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Time-resolved molecular imaging

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2016 J. Phys. B: At. Mol. Opt. Phys. 49 112001

(http://iopscience.iop.org/0953-4075/49/11/112001)

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Topical Review

Time-resolved molecular imaging

Junliang Xu, Cosmin I Blaga, Pierre Agostini and Louis F DiMauro

Department of Physics, The Ohio State University, Columbus, OH 43210, USA

E-mail: dimauro.6@osu.edu

Received 19 January 2016, revised 23 March 2016Accepted for publication 31 March 2016Published 6 May 2016

AbstractTime-resolved molecular imaging is a frontier of ultrafast optical science and physical chemistry.In this article, we review present and future key spectroscopic and microscopic techniques forultrafast imaging of molecular dynamics and show their differences and connections. The adventof femtosecond lasers and free electron x-ray lasers bring us closer to this goal, which eventuallywill extend our knowledge about molecular dynamics to the attosecond time domain.

Keywords: strong-field physics, femtosecond intense laser pulses, ultrfast science, electron andx-ray diffraction, x-ray free-electron lasers, time-resolved molecular imaging

(Some figures may appear in colour only in the online journal)

1. Introduction

Filming the nuclear motion during a molecular transformationwith atomic-scale spatio-temporal resolution is the dream ofthe molecular movie director, the ultrafast scientists [1–9].Imaging, or the direct probing of the atomic structure ofmatter, static or dynamic, has always occupied an essentialrole in physical, chemical and biological sciences [10, 11].For decades, the invention of imaging techniques, such aselectron and x-ray diffraction, neutron diffraction, optical andnuclear magnetic resonance spectroscopy, scanning tunnelingmicroscopy and atomic force microscopy, has expanded ourknowledge about static structures of matter, ranging fromsingle molecules to crystals, and from small molecules tomacromolecules such as DNA and proteins, and to cells andviruses [10, 12–16]. Meanwhile, great effort has also beenconsistently made over the last half century to push forwardthe frontier of ultrafast structural determination [3]. With theadvent of femtosecond lasers and extremely bright freeelectron x-ray lasers, monitoring and ultimately controllingmolecular transformations, such as chemical reactions andphase transitions on internuclear length scales with femtose-cond temporal resolutions [3, 17–22] has become possible.

In this review article we will focus mainly on imagingtechniques for gaseous molecules, as well as, single moleculeabsorbed on a substrate which is ideal for prototypical process

studies [23, 24]. We begin with a brief introduction tocrystallography.

2. Static imaging

Atoms and molecules are the building blocks of matter. Withfew exceptions, atoms are rarely found uncombined in naturewhereas molecular compounds are ubiquitous. Moleculesconsist of two or more atoms which are held together byelectrons shared between them, which is known as ‘chemicalbonding’ [25–27]. In chemistry, stable molecular compoundsare often considered as a rigid combinations of atoms with aunique spatial arrangement. Molecules are depicted with aball-and-stick model, with a set of colored balls representingdifferent atoms and the connecting sticks representing thechemical bonds. All chemical bonds and their orientationswhich are associated with bond angles and torsion angles, i.e.,the spatial distribution of all atomic constituents, defines the‘molecular structure.’ According to the bond types, moleculescan be classified as covalent, ionic, etc, and for covalentcompounds, the chemical bonds come in single, double, andtriple varieties based on the bond order. For any type ofbonds, the typical bond lengths are on the order of the atomicsize, which is about 1Å [28]. The microscopic structure ofmatter, especially the spatial arrangement of atoms in a

Journal of Physics B: Atomic, Molecular and Optical Physics

J. Phys. B: At. Mol. Opt. Phys. 49 (2016) 112001 (17pp) doi:10.1088/0953-4075/49/11/112001

0953-4075/16/112001+17$33.00 © 2016 IOP Publishing Ltd Printed in the UK1

molecule, is essential to its physical and chemical propertiesand is the starting point to study its electronic, vibrational, androtational spectrum, possible isomeric configurations, che-mical reactivity and functions [28].

2.1. Different imaging techniques and typical imaging probes

Ever since the birth of the theory of quantum mechanics,different imaging techniques have been developed to deter-mine the microscopic structure of a molecule in equilibrium.For instance, the revelation of the wave nature of all particlesleads to diffraction methods using light mass particles such aselectrons and neutrons, which are analogous to x-ray dif-fraction. In addition, the discovery of classically forbiddenquantum tunneling led to the development of novel methodssuch as the scanning tunneling microscope (STM) [29]. Thetwo types of methods, diffraction and STM, are com-plementary: the former measures patterns in momentumtransfer space, whereas the latter sees molecules in real space.Meanwhile, spectroscopic techniques based on measuringenergy or mass spectra of molecules have also been inventedand have offered us abundant, yet indirect information aboutthe molecular structure [30]. They were later developed as anew ‘direct’ imaging technique, called Coulomb explosionimaging (CEI), by integrating the spatial distribution of thefragment masses into the energy and mass spectra [31].

Among all these techniques, electrons and photons aremost commonly used as structure probes. In the followingpart of this section, most of the discussion will be devoted todescribing the leading imaging methods, namely electron andx-ray diffraction, whereas all other techniques are introducedbriefly.

2.2. Conventional electron diffraction (CED), synchrotron-radiation-based x-ray diffraction and x-ray crystallography

Among all the conventional imaging techniques, electron andx-ray diffraction are the two principal experimental probes formolecular structure determination, providing knowledgeabout static geometrical configurations of almost all smallmolecules, crystals, and most biomolecules [12, 14, 32, 33].Electrons and photons, strongly interacting with either theatomic cores in the molecule or electronic charge densitycloud are scattered from the molecule, producing a spatialdiffraction pattern, that bears the imprint of molecular struc-ture. To extract the structural information from the measureddiffraction pattern, a Fourier-transform-based inversion pro-cedure is usually employed. To the present day, electron andx-ray diffraction still serve as the major probes in stereo-chemical experiments, and routinely achieve atomic scalespatial resolutions [18, 34, 35].

Both electron and x-ray diffraction microscopes havebeen invented for about one century. Usage of x-ray photonsto study the molecular structure, especially for crystallinemolecules, is attributed to Von Laue’s discovery of x-raydiffraction from crystals in 1912. One year later, Bragg andragg proposed the law of diffraction from crystals, known asBragg’s law, and started to use x-rays to determine the

structural constants of single crystals such as NaCl1. Thismethod later was developed into a powerful imaging techni-que, x-ray crystallography, to determine the atomic positionsinside the unit cells of a crystal, and has since made a tre-mendous impact in physics, chemistry, biology and otherfields [13, 36, 37]. The idea of using electrons as probes isrooted in the revolutionary concept that electron has wave/particle duality in early 1920s, which along with otherground-breaking ideas marked the beginning of a newquantum era [12]. The first electron diffraction investigationof structural determination was carried out in 1930 by Markand Wierl who investigated carbon tetrachloride in gas phase,thus initiating the field of gas-phase electron diffraction(GED) [38].

Electron and x-ray diffraction have many similarities, butalso have some sharp differences. To acquire a good spatialresolution, both techniques use high energy electrons orphotons as probes, to ensure the probe’s de Broglie wave-length is comparable to the size of a chemical bond, which isabout 1Å. Typically, externally prepared and collimatedbeams of electrons or x-rays with energies of tens to hundredsof keV and few to tens of keVs, respectively are used. Bothtechniques employ elastic scattering, and at these incidentenergies, both electrons and photons interact mainly with theatomic core whereas the valence electrons can be treated asessentially transparent. Under these conditions, the interactionof the impinging beam with each atom of the molecular targetis often described using the so-called independent atom model(IAM) [12, 39, 40] so that the diffraction pattern does notdepend on the nature of the chemical bond but only on thedistances between the atomic nuclei. Electrons or photons areelastically scattered off the molecule producing a diffractionspectrum in momentum space, which is subsequently inver-sely transformed into an atomic position map in real space byan inverse sine transform for electrons and Fourier transformfor x-rays. On the other hand, since electrons possess chargetheir scattering cross section is 5–6 orders of magnitudehigher than that of x-rays [12, 41]. Consequently, electrondiffraction is better suited for studying small molecules in thegas phase, thin films and surfaces [10, 19]. In turn, the lowerscattering cross section of x-rays leads to long mean freepaths in bulk samples, so it is easier to apply x-ray diffractionto molecules in condensed phases and macromolecules suchas DNA and proteins. Thus far, GED and x-ray crystal-lography complement, rather than compete with each other,providing most of our knowledge of static molecular struc-tures. One of the latest works in x-ray crystallography is theinvestigation of the subunit structures of the ribosome, aprotein-making machine, by Ramakrishnan, Steitz, andYonath, who were jointly awarded the 2009 Nobel Prize inChemistry2.

