Femtochemistry – some reflections and perspectives

Accepted Manuscript Femtochemistry - some reflections and perspectives Niels E. Henriksen PII: DOI: Reference:

S0301-0104(14)00013-5 http://dx.doi.org/10.1016/j.chemphys.2014.01.003 CHEMPH 9025

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Chemical Physics

Received Date: Accepted Date:

25 November 2013 9 January 2014

Please cite this article as: N.E. Henriksen, Femtochemistry - some reflections and perspectives, Chemical Physics (2014), doi: http://dx.doi.org/10.1016/j.chemphys.2014.01.003

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Femtochemistry - some reflections and perspectives Niels E. Henriksen∗ Department of Chemistry, Building 207, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark (Dated: January 20, 2014) In this perspective we highlight some aspects of femtochemistry, that is, the creation, detection and control of non-stationary states in chemical dynamics. Some recent results are discussed with a view on the challenges and pending scientific questions. We discuss theoretical as well as experimental issues with the emphasis on laser control of chemical dynamics, in the weak-field and strong-field regimes. INTRODUCTION

For many years, the experimental observations of spectroscopy and photochemistry were interpreted in terms of the stationary molecular eigenstates of the molecular Hamiltonian. However, due to the seminal work of E.J. Heller [1], it became clear that the spectroscopy and photochemistry of electronic transitions, e.g., absorption or Raman spectroscopy and final product distributions for a photofragmentation process, can all be interpreted as signatures of the dynamics of the so-called Franck-Condon wave packet. A wave packet is a non-stationary state - which can be represented as a coherent superposition of the stationary molecular eigenstates. In an electronic transition from an initial nuclear state associated with the electronic ground state to an excited electronic state, the Franck-Condon wave packet can be represented by ˆ ex t/~)|Φ(0)i |ψex (t)i = exp(−iH

(1)

where |Φ(0)i is the product between the initial nuclear state and the projection of the electronic transition dipole moment along the direction of a plane polarized electric ˆ ex is the Hamiltonian associated with nuclear field, and H motion in the excited electronic state(s), see Fig. 1. It was also shown that during the interaction with cw (continuous wave) lasers excited stationary molecular eigenstates are created, whereas the creation of a wave packet like the one in Eq. (1) would require an interaction with an ultrashort femtosecond pulse. Nevertheless, this indirect approach to light-induced chemical dynamics [1, 2], showed us that we can see the signatures of dynamics even without actually creating the FranckCondon wave packet. The groundbreaking work of A.H. Zewail [3] and coworkers led to the creation of femtochemistry. Here the goal is to create, detect and control the time evolution of non-stationary states of matter. The creation and control of wave packets are accomplished via interaction with pulsed electromagnetic fields. With a few exceptions, like detection of non-stationary states via time-resolved electron diffraction, the detection is also based on the interaction with pulsed electromagnetic fields.

∗ Electronic

address: [email protected]

30 Potential Energy (arbitrary units)

I.

25 20 15 10 Pump 5 0

4

5

6 7 8 9 10 Internuclear Distance (arbitrary units)

FIG. 1: The vertically excited initial state, the so-called Franck-Condon wave packet of Eq. (1) at t = 0.

The non-stationary states of particular relevance to femtochemistry include, of course, as a central theme the dynamics of the chemical bond, i.e., bond making and bond breaking. However, all types of non-stationary states including rotational, vibrational, and electronic of isolated molecules, as well as non-stationary states of solvents and solids are of interest - as long as they contribute to our understanding of chemistry and biology. Creation and control of wave packets are closely related since the same pump laser is used for both aims, in the latter case using relevant control knobs of the laser. If control is not the goal, the pump pulse is typically a transformlimited Gaussian pulse and in the ultrashort pulse limit, the Franck-Condon wave packet is created. Femtochemistry is often subdivided into structural dynamics and reaction dynamics. Structural dynamics is focusing on the direct determination of the time-dependent atomic positions. The scope of reaction dynamics is broader, it includes, e.g., the study of energy flow between various electronic states. Femtochemistry, like photochemistry, typically starts with an electronic transition and a reorganization of the valence electrons within

