe 42- and 167-fs pulses, which are linearsuperpositions of the V iR) eigenstates, thewave function produced by the 667-fs pulseis essentially a stationary state and will notchange with time.

Scanning the frequency of the excitationlaser, one obtains an absorption spectrum ofthe system. The spectra depend on the tem-poral duration of the laser pulses because ofthe time-energy uncertainty. This depen-dence is included in the an terms [Eq. (3)].The spectra can be calculated simply by thesum

A({J),T) = 2, lan12.n=O

(II)

1.2 Applications

The field of time-resolved spectroscopyhas grown perhaps as fast as the technologyitself, and some of the most important appli-cations have been realized in femtosecondtransition-state spectroscopy (FfS), a tech-nique developed by Zewail and co-workers atCaltech and applied to numerous molecularsystems (Zewail, 1994, 1996). The first appli-cations of FfS were to gas-phase systems ofsmall molecules, but these techniques havenow been applied to large molecules in thecondensed phase.

The basic scenario of these experiments,which directly observe molecular dynamics,is as follows. A short (femtosecond) pumppulse excites the molecule from its (bound)ground electronic state to an excited state.As noted in the previous discussion of the la-ser pulse inducing a transition between twodisplaced harmonic oscillators, a wavepacket is created "upstairs" by the pumppulse. The wave packet, being nonstationary,moves on the upper electronic state potentialas a localized probability density.

The motion of the wave packet (1I11(x,t)12)as a function of time in the upper potentialIn Fig. 4 {right-hand side) spectra for the

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437Ultrafast Spectroscopy

'1 general, the second pulse, of wavelength A2,induces a transition from the intermediatestate V2(R), where the wave packet evolves,to a higher electronic state that is easilydetected by fluorescence or ionization (seeFig. 3). When the initial wave packet ishighly localized, as represented here with the42-fs excitation, there are times when thewave packet is inside the probing region,marked by the dashed lines in Fig. 5, andother times when the wave packet is outsidethis region.

The signal one expects from these types ofexperiments can be simulated using second-order perturbation theory (see QUANTUM ME-CHANICS), which takes into account transi-tions V1(R) --ViR) and ViR) --V3(R) as afunction of the delay between the pump andprobe pulses. Results based on the wave-packet motion are shown in Fig. 6. Theshorter the pump and probe pulses, the bet-ter the wave-packet localization and the bet-ter the modulation depth in the oscillatorydynamics. For long-pulse excitation, no dy-namics is observed in the signal. Notice thatthe results of the pump-probe experiment

is illustrated in Fig. 5 where IfJ(x,t) is givenby Eqs. (1) and (2). For this illustration, theinitial wave packets were generated with 42-,167-, and 667-fs pulses, as shown in Fig. 4.Notice that for the shortest pulse one obtainsthe best localization of the wave packet, andits motion is most similar with that of a clas-sical particle (see Fig. 2). The intermediate(167-fs) pulse shows a more diffuse wavepacket. However, long-pulse excitation leadsto a wave packet that is essentially an eigen-state of the upper potential and is thereforestationary in time. Figure 5 demonstrateshow ultrafast excitation results in the crea-tion of a time-evolving wave packet. The pe-riodicity of the motion is determined by theenergy difference among the states compos-ing the wave packet [see Eq. (8)]. Monitoringthe subsequent motion of the system re-quires an additional ultrashort pulse that isfired at different delay times as described be-low.

To maintain the temporal and spatial res-olution of the experiment, the monitoring orprobe pulse must be of duration equal to orshorter than that of the excitation pulse. In

~'-'

§.:d.ao

~

.§E-t

FIG. 5. Calculated wave-packet motion for excitation of three different pulse widths [using Eq. (7)]. Darkershades 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.

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438 Ultrafast Spectroscopy

FIG. 6. Calculated pump-probe signal forthree different pulse durations. In all casesthe pump and probe lasers are assumed tohave the same pulse width and intensity.Notice the changes in the rise times and thechanges in modulation depth as the pulsesincrease in duration.

with ultrafast pump-probe spectroscopy.However, this process is on a different timescale because rotational energy spacingstransform into much longer times, on the or-der of 100 ps. The basic premise of rota-tional spectroscopy is that the pump pulseexcites a coherent superposition of rotationalstates, a wave packet, which initially de-phases (since molecules possessing differentangular momenta rotate away from their ini-tial alignment at different rates) and later re-phases at time intervals that depend on therotational constants of the molecule. The ro-tational motion is observed experimentallyby using linearly polarized light pulses thatexcite only those molecules having transitiondipole moments aligned with the electricfield of the pulse.

The FfS technique has also found exten-sive application in condensed-phase spectros-copy, including elucidation of solvent dy-namics and solute-solvent interactions (herethe solute is the entity that is photoexcitedand probed, and the solvent provides thesurrounding "bath" molecules). Observationof coherent dynamics in high-pressure gas-phase systems or in liquids is inherentlymore difficult than in gases at moderatepressures because dephasing effects inducedby collisions will "wash out" the coherentmotion. Still, in general, for sufficiently shorttimes after the initial preparation of thewave packet with the pump pulse, motion ofthe vibrational and rotational transients canbe observed before complete relaxation takesplace.

are analogous to a direct measurement ofthe interatomic spacing given by (R) in Eq.(8) and in Fig. 2.

Vibrational motion in the excited tran-sients has been observed in many systems.The FTS pump-probe technique was used toobserve vibrational motion in the excited Bstate of iodine (Dantus et al., 1990) (see be-low), in predissociative systems such as so-dium iodide (Nal) (Rose et al., 1988), and inpurely dissociative systems such as cyanogeniodide (ICN), where the excited state ac-cessed by the pump pulse is purely repulsive(Dantus et al., 1987). In all of these (one-di-mensional) cases, the nuclear motion wasmapped out as a function of time using theaforementioned FTS technique.

Beyond these simple one-dimensional sys-tems, the FTS technique has been applied tomore complex systems that allow for exami-nation of the vibrational motion of a transi-tion state. With time-resolved spectroscopy itis now possible to learn, at least in principle,about the dynamics of the transition-statecomplex, i.e., how these atoms are movingrelative to one another as they are trans-formed from reactants to products. Such in-formation may bring us closer to under-standing the very nature of chemicalreactions themselves. For example, the pho-todissociation of mercuric iodide (HgI2) intoI and HgI gave insight into the nature of the[1-Hg-I]** transition-state complex by againlooking at the vibrational dynamics (Dantuset al., 1989).

Molecular rotation has also been observed

-~

-

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439Ultrafast Spectroscopy

~ 2. EXPERIMENTAL TECHNIQUESAND METHODS

The time scale for measurements usingultrafast spectroscopy is determined by thespacing between the energy levels of the sys-tem under study, as discussed in the Intro-duction. Typically, ultrafast spectroscopymeasurements temporally resolve dynamicsshorter than 10-12 s (1 ps). Given that mostmeasurement equipment, such as oscillo-scopes, have response times in the nanosec-ond time scale, special experimental arrange-ments are required in order to achievefemtosecond time resolution. In this sectionwe describe how ultrafast laser pulses aregenerated and how they are used to measuremolecular dynamics.

short pulses presents great technical chal-lenges (see ULTRASHORT PULSE PHENOMENA).