In state-of-the-art GED, the internuclear distancesobtained could be accurate to the order of 0.001Å, which canbe further improved after a careful error analysis, by takinginto account several sources of errors, e.g., effects of

1 http://nobelprize.org/nobel_prizes/physics/laureates/1915/.2 http://nobelprize.org/nobel_prizes/chemistry/laureates/2009/.

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anharmonic vibrations [12]. However, GED is typically car-ried out for randomly oriented (i.e., isotropic) molecules,therefore the retrieved structural information is restricted toone-dimensional radial distribution function, i.e., internucleardistances. To reconstruct the stereo-structure of a molecule, ingeneral, molecular alignment is required [10, 42], which willbe discussed in detail in subsequent sections. By contrast, incrystals, molecules are perfectly lined up, so x-ray crystal-lography can determine three-dimensional structures withmuch less ambiguity than GED. While, the spatial resolutionit achieved is a little inferior to that of GED, about 0.01Å infavorable cases, using a single crystal sample of sufficient size(typically 1 mm×1 mm×1 mm) and high flatness[13, 37, 43]. X-ray diffraction analysis of molecular structuresis greatly limited by the crystal size and the x-ray photon flux[13]. For instance, the intensities of Bragg peaks are pro-portional to N2, where N is the total number of unit cells in thecrystal and as a result, the strength of diffraction signalsdecreases parabolically with the crystal size. Unfortunately,for many important molecules of interest, especially biomo-lecules such as membrane proteins, it is particularly challen-ging to grow large enough crystals of good quality[19, 37, 44]. To obtain diffraction signals of adequate quality,reducing the size of crystals in turn requires an necessaryincrease in x-ray dose. Today, the best x-ray sources utilizesynchrotron radiation from relativistic electron beams instorage rings. Its low photon flux leads to a scattering signalmuch weaker than that of GED, greatly limiting the spatialresolution that can be achieved. An additional problem forsmall crystals is the radiation damage, which can causedeterioration of the samples due to the long exposure timeneeded to obtain a diffraction image with high contrast [45].New x-ray sources with high intensities generated by freeelectron lasers (FELs) [46, 47] and methods such as thelensless coherent diffractive imaging (CEI) and femtosecondx-ray diffraction have been proposed to overcome the diffi-culties of x-ray diffraction [17, 48], which will be described inmore details in the following session. To date, spatial reso-lutions for micrometer- and nanometer-sized objects obtainedusing x-ray FELs range from few to tens of nanometers andfurther improvements being predicted [44, 48]. Miao et al[49] has predicted theoretically that with the above newtechniques, the resolution can reach up to 2.5Å for sub-micrometer biomeolcules.

2.3. STM and atomic force microscopy

The STM is an important application based on the quantumtunneling effect. It was invented in early 1980s by GerdBinnig and Heinrich Rohrer at IBM Zürich [50, 51] whichlater won them the Nobel Prize in Physics in 19863. A STMtypically consists of a sharp metal tip rastering above thesurface of a conducting sample. When a bias voltage isapplied, electrons can tunnel across the vacuum gap betweenthe tip and the surface, thus producing a steady macroscopiccurrent which depends very sensitively on the tip-sample

distance. By moving the fine tip around over the surface, onecan obtain topographic image of the surface. It should benoted that STM images do not always show the positions ofthe atoms on the surface, as it does not probe the nuclearposition directly, but rather it is a probe of the electron den-sity. Under ideal conditions, e.g. in an ultrahigh vacuumcryogenic environment and if the surface is composed of thesame atoms, the STM allows a very precise mapping of thesurface of the sample with a lateral and vertical resolutions of1Å and 0.1Å, respectively [52].

The STM has already become a useful tool in surfacescience to image the atomic-scale features on the surfaces.However, its application in structure visualization is mainlylimited to metals and semiconductors due to the requirementof the sample conductivity. Right after the invention of theSTM, the idea of atomic force microscope (AFM) wasdeveloped by Calvin Quate and Gerd Binnig in 1986 toextend the STM technique to investigate the electrically non-conductive materials, such as proteins, which are deposited ona metal substrate [53]. The AFM sensor measures the atomicinteraction forces between the tip and the surface instead ofthe tunneling current, which may be either the short-rangerepulsive force in contact mode or the long-range attractiveforces in non-contact mode. In fact, the STM technique hasalso been extended to non-conductive samples by immobi-lizing them on a metal surface. Nevertheless it remains quite achallenge for STM to resolve the internal structures within theadsorbed molecule because the tunneling current is primarilysensitive to the local electron density of states close to theFermi level which extends over the entire molecule. Bycontrast, AFM can not only resolve single atoms in themolecule [54, 55], but also identify the fractional differencesin the chemical bond order [56] and resolve the thermallyinduced complex bond rearrangement [57] (a slow reactionprocess).

2.4. Coulomb explosion imaging (CEI)

Although diffraction and microscopy techniques have provenresolving power capability, the rise of modern molecularscience, especially the formation of the fundamental mole-cular structure theory, is inseparable from remarkable con-tributions of the spectroscopic and fragmentation methods.Although spectroscopic measurements do not provide directaccess to molecular geometries, this limitation can be over-passed by measuring the correlated velocity vectors of allfragment ions while measuring their masses and energies.This new technique, CEI, was invented jointly by ArgonneNational Laboratory in USA and the Weizmann Institute ofScience in Isreal in 1979 [58]. In its original design [31], anensemble of prepared molecular ions is accelerated to avelocity close to the speed of light (∼MeV in energy) andthen pass through a thin solid film. All of the outer bindingelectrons of the projectile molecular ion will be inelasticallyscattered into large angles by dense atoms in the foil andrapidly stripped after penetrating a few atomic layers. Theresulting aggregate of positive nuclear ions explodes owing tothe mutual Coulomb repulsion. Once the three-dimensional3 http://nobelprize.org/nobel_prizes/physics/laureates/1986/.

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fragment momenta is recorded and the fragmentation channelis identified, one can reconstruct the molecular geometry atthe moment of the Coulomb explosion. This requires a rapidionization of the molecule to mark the zero time. Typically,the time-scale of the stripping process is on order of 0.1 fs,much faster than the characteristic vibrational motions of themolecule (∼10 fs), thus the whole molecule still stays intactwhen the electrons are stripped off [31]. Another version ofCEI is to fragment the molecule via collision with slow highlycharged ions instead of the foil [59–61]. This extends the CEIto neutral molecules and reduces the costs of the preparationof high-speed molecular ions.

CEI is an effective and straightforward tool to retrievemolecular structural properties, requiring no a priorassumptions about the molecule. However, by design, bothtypes of CEI discussed above can only be applied to smallmolecules in gas phases. For large molecules, the fragmen-tating processes (multiple channels or stepwise fragmenta-tion) tends to be complicated and on a technical level, theincreasing number of fragments also reduces the detectionefficiencies of the coincidence sensor. Moreover, although theCEI technique can provide the atomically resolved image ofthe molecule, the overall spatial resolution it can offer is alittle inferior to that of diffraction and STM/AFM techniques.Therefore CEI is not as widely used as other techniques formolecular structure retrieval.