low laying excited electronic states. However, it should be noticed that the processes of most interest to chemists occur in the electronic ground state and, furthermore, that these processes typically are thermally activated [4]. Although the timescales of such reactions are not expected to be fundamentally different from reactions in excited electronic states it would, nevertheless, in the future be interesting to further highlight processes in the electronic ground state. An example, which was studied recently, is the femtochemistry of IR-driven cis-trans isomerization of HONO (see Ref. [5] and references therein for additional examples of pump-probe spectroscopy in the electronic ground state). This process can be initiated by a single vibrational transition. In general, the direct initiation of chemical dynamics in the electronic ground state requires multiphoton transitions, hence high intensities; direct overtone excitation is sometimes also possible, like in the ring-opening of cyclo-butene. To that end, it has also been suggested to use ultrashort broadband visible laser pulses in order to excite vibrational modes in the electronic ground state by a stimulated Raman process [6]. Another highly interesting but somewhat underdeveloped topic is the femtochemistry of bimolecular reactions. The dream would be to be able to select the impact parameter and relative orientation of reactants and then follow - on the femtosecond timescale - the reaction as it unfolds on the potential energy surface of the electronic ground state. This would clearly take us beyond crossed molecular beam experiments which only give us postcollision information and an average over all impact parameters. To that end, seminal work has already been performed [7, 8], e.g., on the reaction H + CO2 → OH + CO following photoactivation of a van der Waals complex (IH· · · OCO). There still seems to be room for more direct insights into the time evolution of bimolecular reactions. Consider, e.g., a bimolecular nucleophilic substitution (SN 2) reaction like Cl− + CH3 Br → ClCH3 + Br− . In the gas phase, the potential energy along the reaction coordinate has a double-well shape, reflecting the existence of iondipole complexes [9]. One might imagine that it would be possible to initiate the reaction - starting from an ion-dipole complex - on the ground state surface. An ultrashort optimized laser pulse should then excite the reaction coordinate above the barrier, e.g., by a pumpdump mechanism or a related stimulated Raman process via excited electronic states. Femtochemistry covers everything from small isolated molecules in the gas phase to complex (biological) molecules in condensed phases, including solute-solvent interactions. Thus, the following discussion will be restricted to some selected topics, and will mostly focus on molecules in the gas phase and laser control of chemical dynamics. The rest of this perspective is organized as follows: In Section II., we discuss briefly the generation of wave packets associated with various molecular degrees of free-

dom. In Section III., we focus on laser control of chemical dynamics, and we conclude with some remarks on the detection of chemical dynamics in Section IV.

II.

WAVE PACKETS, CHEMICAL DYNAMICS

In this section, we discuss a few examples of wave packets associated with various molecular degrees of freedom. Clearly we can generate wave packets associated with nuclear and electronic motion where the nuclear motion includes rotation, vibration, and reactive modes like dissociation and isomerization. We consider in the following briefly two examples; time-dependent molecular orientation and electron dynamics in molecules. Molecules are oriented in space if their dipole moment vector has a preferred orientation. The generation of wave packets consisting of superpositions of even and odd rotational states with respect to inversion at the origin (e.g., J = 0 and J = 1 for a linear molecule) leads to fieldfree time-dependent orientation of molecules. Such wave packets can, e.g., be generated directly by pulsed THz excitation [10, 11] or by a strong non-resonant asymmetric two-color (ω, 2ω) laser field which interacts with the molecule via a hyperpolarizability term [12, 13]. Both approaches have recently been demonstrated experimentally [14, 15]. The degree of orientation is, however, quite modest and it could be improved considerably, e.g., when more intense THz pulses become available in the future. With a typical energy spacing of a few eV for electronic states, electronic wave packets [16] oscillate on a subfemtosecond, i.e, an attosecond timescale. Figure 2 illustrates the oscillation in the electron density for a superposition of two electronic states which are even(g) and odd(u), respectively, with respect to bond center inversion. Such electronic wave packets have been studied theoretically [16–18] as well as experimentally [19, 20]. Thus, a time-dependent localization of the electron density has, e.g., been observed in a dissociative state of D+ 2 . Electronic wave packets have also been considered for more complex molecules. Thus, it has been shown how circularly polarized laser pulses can induce unidirectional electronic circulation in ring-shaped molecules [21]. A superposition of the ground and an excited electronic state in benzene has also been studied [22] leading to electronic wave packets with non-aromatic character.

III.