Femtosecond pulse generation is achievedin an oscillator cavity that has a very broadgain bandwidth and contains a nonlinear op-tical element whose properties are highlydependent on laser peak intensity. This ar-rangement favors the propagation of shortpulses (high peak intensity) compared tocontinuous-output operation. There aremany successful oscillator designs of thistype; while some use laser dyes, others maybe all solid state, even imbedded in opticalfibers.

Femtosecond oscillators are capable of di-rectly producing very short pulses (down to8 fs), but energies are typically less than ananojoule per pulse. Ultrafast spectroscopicmeasurements require high-energy pulses,and so the output of the oscillator needs tobe amplified. The most successful techniquefor this uses grating pairs to lengthen. thepulses temporally (Squier and Mourou,1992). These "stretched" pulses are then am-plified to millijoule levels and compressedback to the femtosecond time scale. By thismethod, millijoule pulses as short as 20 fshave been produced (Backus et al., 1995).

Tunability of femtosecond laser systemsmay be achieved by continuum generation,whereby a very intense femtosecond pulse isfocused on a transparent medium such as aquartz window and emerges as a white lightpulse containing all wavelengths within thewindow of transmittance of quartz. The laserpulse induces a very rapid change in the re-fractive index of the medium, causing it toact as an ultrafast shutter. Because of thetransform limit relationship between thetime and energy bandwidths, this results in alarge increase in the pulse bandwidth; con-version efficiency is very high, approaching100%. Spectral selection from the continuumis achieved by filtering. If desired, more in-tense pulses can be generated by opticalparametric amplification. In this process, arelatively weak (seed) pulse is mixed with ahigh-intensity pulse in a nonlinear opticalmedium, resulting in a pulse having a higherintensity than the seed. The fundamental ofthe laser can be used for the amplificationpulse, and judicious selection of the fre-quency of the seed pulse will allow quite in-tense pulses to be produced at a given wave-length.

2.1 Ultrafast Laser Systems

There have been great advances recentlyin the generation of ultrafast laser pulses.This progress has been fueled to a large ex-tent by the communication industry (primar-ily work by Shank, Ippen, and their col-leagues at Bell Laboratories) with the goal ofdecreasing laser-pulse duration so that moreinformation can be transmitted within agiven time interval. The evolution of these la-ser systems has been reviewed (Squier andMourou, 1992; Fleming, 1986; ULTRASHORTPULSES). Here we concentrate on the princi-ples of these systems and the requirementsof ultrafast spectroscopy.

One of the consequences or manifesta-tions of the uncertainty principle is a limitimposed on the temporal pulse width of la-ser pulses such that their duration may notbe any shorter than the inverse of their fre-quency bandwidth. For pulses with a Gaus-sian intensity profile in time and frequency,this relationship can be simplified to

.1VT ~ lln(l)/'IT, (12)

where Llv and 'I" are the FWHM of the laser-pulse frequency and time width, respectively.The shortest pulse measured to date had apulse duration of 5 fs (Baltuska et at., 1997),and the record since 1987 was 6 fs (Fork etat., 1987), corresponding to frequency band-widths of 8.8 X 1013 Hz (2940 cm-l) and7.3 x 1013 Hz (2450 cm-l), respectively, ac-cording to Eq. (12). The generation of such

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440 Ultrafast Spectroscopy

Ts-Iaser amplifier2.2 Detection in Ultrafast Spectroscopy;

the Pump-Probe Method

In general, ultrafast spectroscopy hasbeen associated with time scales shorter thanpicoseconds. This makes it useful for thestudy of molecular motion (see Fig. l)-forexample, rotation (picosecond) and vibration(femtosecond). The second major applicationis to electronic signals extending to the tera-hertz regime and beyond. These frequenciesare considered ultrafast because one is nolonger able to use conventional equipmentfor their measurement. The state of the artin photon detectors is still, as of 1997, lag-ging by almost three orders of magnitude be-hind the generation of short pulses. This facthas forced experimental groups to find tech-niques that depend on two or more ultra-short pulses to initiate and monitor a pro-cess; the time resolution in the resultingsignal is then independent of the detectionmethod. The most common of these arrange-ments is known as the pump-probe tech-nique. This technique, in fact, has been crit-ical in the advancement of time-resolvedspectroscopy since 1949 when millisecondresolution was first achieved (Porter, 1950).

In the pump-probe method, the time res-olution is determined by the convoluted tem-poral width of the pump and probe laserpulses, the degree of experimental controlover the time delay between them, and theirrelative temporal jitter. Present systems forultrafast spectroscopy have been able to pro-duce pulses as short as 5-6 fs, with jitter andtime-delay control better than a single fem-tosecond (Baltuska et at., 1997; Fork et at.,1987). This outstanding level of control isachieved by the use of arrangements such asthe ~ach-Zehnder interferometer shown inFig. 7. An intense femtosecond laser pulseemerging from the amplifier is split by a par-tially reflective optic into two pulses that fol-low different paths in the interferometer.While in the interferometer, techniquesbased on nonlinear optics are used to changethe wavelength of the laser pulses (if re-quired by the particular experiment) whilemaintaining their pulse duration and timingof each relative to the sibling pulse. Thepulses are later recombined using a secondpartially reflective optic before being steeredto the sample region. The time delay be-tween the pump and probe lasers is deter-

Ax ,It

~.Experiment

A (a)

(b)

First case:

path (a) = path (b)

8t=O

Second case:

path (a) + 2t.x = path (b)

~t = 2Ax/c

For Ax = 1 ~m; At = 6.67 fs

FIG. 7. Pump-probe experimental setup showing atypical Mach-Zehnder interferometric arrangementused to control the timing between pump (path a)and probe (path b) laser pulses.

mined by the position of a computer-con-trolled optical-delay line located in one ofthe arms of the interferometer. The principleof the time delay is that the speed of light isconstant and that spatial displacements cor-respond directly to temporal delays. For atypical step of 1 ILm, a pulse is delayed by3.3 fs. Because the light traverses the opticaldelay line twice, the corresponding delay is6.67 fs (see Fig. 7).

Notice that the time resolution of pump-probe experiments depends on the time de-lay between the pump and probe pulses andnot on the temporal response time of a de-tector. In fact, these experiments are inde-pendent of the response time of photon de-tectors or signal-processing electronics. Thishas allowed pump-probe experiments to becarried out in conjunction with a number ofother spectroscopic techniques, e.g., absorp-tion, emission, laser-induced fluorescence,ionization, and Raman spectroscopy.