Nevertheless, CEI still has important applications. One isthe direct visualization of the stereostructure of gas-phasemolecules without aligning them. It has been employed todetermine the molecular bond angles [62] and the chirality ofenantiomers [63, 64]. Another very important aspect of theCEI technique is that it directly measures the momentumdistribution of each fragment, which, when transformed backinto the initial spatial configuration of the molecule, preservesnot only the peak position of each nuclei, but also the densityof the nuclear wave packets. This aspect leads to one uniqueapplication of CEI to image the non-classical molecularstructures [30, 31], e.g., the bridged structure in C2H

+3 and

highly excited molecules with large amplitude vibrationswhich cannot be described using the ball-and-stick model.

3. Time-resolved molecular imaging

3.1. Introduction

Despite the great successes achieved in determining the staticstructure of molecules during last century, chemistry is notjust about the chemical bonding at equilibrium, but also, moreimportantly, about the far-off-equilibrium dynamics and howthose bonds break, form and rotate, that is, chemical reac-tions. The concepts of atomic structure of matter, especiallythe nature of chemical bonding, were well established morethan a half century ago [25–27], and ever since, the theoreticalstudy of structural transformations of a molecule, e.g. trans-ition-state theory formulated by Eyring, Evans and Polanyi in1935 [65, 66], has never been halted [23, 24, 67–69]. Theworld is intrinsically dynamic, and static images of matter do

not always tell how things happen. In experiments, scientistsare not just satisfied with chemistry on macro-scale carriedout by using test tubs and solvents, but also want to under-stand on a atomic/molecular level how a chemical reactiontakes place and how chemical reactants proceed to products. Ithas become a dream of chemical physicists to directly ‘watch’experimentally the migration of atoms during a chemicalreaction, conformational dynamics, or other kinds of mole-cular processes.

3.1.1. Time scales and spatio-temporal resolutionrequirements. Typically molecular transformations involvesthe motion of atoms, which are on the femtosecond time scale,e.g., the molecular vibrational period is about tens offemtoseconds [70]. The time scale of a real reaction processvaries from few tens of femtoseconds to hundreds ofpicoseconds, depending on the size of molecules and thetype of reactions [71–74], but the elementary step (calledelementary reaction) typically takes place on sub-picosecondtime scale [74, 75]. In order to capture atomic motions in themolecular reaction, one generally needs a ‘camera’ with a‘shutter speed’ on the order of one femtosecond. To make thedirect exploration of ultrafast molecular dynamics a reality, thedynamical imaging techniques are required to havefemtosecond time resolution as well as a sub-Ångströmspatial resolution. If electrons or photons are used as probes,the probing pulses should have a pulse duration of tens offemtoseconds or below and a central wavelength compatiblewith the size of the chemical bonds.

3.1.2. Ultrafast laser technology. The generation of ultrashortpulses is a revolutionary development that impacts numerousareas of science by opening new avenues of research.Experimental observation of molecular dynamics on theatomic level did not come true until 1980s when thetechnology of pulse compression became available, whichcan reduce the optical pulse widths to sub-picosecond [70].The ultrashort laser pulses cannot only be used to excite asubstantial fraction of one of the reactant species in amolecular beam to initiate the dynamics, but also to align orCoulomb explode the molecule [76] and generate ultrashortelectron or x-ray pulses [77–80]. The nonlinear interaction ofintense lasers with matter, especially the rescatteringphenomena [81, 82], offers possibilities of new ways fordynamic molecular imaging [83, 84]. Furthermore, the abilityto generate even shorter pulses down to attosecond (10−18 s)timescales [85, 86] can be a tool to ‘steer’ chemical reactionsat the level of electrons, allowing not only to visualize achemical reaction, but also ultimately to control it. Nowadaysultrafast and high-power lasers operating in the UV, visibleand IR spectrum are widely available in universitylaboratories, and have been extensively used in the study ofultrafast processes on the timescale of nanoseconds tofemtoseconds.

3.1.3. Pump-probe scheme. For imaging ultrafast processes,it is crucial to clock the event (atomic motion) by defining the

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zero of time and synchronize the event with the ‘camera’ on afemtosecond time scale [87]. This can be achieved within apump-probe configuration, where a reaction is initiated by anultrashort optical pump pulse followed by a second ultrashortprobe pulse to monitor the progress of the reaction at a timedelay between the two pulses. Repeating the experiment in acontrolled sequence of time delays will map out the time-dependent structural changes and reveal the rich dynamicalinformation that static imaging can never provide. Originallydesigned for optical pump and optical probe, known as time-resolved pump-probe spectroscopy, the technique wassubsequently generalized into new methods by replacing theoptical probe pulse by a different type of probe, e.g. ultrafastelectron diffraction (UED) and time-resolved x-ray diffraction[10, 22, 70]. The time resolution is determined by the durationof the probe pulse, and with the pump and probe technique, atime resolution in the femtosecond range can be achieved,even when the detector has a much slower time constant.

3.1.4. Molecular alignment. For gas-phase structural studies,the alignment of molecular systems are generally required toimprove the contrast of the image signals and moreimportantly to allow three-dimensional imaging of themolecule [10, 88–90]. Molecules can be aligned along afixed direction in the laboratory frame using either intense dc-fields [91] or ac-fields [92], e.g. optical. Extensiveinvestigations have been performed by numerous groupsand the reader is referred to the excellent review paper byStapelfeldt and Seideman [90] for a more comprehensivetreatment. Nonetheless molecular alignment by an intenselaser field is suitable for time-resolved dynamic studies.Generally, laser-induced molecular alignment has beenimplemented in two different ways, adiabatic and impulsivealignment. The method of adiabatic alignment [93] whichuses long laser pulses, although effective, has the drawbackthat the molecular alignment is lost as the laser pulse turns off.A typical rotational period is a few picoseconds thus thealignment pulse’s duration must also be this long, whichinevitably causes the temporal overlap between the alignmentpulse and the pump/probe pulses and immediately results inlose of ability to ‘clock’ the ultrafast dynamics. In contrast,impulsive alignment uses ultrafast laser pulses [94, 95]. Thesharp turn-on of the laser pulses transfers a large amount ofangular momentum to the system and thus alignment existsonly after the turn-off. It has the major advantage ofproducing aligned molecules in a field-free state and allowsthe temporal isolation of the aligning pulse from the pump/probe pulses to avoid any unwanted two-color effects. Nodoubt that impulsive alignment, which can be easilyintegrated into the pump-probe scheme, is more suitable fordynamic molecular imaging.

3.2. Optical pump-probe spectroscopy

Spectroscopy is nowadays a major and matured experimentaltool for investigating many properties of atoms and mole-cules. For instance, from the absorption/emission spectrum ofa free atom or molecule allows one to determine the energy

levels, the transition dipole moments and polarizabilities ofthe target system. For molecules of small sizes and highsymmetries, spectroscopy has been used to find molecularvibrational frequencies and rotational constants (principlemoments of inertia), and then to infer (based on simpleclassical models) the molecular structures (bond lengths, bondangles, and conformations) and its potential energy surface(PES) [96]. Spectroscopy contributed significantly to theemergence and development of quantum mechanism, andwhen it was combined with femtosecond laser pulses, itpioneered the study of the time-resolved structural dynamics.

Using femtosecond laser pulses, the first time-resolvedspectroscopic measurement was the study of short-livedtransition states (transient states) in unimolecular systems. In1985, reaction dynamics, photodissociation (photo-fragmentation) of the ICN molecule in gas phase was firststudied by Zewail’s group [71]. The dissociation process wastriggered and clocked by an optical ultraviolet pump pulseand the reaction progress was monitored by a second opticalultraviolet probe pulse which arrived at different time delayswith respect to the clock pump pulse. They were not able todirectly observe the ICN transient due to the long pulseduration ∼400 fs, but were able to detect the rise of the finalproduct. Soon after, in 1987, with the help of one tenthshorter optical pulses this issue was resolved and they wereable to resolve in real time the transition-state configurationenroute to the dissociation [72, 97, 98]. These seminalfindings established the new technique, referred as femtose-cond transition-state spectroscopy, applied successfully inlater studies to more complicated systems whose dynamicsinvolved two PESs (NaI, NaBr) [72, 99] and substitutionreactions with a saddle-point transition state (IHgI) [100]. Forthis work Dr Zewail was awarded the 1999 Nobel Prize inChemistry ‘for his studies of the transition states of chemicalreactions using femtosecond spectroscopy’4, which enhancedunderstanding of many reactions and opens up a new field offemtochemistry.