LASER CONTROL OF CHEMICAL DYNAMICS

The idea that optimized laser fields can guide the dynamics of an atom or molecule from a given initial state into a desired final state, has attracted much attention in recent years [23–31]. Consider a molecule ABC which is bound in its electronic ground state and where fragmentation can take place in excited electronic states. A generic problem in laser control concerns the control of a

can also modify potential energy surfaces. One mechanism is the so-called dynamic Stark effect [37–40] where a precisely timed strong nonresonant infrared field can reversibly modify the potential energy surface along the reaction path. Related work is based on the so-called “light-induced potentials” [41, 42]. Coherence is lost when the system interacts with an external environment. Thus, de-coherence is, in general, an enemy of laser control (see, however, the next subsection). Laser control has also been demonstrated at finite temperatures (see, e.g., Ref. [43]), that is, it is possible to construct laser fields which at finite times can counteract the influence of de-coherence. The time-dependent phase-coherent electric field of a laser pulse can be represented by ·Z ∞ ¸ iφ(ω) −iωt E(t) = E0 Re A(ω)e e dω (3) −∞

FIG. 2: Schematic illustration of pure electronic motion in a bound diatomic molecule. The molecule is in a superposition of the vibrational ground states of the electronic ground state and an excited electronic state. The electronic ground state is even and the excited state is assumed to be odd with respect to bond center inversion. The wave functions are sketched at their respective potentials. Between the potentials the timeevolution of the electrons is shown as snapshots. We see that the electrons move from one nucleus to the other while the bond length stay fixed. Adapted from Ref. [16].

reaction of the type ½ ABC + coherent light −→

A + BC AB + C

(2)

i.e., to what extent laser control can change the branching ratio between the two channels A + BC and AB + C as well as the final state distribution within each of these rearrangement channels. A related generic problem concerns the control of isomerization reactions [31, 32]. The control of isomerization in the electronic ground state has also been considered in a theoretical study [33]. Another challenging objective is the control of bimolecular reactions. Photoassociation, the formation of molecules and chemical bonds assisted by laser light, is an emerging and challenging field [34]. The formation of a diatomic molecule from (cold) atoms has recently been demonstrated experimentally [35]. In the future, photoassociation might turn into laser-assisted chemical synthesis which could find important applications in chemistry. As emphasized below, the coherent nature of laser excitation plays an important role; without this coherence no wave packets could be created and it allows for the control of quantum mechanical interferences. Laser pulses can initiate and guide wave packet motion, e.g., by the so-called pump-dump mechanism [36] where one takes advantage of the different forces which operate in various electronic states. In the strong-field limit, laser pulses

where A(ω) is the real-valued distribution of frequencies and φ(ω) is the real-valued frequency-dependent phase. The temporal duration and shape of the pulse depends on theRphases whereas theRenergy in the field R ∝ |E(t)|2 dt ∝ |A(ω)eiφ(ω) |2 dω = |A(ω)|2 dω is independent of the phases. Disregarding effects of varying the frequency distribution of the pulse, pulse shaping is obtained by employing a phase modulated excitation pulse. Phase modulation in turn will change the magnitude of quantum mechanical interference terms in the interaction with matter; this is the essence of coherent control. Thus, the laser phases are transferred to the material wave functions. This is most easily illustrated in the weak-field limit. Consider an electronic transition in a molecule, from an electronic ground state to an excited state. Within the electric-dipole approximation and firstorder perturbation theory for the interaction with the electromagnetic field, the state vector associated with the nuclear motion in the excited electronic state is, after the pulse has decayed, given by (see, e.g., Ref. [44]) Z iπ |ψex (t)i = dE cE |Eieiφ(ωE ) e−iEt/~ (4) ~ where excitation into continuum states |Ei associated with a repulsive electronic state is assumed, cE = E0 A(ωE )hE|Φ(0)i

(5)

where ωE = (E − ²0 )/~, |Φ(0)i = µ21 |ψgr i, µ21 is the projection of the transition dipole moment along the direction of the plane polarized electric field, and |ψgr i is the initial vibrational eigenstate. Thus, the expansion coefficient of the wave packet is a product of the frequency distribution of the laser pulse and the overlap between the initial state and the continuum state, i.e., Franck-Condon factors. Furthermore, Eq. (4) clearly displays how the expansion coefficients are multiplied by the frequency dependent phases of the laser pulse. It is often convenient to represent the phase function