3. ULTRAFAST SPECTROSCOPYOF MOLECULES

Ultrafast molecular spectroscopy is thetime-domain analog of frequency-resolvedspectroscopy (see MOLECULAR SPECTROS-COPY). Electronic, vibrational, and rotational

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441Ultrafast Spectroscopy

transitions are interrogated, but in ultrafastspectroscopy, coherence among the quantumstates leads to time-dependent dynamics thatcan be directly associated with the classicalmechanical motion. Among the advantagesof time-domain spectroscopy is the completeseparation of vibrational and rotational in-fonnation, which may be obscured in fre-quency-resolved spectroscopy of molecules atroom temperature. This effect is illustratedfor the diatomic iodine molecule, where it isshown that one can measure rotational spac-ings of 0.027 cm-l with laser bandwidthsfour orders of magnitude larger.

,.,.

FIG. 8. Energy-Ievel diagram for ultrafast spectros-copy of molecular iodine. The first femtosecond laserpulse (A1) excites the iodine molecules to theB 3IIo+u state, with accompanying vibrational and ro-tational excitation. The probing is carried out by asecond femtosecond laser pulse (A2) that takes thewave packet to the upper fluorescent state. The sig-nal detected (~eJ is fluorescence from the upperelectronic state. Absorption or ionization at A2 canalso be used. (Dantus et al., 1990.)

3.1 Ultrafast Rotational Spectroscopy

The electronic excitation of gas-phase io-dine molecules from the ground state to theB state occurs in the 500-630-nm wavelengthregion. Rovibrational spectroscopic lineswith a typical density of 100 lines per inversecentimeter can be resolved by excitation withnarrow-bandwidth light. Even though themolecule is a simple diatomic, the interpre-tation and assignment of these spectral linesis not straightforward because of the hun-dreds of rotational levels associated witheach vibrational level. When the molecule isexcited with an ultrafast laser pulse, thebandwidth is orders of magnitude broaderthan the spacing between spectroscopiclines, which are therefore not observed (seeFig. 4 for example). However, ultrafast pulseexcitation results in a coherent superpositionof rotational and vibrational quantum states.Probing of this coherence in the temporal re-gime can be used to obtain the energy-do-main information with the same accuracy asthe frequency-resolved methods.

In Fig. 8, the relevant electronic states ofiodine are presented; the arrow correspondsto excitation of the ground-state iodine mol-ecule to the excited B state. The vibrationalspacing in the B state of iodine at 620 nm is110 cm -I; the spacing between rotationallines is =0.027 cm -I. To observe ultrafastrotational spectroscopy, the laser pulsesmust be shorter than the inverse of the en-ergy spacing between rotational lines, (2B) -I

where B is the molecule's rotational con-stant, so that a coherence between rotationalstates may be achieved (Felker, 1992; Felkerand Zewail, 1987). For diatomic iodine inthe B state, this time corresponds to =270

ps. For these experiments, a linearly polar-ized laser pulse excites only molecules thathave their transition dipole moment p, paral-lel or nearly parallel to the polarizationplane of the electric field of the laser pulse,~, because the transition amplitude is deter-mined by p, .~. Initial excitation therefore se-lects an ensemble of aligned molecules. Asecond laser pulse, the probe, is then used tointerrogate only previously excited mole-cules; because the probe pulse is also polar-ized, it is sensitive to the initial alignment.As the rotation of the ensemble evolves intime, the coherence decays because mole-cules having different degrees of rotationalexcitation will rotate at different rates.

Because all rotational levels are related tothe same rotational constant by a factor ofan integer quantum number J (the angular

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442 Ultrafast Spectroscopy

FIG. 9. Molecular rotation for an ensemble of threeidealized rotors with angular momenta J = l' 2, and3, showing the initial dephasing and the half and fullrecurrence of the alignment at later times. It shouldbe noted that a quantum-mechanical picture of rota-tions predicts that the half recurrence at (48)-1 is180° out of phase (negative signal). The shaded re-gion of the circles denotes the amount of rotationthat the molecules have executed for each time step.The atoms are shown as black or white for clarity.(Dantus et al., 1990.)

three molecules are depicted, with angularmomenta I = 1, 2, and 3. The molecules areassumed to be aligned at time t = 0 and freeto rotate for all later times. After a time(2B) -1 all molecules have executed an inte-

ger number of rotations that equals I,thereby regaining the original molecularalignment. In an experiment, the initialalignment is achieved by the absorption ofthe linearly polarized pump laser. The probelaser is also linearly polarized and achieves alarger signal when it encounters molecularalignment (provided its polarization matchesthe orientation of the transition dipole). No-tice that at times (4B)-1 and (2B)-I, the di-pole moments are aligned and the signalachieves a maxima. The observation of rota-tional motion in real time is equivalentlymanifested in rotational spectroscopy wherethe spacing between rotational lines in thespectrum is 2B.

In Fig. 10, experimental results obtainedfor iodine using 60-fs pulses are shown andcompared to theoretical simulations (Dantuset at., 1990). The results obtained when thepump and probe pulses are polarized parallelto each other, III' are compared to those ofperpendicular pump-probe polarization, I J. .It can be seen that the rotational signaturesare out of phase for these two cases. At early

momentum), the original alignmentrephasesafter a time (2B) -1 determined by the rota-tional energy constant B. Figure 9 illustratesthe principle of ultrafast rotational spectros-copy of a diatomic. For this illustration only

FIG. 10. Ultrafast study of molec-ular iodine with polarized lasers.(a) Transients showing the initialdephasing due to molecular rota-tion (left) and the appearance offull recurrences at a later time(right). Parallel (~I) and perpendic-ular (I-L) probe orientations areshown and are 180° out of phase,as expected. The rapid oscillationsare due to vibrational excitation;six levels are reached (the solidline through these on the left is aguide to the eye). Half recurrenceswere observed experimentally butare not shown here. Note that thetime scale is discontinuous. (b)Calculated results for rotational de-phasing (left) and rephasing (right)assuming excitation of vibrationallevels 7 to 12 and taking into ac-count vibrational and rotationalcoupling and centrifugal distortion.(Dantus et al., 1990.)

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443Ultrafast Spectroscopy

~ times, there is a clear dephasing of the origi-nal alignment. At long times, there is a seriesof alignments corresponding to (2Bv) -I,where Bv is the corresponding rotationalconstant of the v vibrational level. Analysisof these data accounting for centrifugal dis-tortion reveals the presence of vibrationallevels v = 7-12.

Ultrafast rotational coherence has beenused by various groups to study the structureof large molecules (more than 25 atoms)(Felker, 1992). The principle behind thesemeasurements is the same as described hereexcept for the contribution, in polyatomicmolecules, of the other two rotational con-stants A and c. Because of the high degreeof accuracy obtained and the complete iso-lation of rotational features, these experi-ments have been particularly useful in thedetermination of structures of weakly boundcomplexes such as those formed betweenamino acids that are hydrogen bonded withwater molecules. Time Delay (fs)

FIG. 11. Ultrafast transients of 12 obtained at differentpump laser wavelengths (A1). The time scale for thethree traces is the same (200 fs/division). The pe-riods are measured peak to peak between the sec-ond and third oscillations in order to avoid convolu-tion effects. Complete analysis of these transients willgive better values. (Bowman et al., 1989.)