However, for optical pump-probe spectroscopy, the sig-nals are sensitive to only specific energy states of a moleculeor one of its functional groups [102, 103]. The analysis ofsuch signals usually requires the full knowledge of theinvolved reacting PESs, especially the reaction coordinates(reaction paths) and the dipole coupling between differentPESs, which are not always available or easy to obtain.Moreover, except for a few favorable cases of small mole-cules, such optical probe measurements can seldom lead tothe desired real-time picture of the molecular dynamics as fora molecule in general it is a challenging job to convert theoptical observables into structural information, e.g., bondlengths, bond angles and torsion angles. Nevertheless, asfemtosecond infrared and x-ray pulses with sufficiently shortpulse duration and high flux become available, due to its easyimplementation, operation and strong signal sensitivity,nowadays the time-resolved optical pump-probe spectroscopyand all its derivatives (e.g. mass, kinetic energy, photoelec-tron spectroscopy) are still the most commonly used

4 http://nobelprize.org/nobel_prizes/chemistry/laureates/1999/.

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experimental techniques to trace the ultrafast moleculardynamics and even the electron dynamics [102–113].

3.3. Time-resolved electron and x-ray diffraction

Different from spectroscopic methods, which provide directaccess to the molecular energy spectrum, diffraction techni-ques are more sensitive to the nuclear positions within themolecule. Therefore electrons and x-ray photons are still thepreferred probe to directly ‘see’ the transient positions ofatoms inside a molecule. For this purpose, ultrafast temporalresolutions need to be introduced into the electron and x-raydiffraction, and femtosecond ultrashort electron or x-raypulses are generally required [114–116]. It is necessary topoint out that both electron and x-ray diffraction dominate thetime-resolved studies of structural dynamics and the majorityof those studies were performed on systems in condensedphase. A comprehensive literature exists on history and newdevelopment of the two techniques [1, 2, 18, 19, 35, 116–118], so here we will give only a brief description bothmethods and mainly focus on gas-phase studies.

3.3.1. UED and single electron diffraction. The firstexperimental GED study on ultrafast dynamics was performedby Ischenko and coworkers in 1983 using the stroboscopictechnique, in which the electron sources were generated usingthermal emission [119]. The photodissociation of CF3I in whichthe iodine atom is eliminated was studied by observing changesin the diffraction pattern. However, the temporal resolution waslimited by the electronics to sub-μs, far larger than thefemtosecond requirement required to resolve any detailedreaction dynamics.

Again, the big breakthrough in time resolution improve-ment was brought up in 1980s by the laser pulse compressiontechnique. The newly available femtosecond optical laserpulses were soon used to generate ultrashort electron pulsesvia the photoelectron effect [77, 120, 121] and successfullyreduced the electron pulse duration to picosecond level.

The representative method of time-resolved electrondiffraction is UED, developed from the static imagingtechnique of GED [10, 87, 88, 122]. UED experiments havebeen performed in a number of laboratories in the last decadeor so. In UED, electron pulses are generated by femtosecondlasers from photocathodes and accelerated to tens or hundredsof keVs [123, 124]. Important applications of UED haveprovided structural changes on atomic level of molecules inchemical reactions. The first direct observation of transientstructural changes in gas phase was done by Zewail’s group atCaltech in 1999 when the elimination reaction of 1,2-diiodotetrafluoroethane (C2F4I2) was the focus of interest.With a temporal resolution less than 10 ps, they were able totrace the structural details of C2F4I2 in the course of thereaction and succeeded to observe the non-bridged structureof the reactive intermediate C2F4I after one iodine atom wasremoved from C2F4I2 [125, 126]. Six years later, UED wasapplied to several aromatic molecules by the same group anddetermined the dark structures, one important intermediatestructures in chemistry, formed through radiationless

transitions [127]. The most recent application of UED is byCenturion’s group to structure changes of transient-excitedstates of laser-aligned gaseous CS2 molecule [128].

The time resolution was pushed down to sub-picosecond(about 600 fs) for the first time by Siwick et al in 2003 for thestudy of structural evolution of aluminum undergoing a laser-induced melting phase transition [129]. However, sub-picosecond resolution is still relatively poor compared withthe timescales of many fundamental chemical molecularprocesses. The main limitation stems from the repulsionbetween electrons in one pulse, known as space chargeeffects. This effect limits the brievety of the electron pulse,leading to difficulties to break the femtosecond barrier forUED [10, 130]. Pulsed relativistic electrons (energy ∼MeV)have been proven to suppress the space charge effect andobtain a sub-100 fs pulse duration with a brightness of 108

electrons/pulse, but this technique is still under developmentand its spatial and temporal resolving power needs to befurther confirmed [18, 131]. In summary, up to date,application of UED is limited to probing slow dynamicstimescales longer than a picosecond.

3.3.2. Time-resolved x-ray diffraction. For time-resolvedx-ray diffraction, laser-driven plasma-based femtosecondhard x-ray pulses (100 to 500 fs) have been utilized toexperimentally study the dynamics of phonons and phasetransitions in simple solid systems [132, 133]. But to date, thelow photon flux (104–108 photons per pulse) prohibits theobservation of atomic details of the sample [80, 116].Synchrotron can generate x-ray pulses with a higherintensity (109–1010 photons per pulse), and have been usedfor years to study structural processes in solids, e.g.annealing, crystallization or shock propagation [39, 134–138]. Nonetheless, the shortest pulse duration obtained is∼100 ps, far from the femtosecond requirement [19, 116].

In practice, x-ray pulses generated from either laser-driven plasma or synchrotron radiation are not suitable forphotochemistry studies in gas phase due to the insufficientphoton flux. Consequently, time-resolved x-ray diffraction ofgaseous targets did not materialize until the advent of thex-ray free electron lasers [139, 140], which will be discussedin the next subsection. It is worth noting that femtosecondx-ray pulses are needed not only for the purpose of resolution,but also for avoiding x-ray irradiated damage on crystallinesamples due to the long exposure time. The damage processesusually occurs on order of tens of femtosecond topicoseconds, so diffraction has to terminate before damagebegins [141, 142].

3.3.3. Perspectives for time-resolved electron and x-raydiffraction. Overall, although electron and x-ray diffractiongive good spatial resolutions in their respective fields, themajor limitation of both techniques is their relatively poortemporal resolutions. How to circumvent this limitation andobtain the required femtosecond temporal resolution, i.e., how

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to make femtosecond electron or x-ray pulses, is the mainexperimental challenge in modern time-resolved diffraction.

For electron diffraction, single particle diffraction hasbeen proposed as a new approach to improve the timeresolution [10, 124]. It is known that a single electron packetis fully coherent [10], and moreover, there is no space chargeeffect as there is only one electron in each pulse. Recently,laser-induced photoelectron emission from metal surfacessucceeded to generate femtosecond single-electron pulses, animportant breakthrough in ultrafast atomic-scale imaging[79, 143, 144]. However, the application of this method togaseous molecules is still under development and needs moreinvestigation.