by a Taylor expansion around the central frequency ω0 of the pulse [44], φ(ω) = φ0 + φ1 (ω − ω0 ) + (1/2)φ2 (ω − ω0 )2 + · · · (6) here φ0 is the absolute phase also called the carrier envelope phase which plays an important role for short pulses where only a few cycles are within the envelope. The linear term introduces a time shift in the wave packet, as seen directly from Eq. (4). The non-linear terms will lead to non-trivial changes in the phases of quantum mechanical interference terms. It is not convenient to represent all phase functions, for example, phase jumps by the Taylor expansion. Phase jumps lead to a series of pulses, i.e., pulse trains. As an illustration, we consider an electric field corresponding to a Gaussian frequency distribution (centered at ω0 ) with a quadratic phase function [44], i.e., r τ02 [−τ02 (ω−ω0 )2 /2+iβ0 (ω−ω0 )2 /2] iφ(ω) A(ω)e = e , (7) 2π where 1/τ0 is the frequency bandwidth and β0 is the linear spectral chirp. The time-dependent electric field in Eq. (3) then takes the form "s # τ02 t2 2 E(t) = E0 Re exp(− 2 − iβt /2 − iω0 t) τ02 − iβ0 2τ (8) with pulse duration τ and linear temporal chirp β, which are related to τ0 and β0 via β = β0 /(τ04 + β02 ),

(9)

τ 2 = τ02 (1 + β02 /τ04 ).

(10)

The mathematical technique of optimal control theory (for recent reviews, see Refs. [26, 49]) is used in order to determine the electric field which can drive a system from a given initial state to a desired final state. A particularly interesting perspective in laser control is the possible creation of molecules which cannot be created by other means, like the theoretically predicted high energy cyclic form of ozone. Looking at the previous experimental and theoretical work in laser control, they have - to some extent - followed two different tracks. Thus, experiments are naturally limited by the fixed bandwidth of the laser pulse and have often been limited to phase-only control (i.e., the amplitudes A(ω) are fixed) whereas the frequency distribution as well as the phases have been optimized in optimal control theory. Phase-only control was, however, recently implemented in optimal control theory [50]. An interesting general question is if one can always find an electric field which will drive a system from a given initial state into a desired final state. This question is at the heart of the study of controllability of quantum systems [24, 25]. From a more practical point of view a key question is: What new types of control are possible with shaped laser pulses? To that end it is convenient to distinguish between weak-field and strong-field control. In the weak-field limit, one can focus on pure phasemodulated pulses in order to disentangle the effects of frequency/energy and phase. In the strong-field, one can clearly open new paths which were not open in the weakfield limit, like the vibrational ladder-climbing described above. The yield of a given process can quite readily be improved, however, as illustrated below it is not always straightforward to improve the selectivity/branching ratios compared to the weak-field results.

and

Eq. (10) shows that introduction of a spectral chirp lead to a pulse with a longer temporal duration. The spectral chirp introduces also a time-dependent frequency distribution of the field in Eq. (8) within the Gaussian envelope function. For example, for a negatively chirped pulse with β0 < 0, the frequency will decrease as a function of time. The enhancement of molecular bond breaking in the electronic ground state, involving vibrational ladderclimbing via a negatively chirped IR pulse, has been predicted and demonstrated experimentally [45, 46]. In general, pulse shaping is accomplished experimentally [47, 48] by controlling the frequency dependent amplitudes A(ω) and phases φ(ω) of Eq. (3). Most often pulse shaping experiments have been conducted in the 800 nm (near IR) region. A few examples in the deep UV can be found in the literature, e.g., around 260 nm [32] (see also Ref. [48]). Clearly, further advancements in laser technology would help make pulse shaping a more versatile tool.

A.

Weak-field control

Some time ago, M. Shapiro and P. Brumer showed, in a seminal paper [51], that weak field (one-photon) phase control in the long-time limit of a photodissociation process is not possible. The initial state in this proof was assumed to be a pure eigenstate, e.g., the vibrational ground state. The same authors had previously shown that such phase control is possible when the initial state consists of a superposition of eigenstates (e.g. within the so-called bichromatic control) [52]. In very recent work these findings have been further explored, in particular, concerning the influence of an environment. Coherent control in the weak-field (one-photon) limit where amplitude exclusively is transferred from the electronic ground state to an excited state surface, see Eq. (4) - uses the laser’s phase coherence and exploit quantum (multiple-path) interference in its purest form [25, 52] and is a real extension of traditional (incoherent) photochemistry. However, when excitation out of a single eigenstate of ABC in Eq. (2) is considered and direct fragmentation takes place within a dissociative continuum of