3.2 Ultrafast Vibrational Spectroscopy

When femtosecond pulses excite severalvibrational levels, one is able to observe themolecular vibration of the wave packet. InFig. 11, data are shown for excitation at dif -ferent wavelengths (Bowman et al., 1989).Notice that excitation with shorter wave-lengths forms products having longer vibra-tional periods. This is due to the anharmon-icity of the bound state. As the vibrationalenergy spacing decreases, the oscillationtime increases. This is a characteristic oftime-resolved spectroscopy and means thatthe resolution of the technique improves asthe resolution of conventional (frequency-re-solved) spectroscopy deteriorates (and viceversa).

Data such as those presented in Fig. 11may be analyzed to obtain the shape of theelectronic state. To invert the time-resolveddata into the energy/frequency domain, onecan simply take the Fourier transform of thedata. In Fig. 12, experimental and theoreticalplots are shown of data obtained for iodinemolecules, having the pump and probe laserpolarizations at the magic angle (54.7°) inorder to cancel rotational contributions tothe signal. Notice that the data show rapidoscillations modulated by a much slower os-cillatory envelope. The high-frequency com-

ponent co1Tesponds to the average time ofvibrations, while the long-time-scale modu-lation co1Tesponds to the anharmonicity ofthe electronic state. In this case, one is ableto determine that two vibrational states pri-marily contributed to these data and that theenergy spacing between them co1Tespond tothe vibrational energy spacing of the mole-cule.

Comparing the Fourier-transformed datafrom ultrafast spectroscopy with that of high-resolution spectroscopy, one can observe thegreat simplification because of the separationof rotational and vibrational components. Ro-tational coherence occurs on a much longertime scale and can be discriminated againstby setting the polarization vectors of pumpand probe lasers at the magic angle.

In general, for large and heavy moleculeswhere spectroscopic transitions overlap, ul-trafast spectroscopy is clearly advantageous,allowing a complete separation between vi-

.~

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444 Ultrafast Spectroscopy

(a) 3.3 THz

~I-..I j 5 pa.

Theorelk:al -Two Vibralk>naJ Motions

~ ~ 300 Is

33 THz(b) FIG. 12. (a) Ultrafast transients showing

real-time vibrations of molecular iodine(left). The vertical scale represents theLlF amplitude, which is a probe of the in-ternuclear distance. The correspondingFourier transform is shown on the right.(b) Calculated results for excitation of awave packet comprising the two principalvibrational frequencies and the corre-sponding Fourier transform. (Dantus etal., 1990.)

~yf-JFrequency (THz)Time Delay (rs)

brational and rotational information becauseof their differences in time scales.

order to understand the behavior of mole-cules in solution (Zewail et al., 1992; Lienauet al., 1993; Lienau and Zewail, 1994, 1996;Matemy et al., 1996; Liu et al., 1996).

As an illustration, Fig. 13 shows a studyof the vibrational coherence of 12 in the pres-ence of argon gas at various pressures. Atpressures below 10 bar, there is no colli-sional effect on the vibrational coherence be-cause the average time between collisions ismuch longer than the time range probed inthis experiment. However, an increase inpressure to 100 bar causes a loss of vibra-tional coherence as well as electronicquenching. Studies at higher pressures (not

3.3 Coherence and Dephasing

The ultrafast data presented in the previ-ous section retain coherent excitation for along time. This condition is easy to achievein the gas phase at low pressures. Whenthese types of experiments are carried out inhigh pressures approaching the density ofthe liquid phase, the coherence is lost by col-lisions. Experiments have been carried out toexplore this transition from gas to liquid in

620/390 (340)10 bar Ar

620/390 (340)

100 bar Ar

~

""""-FIG. 13. Femtosecond transients of12 dissociation obtained as a functionof increasing argon gas pressure. Athigh pressures the decay of thewave packet is evident. (Zewail etal., 1992.)

0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 140 2 4 6 8 10 12 14

Time Delay (ps) Time Delay (ps) Time Delay (ps)

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445Ultrafast Spectroscopy

shown) have reproduced the dynamics ob-served in the liquid phase, where vibrationalcoherence survives for a few picoseconds(Zewail et al., 1992; Lienau and Zewail, 1994,1996; Matemy et al., 1996; Liu et al., 1996).

~

4. CHEMICAL REACTIONS

as the transition states of the reaction. ultra-fast spectroscopic data of this reaction areshown in Fig. 14. Clocking the emergence offree CN radicals yielded a bond-breakingtime of 205 fs (Rosker et al., 1988). This timemay be directly related to the repulsionlength scale (L) between the fragments if apotential of the form V(R) = E exp[ -(R -RJ/L] is assumed.

Bond breakage is not always a direct pro-cess; in some cases, there are crossings be-tween two or more electronic states, causinginterference in the dissociation. The use ofultrafast spectroscopic techniques has al-lowed researchers to observe these interfer-ences in real time during the reaction.

Photodissociation of alkali-metal halidesleads to this type of crossing between theionic and covalent coordinates (see Fig. 15)(Rose et al., 1988). The study of this processis as follows. A diatomic alkali-metal halide(for example, NaI) is excited by a femtosec-ond pump laser to the covalent state, form-ing the activated complex [NaI]**. Becauseof the crossing with the ionic state, the acti-vated complex resides in the well; coherentexcitation of the complex results in vibra-tions detectable by ultrafast pump-probespectroscopy (see Fig. 15). The curve cross-ing allows a percentage of the vibrating mol-ecules to escape from the well, producing Na+ I. When the complex inside the well isprobed, an exponentially decaying amplitudeof coherent vibrations are observed. How-ever, when one monitors the free sodium at-oms resulting from the reaction, the signalincreases in steps, reaching a plateau whenall of the complex has escaped the boundwell.

One of the most important applications ofultrafast spectroscopy has been to the studyof short-lived species such as transitionstates in chemical reactions. This type of ex-periment has allowed experimentalists tomeasure for the first time how long it takesto break or form a chemical bond. Ultrafastspectroscopy of chemical reactions, or fem-tochemistry , has allowed the study of manytypes of chemical reactions in real time. re-vealing details about the mechanisms in-volved (Manz and Woste, 1995). There havebeen numerous studies from various re-search groups around the world, but the dis-cussion here is limited to a few model caseswithout attempting a thorough review (seeFurther Reading).

4.1 Unimolecular Photodissociation alonga Single Reaction Coordinate

One of the simplest chemical reactions isunimolecular photodissociation. The fre-quency-resolved spectrum associated withexcitation to a repulsive electronic state lead-ing to photodissociation is usually a feature-less continuum that gives very little infor-mation about the dynamics involved.Ultrafast spectroscopy of the same system al-lows one to observe the progress of bondbreakage, giving the researchers additionalinformation about the electronic state suchas the potential energy as a function of inter-atomic distance. In addition, the length oftime required to break a chemical bond canbe determined by this method. The first suchstudy was carried out on the elementary re-action

ICN -+ [I CN]** -+ I + CN, (13)

where the [I. ..CN]** species represent ex-cited cyanogen iodide molecules (ICN*) inthe process of becoming products. Thesetransient species are sometimes referred to

4.2 Unimolecular Photodissociation alongMultiple Reaction Coordinates

When more than one reaction coordinateis available, the potential-energy surface ofthe reaction has a saddle point where pro-gress along one of the coordinates is deter-mined. The first direct spectroscopic probingof a saddle point was achieved in the photo-dissociation of Hgl2, shown in Fig. 16 (Dan-tus et al., 1989).