For x-ray diffraction, the newly developed FELs generateintense ultrashort x-ray pulses and greatly extend x-raydiffraction microscopy to the femtosecond realm with spatialresolutions on the atomic scale [17, 19]. It has been reportedthat ultrabright (more than 1012 photons per pulse) x-raypulses at a wavelength of 0.69 nm with durations of 10, 70,and 200 fs have been available in linac coherent light source(LCLS) at SLAC [44]. The unprecedented high x-ray photonflux lifts the limitation on the size of the crystalline molecules[145] and recently the structures of nanocrystals has beenreported [44]. This promising development is currentlyviewed as a stepping stone for further investigations ofmolecules in liquid and gas phase, with the potential to evenimage a single macromolecule in a single shot [19], whichleads to a new powerful imaging approach, coherentdiffractive imaging (CDI) [48]. CDI borrows the idea ofphase retrieval from the traditional x-ray crystallography andextends the x-ray diffraction to non-crystalline specimenswith the ultimate goal to achieve high-resolution single-particle imaging [146, 147]. Single-shot diffraction ofnanoscale systems with x-ray FELs has been carried out atFLASH to image an artifacial structure on a Si3N4 membrane[142] and at LCLS to image a living single mimivirusparticles [148]. Both experiments achieved a nanometer-scalespatial resolution and demonstrated that the diffractionterminated before the onset of radiation damage (diffraction-before-destruction [141]).

A pioneering time-resolved gas-phase x-ray diffractionexperiment was carried out by Minitti et al at LCLS to studythe ring-opening reaction of 1,3-cyclohexadiene to formlinear 1,3,5-hexatriene [140]. The reaction was triggered bythe absorption of a 267 nm optical pump photon and thestructural evolution was monitored by a time-delayed x-rayprobe (8.3 keV, 30 fs, 1012 photons/pulse). Dramatic changeswere observed in the difference scattering signal within 200 fsafter the reaction was initiated, thus revealing ultrafastchanges in the molecular structures. Although the analysisof the experimental data heavily relies on quantum chemicalcomputations, there is no doubt that this experiment made acritical step toward the goal of femtosecond imaging ofchemical reactions and opens up a new direction in studies ofultrafast chemical reactions in gas phase.

Although one must be optimistic about future develop-ments of x-ray FEL technology, FEL-based x-ray diffractionhas yet to achieve atomic scale spatio-temporal resolution for

single molecules [7]. Furthermore, x-ray FELs are costlylarge-scale facilities (LCLS at Stanford SLAC and EuropeanXFEL at DESY in Hamburg) where beamtime is limited, sodeveloping other techniques in general and table-top inparticular is desired.

3.4. Ultrafast x-ray spectroscopy: imaging molecules fromwithin

X-ray absorption spectroscopy (XAS) is an imaging tooldifferent from other spectroscopic methods. The history ofXAS mirrors the development of synchrotron technology.XAS is based on the photoionization of core atomic electronsfrom within a molecule and measures the x-ray absorptioncoefficient as a function of x-ray photon energy. A typicalx-ray absorption spectrum consists of a sharp peak (absorp-tion edge) followed by a series of downward oscillations, socalled x-ray absorption fine structure (XAFS), caused by theinternal scattering and interference of the outgoing photo-electron waves. In 1971, Sayers and coworkers revealed thatthe fine structure can be inverted into geometric structuralinformation based on Fourier analysis [149]. Since then, twoimportant imaging techniques emerged out of XAS: the near-edge x-ray absorption fine structure (NEXAFS) by using thelow-energy part of the XAFS and the extended x-rayabsorption fine structure (EXAFS) by using the high-energypart [8, 150, 151]. Both near- and extended-edge fine struc-tures have the similar physical origin (intermolecular scat-tering), but only NEXAFS has the additional benefit ofdelivering information about the electronic structure as itsfeatures originate from core-valence transitions [152].

Time-resolved XAS with microsecond to picosecondresolutions is routinely achieved for crystals, bulk amorphousmaterials and molecules in liquids [8, 153–158]. Femtosecondtime resolution was obtained recently by Bressler and co-workers in studying the light-induced spin crossoverdynamics in an iron(II)-based complex [152]. However, dueto the low molecular density in gas phase, it is challenging toconduct time-resolved gas-phase NEXAFS/EXAFS experi-ments, although the reliability of the gas-phase EXAFS havebeen demonstrated experimentally in the static case [159].The first attempt was made by Ráksi and co-workers to probethe photoinduced dissociation process of gas phase SF6molecules near the K-edge of sulfur using 1.5–3 ps x-raypulses from a plasma source, but no real-space images of thetransient structure were reconstructed [160].

To push XAS toward the limit of isolated molecules, onemay have to rely on brighter sources, e.g. using x-ray pulsesgenerated from x-ray FELs. Alternatively methods byexploring other aspects of the x-ray absorption such as usingphotoelectrons are being developed: intramolecular photo-electron diffraction (IPD) [161], photoelectron holography(PH) [41], and time-resolved photoelectron diffraction[162, 163].

Intramolecular photoelectron diffraction. IPD is basedon the fact that if the intramolecular interference pattern of theoutgoing photoelectron exists on the x-ray absorption spec-trum, it should also manifest itself on the energy-resolved

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photoelectron spectrum. This was confirmed experimentallyby Söderström et al who measured the core photoelectronspectrum against the photoelectron energy of three chlori-nated ethane molecules (CH3CH -x3 Clx) and observed an‘EXAFS-like’ oscillation on the photoionization crosssections that was interpreted as an interference pattern of thephotoelectron diffraction [163]. The effect of photoelectrondiffraction was also observed in the vibrationally resolvedphotoionization cross sections of gas-phase CF4, BF3 andCH4 by Ueda et al [161] who successfully retrieved molecularbond lengths with a sub-Å resolution [165].

Photoelectron holography. PH was first proposed byKrasniqi et al [41]. The physical mechanism behind it isessentially the same as in IPD, except that the PH measures theangular distribution of the photoelectron at a fixed kineticenergy. It has been experimentally confirmed in 2001 that arichly structured photoelectron diffraction pattern was presentin the angular distributions of the K-shell photoemission fromgaseous CO and N2 molecules [166, 167]. The spatial resol-ving capability has been demonstrated in theory [41] to be onÅngström level. In addition, optimal theoretical PH parameterswere proposed in order to improve the quality of the recon-structed image [168], although to our knowledge no exper-imental verification has been reported.

Time-resolved photoelectron diffraction. Time-resolvedphotoelectron diffraction on laser-aligned molecules in gasphase was soon proposed by combining both proposalsabove, which requires a measurement of both energy- andangle-resolved photoelectron spectrum [162, 163] within asingle shot of an x-ray pulse. This idea is currently beingtested experimentally but no signature of transient structurehas been reported yet [169–171].

The main and common limitation of XAS-based techni-ques is the short probing range, i.e. only the local instead ofthe full structure of the molecule can be probed. Nevertheless,these techniques also have strong advantages: they are veryselective on atomic species and can be implemented in anytype of medium. With the availability of femtosecond x-raypulses generated from FELs, one is optimistic about theextended application of these XAS-based imaging techniquesfor femtochemistry studies in gas phase.

3.5. Emergence of new ultrafast laser-based imaging tools

There is no doubt that development of novel ultrafast lasertechniques has always been and continues to be a major thrustof time-resolved transient molecular dynamics [84, 107, 172–177]. Presently, high-intensity femtosecond optical lasersoperating at various wavelengths are available in universitylaboratories worldwide. Naturally, giving the inherent brevityof these laser pulses, integrating them with traditional staticimaging methods could provide the desired ultrafast temporalresolution. For instance, by mating with femtosecond lasers,scanning tunneling miscroscopy has been greatly extended tothe picosecond and sub-picosecond time domain [178–189].

3.5.1. Laser-assisted electron diffraction (LAED). LAED is avariant of GED developed to achieve the femtosecond

temporal resolution not by using ultrashort electron pulses,but by a laser-assisted electron scattering (LAES) process. In2010, an experiment in which a 1 keV electron beam scatteredby Xe atoms in the presence of an ultrashort infrared intenselaser field (intensity ∼1011–1012W cm−2) was reported byKanya et al [190]. The authors were able to observe sidesignals (though weak) around the incident electron energy inthe diffraction image with the kinetic energy shift of wn(w is the photon energy). The side structures are formedwhen the scattered electron gains or loses during the collisionan energy equal to an integer number of photons due to theinteraction of the incident electron beam with the assistedlaser field. Therefore, the side signals conveys structuralinformation of the target where the LAES process acts as anultrafast optical gate.