Time-resolved data from the reactionshow vibrational motion in the nascent HgIfragment (300-fs period) as well as rotationalmotion (1.3-ps) caused by the torque of the

-

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446 Ultrafast Spectroscopy

f?:..."..

Em"ocn

-+-

TIme delay (Is)

(b)(a)

FIG. 14. Measurement of bond dissociation in the reaction ICN + hv-+ I + CN. (a) A cartoon illustrating theexperiment. A simple (slice through a) one-dimensional picture, with no angular dependence, is considered forthe 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 re-sults. The heavy line is the measured ICN transient, and the thin line is the reference t = 0 transient. The fig-ure 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 mo-tion indicates that the activated complex hasa bent geometry (see Fig. 16). The coherentvibrational motion in the product (all HgIfragments vibrating in concert) was unex-pected and is the result of a prompt dissoci-ation, which imparts an impulse perpendic-ular to the reaction coordinate. Coherence inthe vibrational motion of products of reac-tions initiated with ultrafast lasers has nowbeen observed in more complex systems in-cluding proteins such as rhodopsin (Wang etat., 1994) and myoglobin (Zhu et at., 1994).

tion allows a direct assessment of the mech-anism and dynamics of these reactions. Thisis particularly important in more complexreactions where one wants to determine thetiming between multiple bond-breaking andbond-forming steps. Among these types ofstudies, the reaction of the cyclic carbonylcompounds is a classic example of mecha-nism determination (see Fig. 17) (Pedersen et

al., 1994).Concerted chemical reactions, whereby

more than one chemical bond is broken orformed in concert, are best studied by ultra-fast spectroscopy in order to follow mecha-nisms and learn about the dynamics of suchprocesses. One such reaction has been stud-ied in which two bonds are broken and oneis formed within a time that is much fasterthan molecular vibrations ( <60 fs). The pho-todissociation of methylene iodide,

4.3 Other Unimolecular Reactions

Ultrafast spectroscopic techniques havebeen used to study a wide variety of chemi-cal processes such as isomerization, chargetransfer, and proton transfer. Time resolu-

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447Ultrafast Spectroscopy

~

-~-

Covalent: Na + I>-0)wc

w

:"@c0)a~

f

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

0 5 Rx=6.93A 10 15

Internuclear Separation (A)

20 Time O(Is)

5 10 15

Internuclear Separation (A)

20

(a)

rot=0)

Ci5

-2 -1 0 1 2 3 4

Time delay (ps)

5 6 7 8

(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 correspond-ing 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 ofthe 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 mechanisminvolves the concerted breaking of the twocarbon-iodine boncfs as the iodine atomscome into close proximity and form a bond.The fact that these steps occur simulta-

undergoes such a concerted mechanism.Upon 12-eV excitation by the pump pulse,iodine molecules are produced. Probing ofthese molecules reveals that all iodine mole-

'I

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448 Ultrafast Spectroscopy

[A]:!:

"

I I I I I I I I I

-500 0 500 1000 1500 2000 2500 3000 3500

Time (femtoseconds)

Theoretical: Quantum wave packet motion

~

°"'t.,=

(t=1.3 ps)(t=o ps)

(a) (b)

FIG. 16. Femtosecond dynamics of the reaction Hgl2 + hv-+ Hgi + I. (a) Potential energy surfaces, with aclassical trajectory showing the coherent vibrational motion as the diatom separates from the I atom. Two snap-shots of the wave-packet motion (quantum-molecular dynamics calculations) are shown for the same reaction att = 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 (oscilla-

tions) is observed in both polarizations of FTS (femtosecond transition-state spectra). The rotational orientationcan 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-ent," vibrational motion of the iodine mole-cules.

4.4 Bimolecular Reactions

The study of bimolecular reactions usingultrafast techniques has been limited becauseof the difficulty of initiating these reactionswith a laser pulse; they depend on collisionsthat occur at random times. This difficultyhas been addressed by two separate ap-proaches. One of them has been to take ad-vantage of van der Waals complexes as pre-cursors to the reaction (Hoffman et al., 1990;Wittig and Zewail, 19rJ6). If, for example,one wants to study the reaction between Hand CO2, one can start with a precursor such

as CO2 ...HI, which upon laser excitationreleases the hydrogen reactant with a knownkinetic energy. This technique helps establishthe initial geometry , the energetics of the en-counter, and the time of initiation of the bi-molecular encounter. Figure 19 shows datafrom this type of study for the CO2 ...HIsystem. The emergence of the OH product,probed in this experiment by laser-inducedfluorescence, is seen to occur within a pico-second of the initiation of the reaction.

An alternative approach for the study ofbimolecular reactions in real time is to cap-ture the collision pairs with an ultrafast laserpulse that excites the reactants to a newelectronic state. This process is called pho-toassociation and has been shown to be use-ful in frequency-resolved spectroscopy tostudy molecules having dissociative ground

.,..1

(!=3 ps)

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449Ultrafast Spectroscopy

,-

(a)

~ parent

/

{~6000 e'

t {i~

3. ..~ FIG. 17. Femtosecond dynamics of addi-

tion/cleavage reaction of the cyclobutane-ethylene system. (a) The PES showing thenonconcerted nature of the reaction, to-gether with three snapshots of the struc-tures at to (initial), td (diradical), and tf (fi-nal). The parent precursor is also shown.(b) Experimental observation of the inter-mediate diradical by mass spectrometry.

(Zewail, 1996.)

=T=-:D.l .L : .....:: 4: 5 6 7

1 2 i i 3 ii i Time-of-Flight, fls

i; ii ;

0

28 41 5556 84 Mass, amu

(b)

states. It has also been demonstrated withultrafast lasers (Marvet and Dantus, 1995),and the products show signs of coherencesimilar to those described earlier for boundmolecular systems even though the initialstate is a thermal distribution of incoherentstates. In particular , a bulb containing gase-ous mercury atoms has been shown to pro-duce Hg2 molecules in the state labeled V 1 inFig. 20 under femtosecond laser excitation.Probing of these newly formed molecules isachieved by population depletion that causesa decrease in the laser-induced fluorescence(LIF) signal. The product molecules displayrotational alignment that is similar to that

seen in rotational coherence spectroscopy;

see Fig. 20.

5. OTHER APPLICATIONS OFULTRAFASTSPECTROSCOPY

Ultrafast spectroscopy has also been usedin the study of fast dynamics in liquids, clus-ters, semiconductors, and large biochemicalsystems. Observation of coherent dynamicsin the condensed phase is inherently moredifficult since dephasing effects induced bysurrounding atoms and molecules will "washout" the coherent motion. Still, for short

-

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450 Ultrafast Spectroscopy

times after the initial preparation of thewave packet with the pump pulse, motion ofthe vibrational and rotational transients canbe observed before complete relaxation takesplace.

hv(i)

hv(ii) -

(iii)

-,~i~J

(a)

(b)

FIG. 18. Femtosecond dynamics of a concertedchemical reaction, CH212 + hv ---CH2 + 12. (a)Schematic of the reaction mechanisms. All fragmentsare drawn relative to carbene-fixed coordinates. (i)

Stepwise (sequential) dissociation; the first iodineatom released has time to move away from the mo-lecular fragment before the second carbon-iodinebond breaks. Molecular iodine is formed later bythree-body collisions. (ii) Mechanism in which the firstcarbon-iodine bond breaks and an iodine-iodinebond is formed while the second iodine is still part ofthe molecule thus forming an ylide. This stage isconcerted; subsequent breaking of the second car-bon-iodine bond completes the reaction. (iii) Con-certed bond breaking and formation process; break-ing of the two carbon-iodine bonds is simultaneouswith formation of an iodine-iodine bond. This mech-anism would be expected to produce a molecular io-dine product with a large degree of vibrational coher-ence. (b) Experimental measurement showing theprompt appearance of oscillatory dynamics due tothe product 12 molecules vibrating synchronously. Theline is a model of the vibrational motion and thephase of these oscillations and is consistent withmechanism iii. (Marvet and Dantus, 1996.)

5.1 Liquids

Over the past few years numerous theo-retical and experimental studies on photoex-citation and photodissociation in the liquidphase have been performed. In the gasphase, accurate measurements of the reac-tant and product in terms of how energy isdistributed among electronic, vibrational,and rotational degrees of freedom is, at leastin principle, possible. However, in liquids,where the solvent continuously interactswith the solute molecule in question, suchdetailed information is impossible. Neverthe-less, ultrafast spectroscopy has been success-fully used to learn about dynamical and en-ergy-transfer processes between the soluteand solvent and within the solute moleculesthemselves (Sitzmann and Eisenthal, 1989;de Boeij et al., 1995).

Wave-packet motion has been experimen-tally observed in 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, ultrafastpump-probe techniques have been used tostudy the time scales of solvation and vibra-tional relaxation of photoexcited dye mole-cules in liquids (Bingemann and Ernsting,1995). Femtosecond studies of chemical re-actions in liquids include the photodissocia-tion of 13 -.Ii + I; here, the transient vi-brational motion of the diatomic anion wassimulated and the vibrational dephasingtimes for different solvents determined(Banin et al., 1992).

Detailed femtosecond studies of HgI2 pho-todissociation in various solvents have alsobeen performed; these studies should be con-trasted with the previously mentioned gas-phase studies by Zewail and co-workers(1992), Such studies are useful in learningabout how solvents affect the nuclear motionin the transition state and how they affectthe coherent vibrational and rotational mo-tion of the fragment products, in this caseHgI (Voth and Hochstrasser, 1996). As theinitial and final states before and after appli-cation of the laser pump pulse are sensitive

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451Ultrafast Spectroscopy

~

..12 f-c

1u'6

~>.~0)0:wmE

*a.

FIG. 19. Femtosecond dynamicsof the abstraction reaction H +GO2 --+ OH + GO reaction. The

potential energy along the reactioncoordinate is shown schematically.The experimentally observed riseof the OH from the breakup of thecollision complex [HOGO]* isshown with a lifetime Tc ~ 1 ps.

The corresponding structures arenoted with emphasis on threesnapshots to, TC' and t, (final) atthe asymptote region. (Zewail,

1996.)

tf

Experimental

l r- r ,1

olDQ3

t"

~~ To-1ps

-2 -; ~ j ~ ~ ~ .1lme de~y(jJs)

4110..

to 't"'c

~

.Reaction Coordinate

periment of the photodissociation of HgI2 inethanol (Pugliano et al., 1996) are shown.The oscillations in the signal are from the vi-bration of the HgI photoproduct; the probe

to the solvent dynamics, the effect of the sol-vent can be investigated with this femtosec-ond laser technique.

In Fig. 21 the results of a pump-probe ex-

, ~

'-'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 systemhaving a repulsive ground state Vo. Binding by the laser is followed by excitation to a higher state V2; the evo-lution of the wave packet along V1 is probed by varying the delay between Abind and Aprobe and monitoring thefluorescence 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 theinitial anisotropy. (Marvet and Dantus, 1995.)

\

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452 Ultrafast Spectroscopy

-0.5 0.5 1

Time (ps)

1.5 20

560 nm Probe

~(I)

0-

~

-0.5 0 1.5 20.5 1Time (ps)

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

, " '1'

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453Ultrafast Spectroscopy

- organic crystal (a-perylene). The techniqueinvolves a sudden (impulse) driving force ex-erted by a short pulse on a Raman-active vi-brational mode of the crystal. The force ini-tiates coherent vibrational oscillations thatare monitored by a delayed probe pulse; no-tice the great similarity with gas- and liquid-phase experiments. Using a train of femto-second pulses with a time separation that isin resonance with the oscillation of the crys-tal, Weiner et al. show an enhancement ofthe amplitude of the motion. The datashown in Fig. 22 are the result of excitationwith a series of short pulses [Fig. 22(a)] ap-plied to a crystal along a selected lattice co-ordinate (Weiner et al., 1990). Like someonepushing a child on a swing "on resonancesuch that the child acquires a small amountof energy with every push," the amplitude ofthe crystal oscillation is increased. The effectis shown in Fig. 22 where the femtosecondtrain of pulses sequentially "push" the crystallayers in a certain direction; acquisition ofthis energy is demonstrated by the increasesin the scattering signal [Fig. 22(b) and thesimulation, Fig. 22(d)]. When the train ofpulses is not resonant, the enhancement islost [Fig. 22(c)].

Charge-carrier dynamics in nanoscalesemiconductor materials have also beenstudied with femtosecond pulses. These areof interest due to their potential technologi-cal applications in photocatalysis. Pump-probe experiments can be performed tostudy the primary events of electron trappingin semiconductor nanoclusters (Caveleri etal., 1995; Kashcke et al., 1990). Electron-transfer mechanisms in photovoltaic cellscan also be studied from the transient ab-sorption data. Phonon dynamics, excitons inquantum-well structures, and spin quantumbeats in GaAs heterostructures have alsobeen studied with ultrashort laser excitation(see Further Reading, esp. Chergui, 1996).

pulse excites the ground electronic state ofHgI to the excited B state. Different probewavelengths access different regions of theHgI ground potential and therefore monitordifferent vibrational states of the HgI popu-lation. Note that all vibrational transient sig-nals decay on account of the dephasing ef -fects of the solvent. Compare the data in thepresence of the solvent (Fig. 21) with thedata obtained in the gas phase (Fig. 16).