Four years later, a substantial step was taken by the samegroup towards femtosecond molecular imaging [191], inwhich gas-phase CCl4 molecules were probed by 15 ps, 1 keVelectron pulses assited by a femtosecond near-infrared laserfield with a controlled time delayDt (D =t 0 is defined as themaxima of the two pulses overlap). Scattering images wererecored in the forward direction over an angular range of

q 2.5 12.5 at D = -t 70 ps, 0 ps, +70 ps, respec-tively, with clear LAES signals seen only atD =t 0, depictedin figures 1(a)–(c). In figures 1(e), (f), the angle-resolvedLAED patterns were also extracted in good agreement withtheoretical predictions, as simulated using the Kroll–Watsonformula [192] with scattering cross sections calculation underthe independent atomic model. The numerical simulationsalso confirms that the observed modulation patterns are theelectron diffraction patterns of CCl4 reflecting its geometricalstructure. In spite of no real dynamics under investigation,this experiment is an important proof of principle demonstra-tion of high temporal (<10 fs) and spatial (∼1 pm) resolutionsfor LAED.

3.5.2. Laser-induced CEI. CEI for time-resolved studies wasintroduced around 1990 [193–196] using ultrafast intenselaser pulses which replaced the foil or the slow highly chargedions. The Coulomb explosion is triggered via the rapidionization of the molecule to its highly excited ion states bythe intense pulses. Laser-induced CEI has been demonstratedexperimentally to possess similar resolving power to foil- andcollision-induced CEI in determination of the static structure[197–199] and absolute configuration (chirality) [200, 201] ofmolecules.

Time-resolved laser-induced CEI of dissociation androtational dynamics of small molecules have been carried outaround 2000 [202–204]. Perhaps the most notable example isthe experiment performed in 1998 by Stapelfeldt and co-workers in which the structure and dynamics of nuclear wavepackets of I2 molecules (see figure 2) with a 2–4Å spatialresolution and 80 fs temporal resolution [202] were recorded.First, the ground-state ( S+X g

1 ) I2 molecule was excited via asingle-photon excitation to the excited state PA u

31 by a

625 nm laser pulse. The I2 molecule dissociated and thenuclear wave packet started to move along the PA u

31 potential

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energy curve. The position and the structure of the nuclearwave packet was then probed by Coulomb exploding themolecule with a second, 80 fs temporally delayed pulse. Thespatial resolution demonstrated in this experiment apparentlyis worse than that achieved in foil- or collision-induced CEI.

However, it should be noticed that different from foil/collision-induced CEI, the interaction time in laser-inducedCEI depends on the probe pulse duration, which was 80 fs inthe above experiment. The long pulse duration will not onlydirectly affect the temporal resolution, but also ‘blur’ the

Figure 1. Left panel: electron kinetic energy spectra scattered off CCl4 atD =t 0 (a), −70 ps (b), and +70 ps (c), whereDt is the delay timebetween laser and electron pulses. The kinetic energy spectra are obtained by integrating the electron signals over the scattering angle θ in theentire recorded range ( q < < 2.5 12.5 ). The main peak is the background signal due to laser-free electron diffraction. Only when theelectron pulse overlaps with the laser pulse (D =t 0), signals from laser-assisted scatterings arise at the energy shifts of one-photon and two-photons. The intensities are normalized by their peak intensity at D =E 0 and the broken line in each subfigure shows the same spectrummultiplied by a factor of 1/1000. Right panel: angle-resolved laser-assisted electron diffraction patterns of CCl4. Red circles show theexperimental LAED patterns at wD = +E (e) and wD = -E (f). These distributions are obtained by integrating the electron signals atD =t 0 over 0.4 eV energy range centered at wD = E . Background signals obtained whenD = t 70 ps were subtracted. The error barsrepresents one standard deviation. The blue solid lines are the simulated LAED patterns. The green broken lines show the simulated LAESangular distribution when the interference effects are neglected. Figure adapted from [191].

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detected image of the fragments which in turn deteriorates thespatial resolution. The long probe pulse also introduces extrauncertainty in determination of the Coulomb explosion timewhich needs to be as small as possible compared with thevibrational time scale. To ensure the atomic scale spatio-temporal resolutions, few-cycle probe pulses as well as pumppulses are necessary.

Sub-5 fs and sub-Å resolution were demonstrated in 2005by Légaré et al in their laser-induced CEI experiment on D2

and SO2 within the pump-probe scheme, in which both pumpand probe pulses contain few cycles with a duration of 8 fs[205]. Pump pulses was used to create the vibrating +D2 ionsand dissociating SO +

22 and SO +

23 ions, whereas time-delayed

probe pulse Coulomb exploded the evolving molecular ions,thus capturing their transient structures. The real-timeevolution of +D2 , SO

+22 and SO +

23 were obtained over a large

time range (75 fs for +D2 and 220 fs for SO +n2 ) uncovering the

concerted nature of the breakup of SO +n2 ions into their

constituent atomic ions.Hydrogen migration in organic hydrocarbons is one of

the most important ultrafast dynamics in photochemistry thatwere intensively studied by laser-induced CEI [206–210].Hydrogen migration, i.e., the transfer of proton/deuteronfrom one nuclear site to another, is a ubiquitous process in avast variety of chemical and biochemical reactions. However,due to its ultrashort time scale (sub-picoseconds) and smallhydrogen scattering signals [19, 206, 209], this important

dynamics is hard to be visualized even with powerful ultrafastelectron and x-ray diffraction imaging techniques. In varioustime-resolved experimental hydrogen migration studies bylaser-induced CEI, acetylene was often used as a prototypicalsystem [206, 208–210]. To date, hydrogen migration has beenobserved experimentally in both the cation and dication ofacetylene within a pump-probe scheme, performed either withintense ultrashort infrared pulses or femtosecond x-ray pulsesfrom FELs, demonstrating the power and unique role of thelaser-induced CEI technique in time-resolve molecularimaging.

As with the static variant based on foil/collision-inducedprocess, the application of laser-induced CEI is also limited tosmall molecules. However, in special circumstances, wherethe structural dynamics under study can be solely determinedby detecting a few key fragments, laser-induced CEI can alsobe applied to larger molecules, for instance, the torsionalmotion of 3,5-difluoro-3′,5′-dibromo-4′-cyanobiphenyl (rela-tive rotation of the two phenyl planes) [211, 212]. Effortshave been made recently to extend this technique tomoderately large polyatomic molecules in general by usinga newly designed pixel-imaging mass-spectroscopy cam-era [213].

3.5.3. Laser-driven recollision phenomena and strong-fieldimaging. A new imaging paradigm emerged in the lastdecade based on the phenomena that occur when strong fieldlasers interact with gaseous targets. When the linearlypolarized laser electric field strength is comparable with theCoulomb field (intensity ∼1016W cm−2) that governs theelectron dynamics in atoms or molecules [214], the targetatom or molecule will tunnel ionize, releasing a valenceelectron. Born in the laser’s oscillating field, thephotoelectron can fly directly to the detector or may bedriven back in a semiclassical motion by the laser field torecollide with the parent ion (dubbed direct and rescatteredelectrons, respectively). Upon return, the electron mayelastically scatter, kick out secondary electrons or photo-recombine into the initial electronic state. These highlynonlinear phenomena are called high-energy above thresholdionization, non-sequential ionization, and high-orderharmonic generation, respectively [81, 82]. Since bothelectron scattering and photoionization are conventionaltools for probing the structure of matter, there has beengreat interest in using the returning electrons and the emittedhigh-harmonic photons for self-imaging the target[20, 215–217].

The ponderomotive energy and the wavelength scaling.The ponderomotive or quiver energy, Up, is an importantstrong field metric since it defines the field energy coupledinto the quivering continuum electron wave packet. Themotion of ionized electron in the laser field is classical, andthe propagation time for rescattering electrons is proportionalto the optical cycle period as well as the laser wavelength.The maximum energy of the direct electron is 2Up (the blackcircle in figure 3(a)). The rescattering electrons propagatefurther and acquire a significant kinetic energy ~ U3.2 p from

Figure 2. The square of the internuclear wave function, Y R 2∣ ( )∣ , ofthe dissociating I2 molecule measured at different times afterexcitation by the pump pulse. The full curves are the measurementsbased on the kinetic energy spectra of +I recorded at different timedelays. The broken curves represent a simulation of the wave packetmotion on the PA u

31 potential energy curve of I2 along which the

dissociation happens. The amplitudes of the simulated wave packetsare scaled to match the observations. Figure adapted from [202].

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the field prior to recollision. This leads to a cutoff energy ofhigh harmonics~ +U I3.2 p p (Ip is the binding energy), whichis just the maximum energy the rescattering electron loses byjumping back to its ground state. For electrons which arebackscattered, the non-zero additional momentum Ar = A(tr)

picked up at the recollision time tr will extend its maximumenergy up to U10 p (A(t) is the vector potential of thelaser field).

Up is proportional to lI 2, where λ and I are the laserwavelength and intensity, respectively. The scaling means

Figure 3. Upper panel: the LIED principles of analyzing the momentum distribution of photoelectrons (a). Electron momentum distributionresulting from strong-field ionization of N2 at 2 μm. The laser polarization is along the horizontal axis. The black circle shows the limitingmomentum for direct electrons (corresponding to 2Up). Ar is the field vector potential at the time of rescattering. After backscattering anelectron gains additional momentum from the field, resulting in a larger dected momentum (magenta circle). The detected momentum,p=pr − Ar. The inset defines the rescattering angle, θ, and the momentum transfer, q. The QRS theory states that the distribution sweptalong magenta circle is equivalent to the field-free elastic DCS taken at constant incidence momentum, pr. Lower panel: illustration of bondlength changes for N2 (b) and O2 (c). Retrieved bond lengths from LIED measurements at three wavelengths (squares, 2.3 μm; circles, 2 μm;diamonds, 1.7 μm) are shown. The equilibrium bond lengths are also indicated for the neutral (black solid line) and the ionic (gray dashedline) molecules. The red solid curves depict the evolution of the peak of the nuclear wave packet, which is simulated in the Frank–Condonapproximation. Figure adapted from [84].

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that Up can easily exceed the binding energy, particularly atlong wavelengths. For example, helium ionization saturated(1 PW cm−2) by 0.8 μm pulses yields a value of Up ≈ 60 eV.By increasing the wavelength to 4 μm, Up will increase 25-fold producing Up of 1.5 keV. To obtain an equivalent valueat 0.8 μm would require 25 PW cm−2, an intensity no neutralatom would experience. So this simple case stresses theadvantage of the l2-scaling ‘knob’ towards longer wave-lengths for studying atomic or molecular systems inunprecedented large ponderomotive potentials, which is acrucial factor in strong-field imaging techniques.

Laser-induced electron diffraction (LIED). Elastic scat-tering of those returning electrons from the target ions, aprocess dubbed LIED, received intensive attention for itspotential for structural determination [175, 177, 217–223].The high-energy photoelectron spectrum generated by therescattering electrons in the far field conveys target structuralinformation. The basics of LIED is the same as CED exceptthat the probing electron pulse is generated from its parenttarget based on tunnel ionization by an intense laser. Thecombined elements of scattering occurring on an optical-cycletime scale, e.g., femtoseconds, confer LIED the potential to bedeveloped into an ultrafast structural probe. The firstexperimental LIED application on dynamic systems wereperformed by Blaga and co-workers to study the molecularvibration of nitrogen and oxygen after tunnel ionization [84].

In the work of Blaga et al, 2D photoelectron momentumdistributions for nitrogen and oxygen were recorded understrong field irradiation with 50 fs pulses at three wavelengths(1.7, 2.0, and 2.3 μm). Using the recently developedquantitative rescattering (QRS) theory, from each distributionthe e--scattering differential cross sections (DCS) at largescattering angles were extracted [20]. The QRS theory relatesthe experimental momentum distribution I p( ) to the field-free e− -ion DCS s qp ,r( ) via

s q =I p W p p , ,r r( ) ( ) ( )

where W pr( ) is the electron returing wave packet (eRWP),and p and pr= qp ,r( ) are detected and rescatteringmomentum, respectively. In the long-wavelength limit, thedetected momentum of the photoelectron p displayed infigure 3(a) is related to the electron’s momentum pr atrescattering by p=pr−Ar. The additional Ar = A(tr) is thevector potential of the laser field at the time of rescattering, tr.

The mid-infrared lasers, or the long wavelengths arecrucial to generate high-energy (>100 eV) electrons toresolve the atomic core in the molecule. Although the energyis relatively low compared to multi-kilovolt energy of theelectrons used in CED, LIED employs backscattering signalswhile in CED the scattering DCS is measured typically atsmall angles in the forward direction [224]. These laser-driven multi-hundred volt energy electrons incur core-penetrating backscattered collision where the momentumtransfer q=q p2 sin 2r ( ) is comparable to those attained inmulti-keV CED [224, 225]. Consequently, a simple model,IAM, which has been widely used in keV CED, also appliesfor LIED [224].

According to IAM [224], for randomly aligned homo-nuclear diatomic molecules, the e--molecule angle-resolvedDCS s q( ) can be expressed as

s q s q s q= +qR

qR2 2

sin.A A( ) ( ) ( ) ( )

The first term on the right is the incoherent summation ofatomic DCSs s qA ( ) and conveys no structural information.The second term is called molecular interference term, whichexplicitly depends on momentum transfer q and internucleardistance R. A molecular contrast factor (MCF) is defined asthe ratio of the second term to the first term, which contains asinusoidal term sensitive to the small bond length changes.

The procedure to retrieve the molecular bond length fromthe measured photoelectron spectra is as follows: (1) measurethe electron momentum distribution generated by a mid-infrared laser; (2) following QRS theory, extract the e−-molecule collision DCSs at back-scattering angles; (3)retrieve the bond length by fitting to experimental MCF,which is obtained by subtracting the atomic scatteringbackground s qA ( ) from the total DCS s q( ).

Figures 3(b) and (c) plots the bond lengths extracted atthe three wavelengths (1.7, 2.0, and 2.3 μm) against theelectron propagation time before recollision. The corresp-onding laser intensities are 170, 260, and 290 TW cm−2,respectively, for N2 and 130, 133, and 150 TW cm−2,respectively, for O2. One can see that the retrieved bondlengths of N2 are nearly constant at the three wavelengths,around the equilibrium N–N distance of N2, within a 5 pmuncertainty; for O2, all three sets of data are also consistentwith a bond length contraction of 0.1Å within 4–6 fs aftertunnel ionization, which is due to the motion of the two nucleitowards each other initiated by the ionization. As we know,the bond lengths of neutral (1.10Å) and ionic (1.12Å)nitrogen are about the same, whereas for oxygen, the bondlength of +O2 (1.12Å) is much shorter than that of O2

(1.21Å). So after the photoelectron is peeled off, th O–Obond will start to shrink whereas there is almost no change inN–N bond. In figure 3 red curves illustrate the bond changesfor N2 and O2 after ionization, simulated under a simpleFrank–Condon approximation. Clearly, the three exper-imental points of O2 fit the Frank–Condon curve better thanthe bond length of the neutral molecule, showing astatistically significant reduction in the bond.

In this experiment, the valence-electron ionization acts asa pump to initiate the nuclear vibration in +O2 , the rescatteringelectron probes the position of the nuclear wave packet andthe wavelength of the intense laser pulse is used as a ‘knob’ tovary the pump-probe delay time. This result provides the firstexperimental demonstration of LIED for achieving sub-Åspatial resolution and femtosecond time resolution. With theemergence of intense mid-infrared sources in many labora-tories, LIED has the potential to become a powerful tool fordynamic imaging of transient molecules on atomic-scalespatio-temporal resolution.