Another important issue in condensed-phase processes is energy dissipation. Therate of vibrational energy transfer from theexcited solute into the solvent-molecule mo-tions can be described as frictional energyloss, and femtosecond studies allow one tomeasure these relaxation rates. Frictional ef-fects on chemical reactions in the condensedphase such as isomerization of large mole-cules like stilbene can also be examined. Inparticular, comparisons of ultrafast studiesthat monitor the dynamics of stilbene isom-erization both as an isolated molecule and insolution can help to elucidate the effect ofsolvents on intramolecular vibrational redis-tribution (IVR) within stilbene (Sension etat., 1993). Thus, in addition to measuring therate of energy transfer from solute to sol-vent, FTS techniques allow one to study theinfluence of solute-solvent interaction on en-ergy-transfer dynamics (i.e., between differ-ent vibrational modes) within the solute it-self.

One technique to explore solute-solventinteractions is photon-echo spectroscopy(Yang et at., 1995; de Boeij et at., 1995). Herethree sequential ultrashort pulses are used todistinguish between system-bath and vi-bronic dynamics by reason of the differencein time scales. For example, upon optical ex-citation of a solute molecule that subse-quently dephases, one can separate whichdephasing effects occur because of the sol-vent and which occur because of intramolec-ular vibrations. This technique has been ex-ploited in observing dephasing rates of dyemolecules in different solvents.

5.3 Biological

Femtosecond pulse technology has madeinroads in biology as well. Ultrafast pro-cesses such as electron transfer in photosyn-thetic systems can now be studied, includingthe dynamics of primary events in photobio-logical systems such as the conversion of so-lar energy to chemical energy .One of themajor goals in these studies is to learn how

5.2 Solids

Observation of molecular motions in thesolid phase has also been achieved with fem-tosecond pulses. The example chosen to il-lustrate these observations is the impulsivestimulated Raman scattering (ISRS) of an

"""'-

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454 Ultrafast Spectroscopy

Z;-'inc"'

£

d

the energy is distributed, both within themolecule and in the solvent. These studiesare an important complement to structuralstudies of photosynthetic reaction centers,and, in particular, femtosecond studies ofthe vibrational transients show how the pro-cess of electron transfer and vibrational nu-clear dynamics are related. Another impor-tant process in biological systems is protontransfer. Again, as with electron transfer, thisprocess is strongly dependent on the subpi-cosecond solute-solvent interactions, whichcan now be studied with ultrafast pulse tech-niques.

Other applications of ultrafast spectro-scopic techniques to biological molecules in-clude observation of the cis-trans photoisom-erization of rhodopsin, which has beenstudied by examining the transient absorp-tion spectra of an excited wave packet cre-ated by a 35-fs pump pulse (Wang et at.,1994). Specifically, a pump-probe differentialabsorption technique was used whereby the11-cis molecule in the So electronic state ispumped up to the SI state, where the wavepacket can move from its original cis config-uration to the trans configuration whence itdecays back to the ground electronic state[Fig. 23(a)]. As shown in the figure, the cis-trans conformational change is inhibited bya potential barrier in the So state.

However, as the pumped wave packet is acoherent superposition of vibrational states,this wave packet still oscillates coherentlyeven after decaying to the trans conforma-tion in the electronic ground state. These os-cillations are detected at various probe wave-lengths as shown in Fig. 23(b), which excitethe trans molecules back up to the SI state.

9~ -3 a 3 6

Time (ps)

12

FIG. 22. (a) Cross-correlation measurement of a se-quence of femtosecond pulses with a repetition rateof 2.39 THz (419 fs between pulses) producedthrough pulse-shaping techniques. The pulses canrepetitively drive a selected vibrational mode to in-crease the vibrational amplitude. (b) Impulsive stimu-lated Raman scattering (ISRS) data from the a-pery-lene organic molecular crystal driven by a sequenceof (b-polarized) pulses spaced at 419 fs to match thevibrational period of the 80-cm-1 mode. The dif-fracted signal from the mode grows stronger witheach successive pulse, eventually reaching intensitylevels comparable to the strongest electronic re-sponse. Selective amplification of the 80-cm -1 mode

is demonstrated. (c) ISRS data from a-perylenedriven by a sequence of (b-polarized) pulses spacedat 429 fs, slightly off resonance for the 80-cm-1mode. The signal intensity is reduced relative to thatin (a), but the vibrational oscillation period is still 419fs. (d) Simulation of data in (b), assuming a Gaus-sian temporal profile for the excitation pulse train. In(a) through (d), the zero of time is defined as thecenter of the input pulse train. (Weiner et al., 1990.)

GLOSSARY

Coherent: This term describes a systemhaving a well-defined phase relationship inits energy states such that the dynamics canbe clearly measured.

Dephasing: The process of losing coher-ence, i.e., becoming incoherent.

Eigenfunction: In general, a mathemati-cal function that is regenerated to within aconstant when an operator H operates on it.Schrodinger's equation, HI/I = E 1/1, is an ei-genvalue equation where H is the Hamilto-

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455Ultrafast Spectroscopy

~

(a)

nian operator, "' is the eigenfunction, and Eis the eigenvalue (see QUANTUM MECHANICS).

Eigenstate: The wavefunction "' in Schro-dinger's equation represents a characteristicstate (hence, "eigen"-state) of the system de-scribed by the hamiltonian operator H.

IVR: Abbreviation of "intramolecular vi-brational relaxation." A process by which en-ergy deposited in one vibrational mode of amolecule is randomized through the rest ofthe vibrational modes.

Pump-Probe Method: A technique usedin ultrafast spectroscopy based on a pair oflaser pulses. The first pulse, the pump, initi-ates the process of interest, and the secondpulse, the probe, monitors the progress as afunction of delay time between the pumpand probe.

Superposition of States: In quantum me-chanics a superposition of states refers to thelinear sum of eigenfunctions with a well-de-fined phase relationship. A superposition ofstates is time dependent.

Wave Packet: A more or less spatially re-stricted wave, formed by a superposition ofstates.

s~

1000Delay {Is)

2000 3000

(b)

FIG. 23. Ultrafast study of the fundamental steps in-volved in vision. (a) Schematic potential-energy sur-faces for the femtosecond isomerization of rhodopsinafter optical excitation of the molecule from theground state 50 to the excited state 51. The wavepackets in the photoproduct potential well illustratehow the ground-state vibrational motion effects thephotoproduct absorption. The dashed lines indicatethe diabatic pathway along which the reaction pro-ceeds. (b) Differential transient absorption measure-ments probing the photoproduct absorption after ex-citation of rhodopsin with a 35-fs pump pulse at 500nm. Measurements at 620 and 630 nm are multipliedby a factor of 2 for clarity. (Wang et al., 1994.)

Works Cited

Backus, S., Peatross, J., Huang, C. P., Murnane,M. M., Kapteyn, H. C. (1995), Opt. Lett. 20, 2000--2002.

Baltuska, A., Wei, Z., Pshenichnikov, M. S.,Wiersma, D. A. (1997), Opt. Lett. 22, 102-104.