Fixed-angle broadband laser-driven electron scattering(FABLES). The above imaging method LIED relies onextracting the angle-resolved elastic DCS from the two-

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dimensional photoelectron momentum distribution. However,the generated eRWP by the strong field is broadband. Thisbroadband aspect can also be developed into a new imagingmethod for structural determination: fixed-angle broadbandlaser-driven electron scattering (FABLES) [226]. FABLES isanalogous to white light interferometry in optics, and it hasbeen proved in experiment that the broadband eRWP can beused for accurate structure reconstruction [226].

In the experiment, the energy distributions of photoelec-trons were measured along the laser polarization direction (thehorizontal axis in figure 3) for nitrogen and its companionatom argon. The on-axis high-energy photoelectron spectrum(2–10Up) results from elastic backscattering of laser-drivenEWP. The scattering DCS for argon and nitrogen atoms areapproximately an order of magnitude different, which isresponsible for the most visible difference: the spectrum forargon is larger than that of nitrogen. Closer inspection of thephotoelectron spectra reveals that the essential differencebetween the two distributions is a clear modulation seen in theN2 spectrum but absent in argon atom. At high collisionenergies, the energy-dependent electron-atom backscatteringDCS is monotonically decreasing and structureless. Conse-quently, the oscillation in the N2 distribution must be ascribedto an intramolecular effect, that is, the interferences betweenthe scattered electron waves emitted from each atomic core.The intramolecular interference ‘fringes’ were extracted byremoving the background signal, and its Fourier transformgave an internuclear distance distribution peaked at 1.09Å, ingood agreement with the known nitrogen equilibriumdistance 1.10Å.

High-order harmonic tomography. The molecular tomo-graphy method relies on observing high harmonic photonsgenerated by the field-driven eRWP recombining with theinitial state, e.g. the highest occupied molecular orbital(HOMO). The salient features of this method are that theharmonic emission comb spans a large photon energy rangeand the strength and spectrum of the emission changes as thepolarization of the intense field is varied with respect to themolecular axis. In essence, the broad spectral comb samples alarge k-space (k is the wave vector) and thus is sensitive tothe orbital symmetry. Formally, each spectrum at fixedalignment is a one-dimensional projection of the transitiondipole moment q qáY Y ñr r r, ,g c( )∣ ∣ ( ) that produces theharmonic distribution, where qY r,g( ) and qY r,c( ) are theground state and continuum state, respectively. The dipolemoment is the essential quantity needed to measure themolecular orbital qY r,g( ). The extraction of qY r,g( ) alsodepends upon satisfying the strong-field tunneling condition

so that the plane wave w

e k ri ( )· approximation is a gooddescription of the continuum wave function, qY r,c( ).

High harmonic tomography was developed by the NRCgroup [83] to reconstruct a 3D image of the HOMO of N2

from a series of 1D projection of its transition dipole, aprocedure similar to medical imaging. First, the molecularaxis of N2 is ‘fixed’ in the laboratory frame via impulsivealignment using an ultrashort laser pulse. Second, an

independently delayed linearly polarized intense 800 nmpulse excites the aligned molecules producing a spectral combof high harmonic radiation. The harmonic comb is dispersedin a spectrometer and recorded thus providing a 1D projectionof the process. A series of 1D projections are produced byvarying the molecular orientation in the laboratory frame,which is simply accomplished by rotating the polarization ofthe alignment laser relative to the polarization of the intenseharmonic generating pulse. Finally, the series of 1Dprojections of the harmonic comb are mathematicallytransformed to generate a 3D spatial rendering of themolecular orbital under the plane wave approximation.

The NRC experiment reconstructed the HOMO of theS+N g2

1 ground state using the following three ingredients: thehigh harmonic spectral comb, a calibration procedure usingargon atoms (N2) to determine the amplitudes of thecontinuum electron wave packet and an assumed knowledgeof the harmonic phases (inferred from calculations in thiswork) which should also be measured in a more completeexperiment. Using this information the NRC group was ableto reconstruct the N2 HOMO which yielded stunningagreement with the ab initio calculation.

However, the tomographic procedure is based on anumber of questionable assumptions and approximations[227–231], among them is that the continuum electronwavefunction qY r,c( ) can be represented by a plane wave.This assumption, which is essential to the tomographicprocedure, is in strong contradiction to the well-establishedelectron-ion collision theories [232]. Besides, to date therehas been only one complete tomographic measurement whichwas performed by the group of Salières at Saclay [233]. Theirstudies on N2 and CO at 800 nm raised some addition pitfallswith methodology but also pointed to some surprisingsuccess. It is safe to state that this method is highlycontroversial and many questions remain to be resolved.

A new table-top high-harmonic-based x-ray source.Aspreviously mentioned, working at sufficiently long wave-lengths can extend the high harmonic photon energies into thex-ray regime [234]. By guiding a 3.9 μm femtosecond laserinto a waveguide filled with a high-pressure helium gas,bright high-harmonic x-ray supercontinua with photonenergies spanning from the EUV to x-ray (1.6 keV) weregenerated in 2012 [235], which, in principle, allows thegeneration of an isolated coherent x-ray pulse with a 2.5attosecond duration. The brightness of the high-harmonic-based x-ray pulse is about 105 photons per pulse, which isrelatively low in comparison with the other table-top x-raysources generated by laser-driven plasma. However, itspotential attosecond pulse duration is far shorter than otherx-ray sources, being plasma-driven, synchrotron- or FEL-based.

Other imaging methods or proposals. The distinctivestrong-field recollision phenomena also created other usefulimaging methods or proposals. Two notable ones are brieflydiscussed below.

As the high harmonics are directly linked to themolecular orbitals, it would be natural to use them to probe

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the electronic dynamics. The high-harmonic spectroscopybroadens the family of traditional spectroscopic techniquesand has been used in studying the large-scale vibrationalmotion in N2O4 [174], the dissociation dynamics in Br2 [236],and the conical intersection dynamics in NO2 [237].

The strong-field PH variant was reported in 2011 byHuismans and co-workers [176]. In the experiment, therecorded 2D photoelectron angular distribution displayed aclear fork-like pattern along the laser polarization direction.The pattern was attributed to an interference mechanismbetween direct (reference) and the forward scattering (signal)electron wave packets. Although theory has shown that thepattern changes slightly as a function of the atomic orbitalshape [238], to date no experimental confirmation has beenreported. This proposal is still on the conceptual level andstructural retrieval procedure is still unclear.

4. Concluding remarks

The real-time imaging of a chemical reaction at the level of asingle molecule is of fundamental importance for scientists asit will pave the way to directly visualize, understand andultimately control the reaction dynamics. As reviewed above,the critical ingredient in all techniques is an approach thatachieves atomic-scale spatio-temporal resolution. In most ofthe cases, the main technical difficulty is not the imple-mentation of the imaging method, but on the development ofprobes, i.e. how to generate a ultrashort probe pulse withenough brightness. However, one has to be optimistic that thistechnical difficulty will be overcome as rapid developments inultrafast optical technology and FELs take place.

In particular, intense ultrafast lasers propelled the field ofthe dynamic imaging by creating novel tools and new ways togenerate probe pulses, extend resolving capability to thefemtosecond and attosecond time domain, and enabledinterrogation of not only the nuclear but also the electronicdynamics [5, 6, 85, 86, 239], which in tandem are theessential parts of a chemical reaction. Nevertheless, the routeto time-resolved ultrafast imaging is going to be long andchallenging. The challenges are not only on improving theresolving power by increasing the probe pulse brightness orby aligning the molecule [10, 88, 89], but also on the fact thatour knowledge about far-off-equilibrium states is very limitedcompared to that about static molecular structures. To miti-gate this problem, different imaging techniques might need tobe combined. For instance, spectroscopic methods (which wesaw cannot provide a real-space image) can still be employedto gain considerable knowledge about the reaction dynamics,which, along with quantum chemical computations[23, 24, 67–69, 240], will be used to guide future diffractiveimaging studies. Though challenging, one has to agree thatreal-time investigation of ultrafast dynamics will be scienti-fically rewarding. However, the adventure is not finished butjust barely starting.

Acknowledgments

The work was supported by DOE/BES contract DE-FG02-06ER15833.

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