Banin, U., Waldheim, A., Ruhman, s. (1992), J.Chem. Phys. 96, 2416-2419.

Bigot, J.-Y., Portella, M. T., Schoenlin, R. W.,Bardeen, C. J., Migus, A., Shank, C. v. (1991),Phys. Rev. Lett. 66,1138-1141.

Bingemann, D., Ernsting, N. P. (1995), J. Chem.Phys. 102, 2691-2700.

Bowman, R. M., Dantus, M., Zewail, A. H.(1989), Chem. Phys. Lett. 161, 297-302.

Caveleri, J. J., Colombo, Skinner, D. E., Bow-man, R. M. (1995), J. Chem. Phys. 103,5378-5386.

Chesnoy, J., Mokhtari, A. (1988), Phys. Rev. A38, 3566-3576.

Dantus, M., Rosker, M. J., Zewail, A. H. (1987),J. Chem. Phys. 87, 2395-2397.

Dantus, M., Bowman, R. M., Grueble, M., Ze-wail, A. H. (1989), J. Chem. Phys. 91,7437-7450.

Dantus, M., Bowman, R. M., Zewail, A. H.(1990), Nature 343,737-739.

de Boeij, W. P., Pshenichnikov, M. S., Wiersma,D. A. (1995), Chem. Phys. Lett. 247,264-270.

Felker, P. M. (1992), J. Phys. Chem. 96, 7844-7857.

,-..

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456 Ultrafast Spectroscopy

Wang, Q., Schoelein, R. W., Peteanu, L. A.,Mathies, R. A., Shank, C. V. (1994), Science 266,422-424.

Weiner, A. M., Leaird, D. E., Wiederrecht, G.P., Nelson, K. A. (1990), Science 247,1317-1319.

Wittig, C., Zewail, A. H. (1996) in: E. Bernstein,(Ed.), Chemical Reactions in Clusters New York:Oxford.

Yang, T.-S., Vohringer, P., Arnett, D. C.,Scherer, N. F. (1995), J. Chem. Phys. 103, 8346-8359.

Zewail, A. H. (1994), Femtochemistry-UltrafastDynamics of the Chemical Bond, vols. 1,2, Singa-pore: World Scientific.

Zewail, A. H. (1996), J. Phys. Chem. 100,12701-12724.

Zewail, A. H., Dantus, M., Bowman, R. M.,Mokhtari, A. (1992), J. Photochem. Photobiol. A:Chem. 62, 301-309.

Zhu, L., Sage, J. T., Champion, P. M. (1994),Science 266, 629-633.

Further Reading

Barbara, P. F., Knox, W. H., Morou, G. A., Ze-wail, A. H. (Eds.) (1994), Ultrafast Phenomena IX;Berlin: Springer-Verlag.

Barbara, P. F., Fujimoto, J. G., Knox, W. H.,Zinth, W. (Eds.) (1996), Ultrafast Phenomena X,Berlin: Springer-Verlag.

Chergui, Majed (Ed.) (1996), Femtochemistry,Singapore: World Scientific.

EI-Sayed, M: A., Tanaka, I., Molin, Y. N.(1994), Ultrafast Processes in Chemistry and Photo-biology-Chemistry for the 21st Century, Oxford:IUP AC/Blackwell Scientific.

Fleming, G. R. (1986), Chemical Applications ofUltrafast Spectroscopy, New York: Oxford Univ.Press.

Harris, C. B., Ippen, E. P., Mourou, G. A., Ze-wail, A. H. (Eds.) (1990), Ultrafast Phenomena VII,Berlin: Springer-Verlag.

Manz, J., Woste, L. (Eds.) (1995), FemtosecondChemistry, New York: VCH.

Martin, J. L., Migus, A., Morou, G. A., Zewail,A. H. (Eds.) (1992), Ultrafast Phenomena VIII, Ber-lin: Springer-Verlag.

Weirsma, D. A. (Ed.) (1995), FemtosecondChemistry, Weinheim: VCH.

Zewail, A. H. (1994), Femtochemistry-UltrafastDynamics of the Chemical Bond, Vols. 1,2, Singa-pore: World Scientific.

Fe1ker, P. M., Zewail, A. H. (1987), J. Chem.Phys. 86, 2460-2482.

Fleming, G. R. (1986), Chemical Applications ofUltrafast Spectroscopy, New York: Oxford Univ.Press.

Fork, R. L., Brito-Cruz, C. H., Becker, P. C.,Shank, C. V. (1987), Opt. Lett. 12,483-486.

Hashe, T., Ashworth, S. H., Riedle, E., Woener,M., Elsaesser, T. (1995), Chem. Phys. Lett. 244,164-170.

Hoffman, G., Oh, D., Chen, Y., Engel, Y. M.,Wittig, C. (1990), Israel J. Chem. 30, 115-129.

Kaschke, M., Emsting, N. P., Muller, U., Wel-ler, H. (1990), Chem. Phys. Lett. 168, 543-550.

Lienau, C., Zewail, A. H. (1994), Chem. Phys.Lett. 222, 224-232.

Lienau, C., Zewail, A. H. (1996), J. Phys. Chem.100, 18629-18649.

Lienau, C., Williamson, J. C., Zewail, A. H.(1993), Chem. Phys. Lett. 213,289-296.

Liu, Q., Wan, C., Zewail, A. H. (1996), J. Phys.Chem. 100, 18650-18665.

Manz, J., Woste, L. (Eds.) (1995), FemtosecondChemistry, New York: VCH.

Marvet, U., Dantus, M. (1995), Chem. Phys.Lett. 245, 393-399.

Marvet, U., Dantus, M. (1996), Chem. Phys.Lett. 256, 57-62.

Matemy, A., Lienau, C., Zewail, A. H. (1996), J.Phys. Chem. 100, 18666-18682.

Pedersen, S., Herek, J. L., Zewail, A. H. (1994),Science 266, 1359-1364.

Porter, G. (1950), Proc. R. Soc. London A200,284-285.

Pugliano, N., Szarka, A. Z., Hochstrasser, R. M.(1996), J. Chem. Phys. 104, 5062-5079.

Rose, T. S., Rosker, M. J., Zewail, A. H. (1988),J. Chem. Phys. 88,6672-6673.

Rosker, M. J., Wise, F. W., Tang, C. L. (1986),Phys. Rev. Lett. 57, 321-324.

Rosker, M. J., Dantus, M., Zewail, A. H. (1988),Science 241, 1200-1202.

Sension, R. J., Repinec, S. T., Szarka, A. Z.,Hochstrasser, R. M. (1993), J. Chem. Phys. 98,6291-6315.

Sitzmann, E. V., Eisenthal, K. B. (1989). J.Chem. Phys. 90, 2831-2832.

Squier, J., Mourou, G. (1992), Laser FocusWorld (June), 51-60.

Voth, G. A., Hochstrasser, R. M. (1996), J.Chem. Phys. 100, 13034-13049.

Walmsley. I. A.. Tang, C. L. (1990), J. Chem.Phys. 92, 1568-1574.