states, a seminal proof showed that no phase control of final state distributions of the fragments [51, 53] is possible in the long-time limit. Laser phase dependence can, however, be observed when weak-field excitation out of a non-stationary superposition of bound vibrational states of ABC is considered (see Fig. 3). With an appropriate distribution of frequencies A(ω), the branching ratio depends, e.g., on the linear part of the phase function φ(ω) which is related to the time shift/delay of the laser pulse [54–56]. Recently, the weak-field excitation out of a single stationary state has attracted considerable renewed attention [50, 57–62]. Thus, a reinvestigation of the circumstances under which weak-field coherent control is possible has been undertaken. As mentioned above, for direct fragmentation in the long-time limit, it has been shown that such control is not possible [51].

A

B

+ C

UV-pulse

As an illustration, we consider the photofragmentation of NaI [63], ½ NaI + coherent light −→

Na+ + I− Na + I

(11)

A A

at low energies such that only the Na + I channel is open. Dissociation takes place via non-adiabatic dynamics due to a crossing of the “ionic” ground state potential with a “covalent” excited state potential. This leads to the wellknown stepwise increment in the dissociation probability when excitation is induced by an unchirped pulse [63]. The dissociation probability as a function of time as well as the relative momentum distribution for Na + I can be modified with phase modulated pulses [50, 62]. Thus, at a given time, the dissociation probability can be larger or smaller than the result obtained with a transform-limited Gaussian pulse. This phase dependence associated with a fixed bandwidth phase modulated pulse can be observed and persists for some ps after the pulse is over. Phase control is, however, lost at longer times, in agreement with previous findings [51]. Phase dependence of isomerization yields has also been reported recently in the weak-field limit [57–60]. It was shown that phase dependence can persist over long times when the few modes that are active in the isomerization are coupled intramolecularly to the many vibrational modes in a large molecule or, in general, to an external environment. This coupling allows for dissipation of energy from the isomerization coordinates and effectively constrain the observables to finite times of the system dynamics. One can also envision control using a series of weakfield excitations, at different frequencies, see Fig. 3. A wave packet corresponding to a non-stationary superposition of bound vibrational states of ABC can be created by a short-pulse excitation between two displaced bound states. A second ultrashort weak-field excitation at a proper time delay can lead to control.

B

B

C A

C A

B

B

C

C

FIG. 3: Schematic illustration of selective bond breakage in a molecule, say the BC bond in ABC. The potential energy surfaces in the figure corresponds to a symmetric molecule (including the possibility of isotopic substitution) with a repulsive excited state. In the lowest electronic state, the molecule is in a non-stationary vibrational state. In the harmonic normal mode limit, the motion of the center of the wave packet can be described by a Lissajous figure. The two frequencies involved correspond to symmetric and asymmetric stretching. An ultrashort UV-pulse is fired when the wave packet is located such that the dissociation dynamics evolve solely in the desired channel. Adapted from Ref. [16].

B.

Strong-field control

The potential of pulse shaping in the strong-field limit has been demonstrated nicely in the control of a twophoton transition in a two-level system, where it was shown that it was possible to cancel the transition completely by tailoring the spectral phase [64]. Beyond the weak-field limit, coherent control plays an important role in the pulsed strong-field excitation out of a single stationary vibrational state of ABC. In the strong-field limit, amplitude can be transferred from the electronic ground state to an excited electronic state and back to the electronic ground state. This can lead to a non-stationary superposition of bound vibrational states of ABC which subsequently is transferred to an excited electronic state where fragmentation takes place [36, 65, 66]. The optimal pulse shape can often be decomposed into

properly timed pump and dump pulses between various potential energy surfaces. The optimal pulses are based on proper time delays and pulse shapes, i.e., coherent control plays again an important role. The use of strong fields create, however, potential problems with the population of unwanted channels, e.g., related to ionization. In the following we consider the control of branching ratios in photofragmentation and, in particular, whether strong-field control can lead to branching ratio control beyond what is obtainable in the weak-field limit. As an illustration, we discuss in the following the photofragmentation of HOD: ½ H + OD HOD + coherent light −→ (12) D + OH which has been studied extensively in the first absorption band (with a maximum at λ ∼ 166 nm). The (adiabatic) dissociation dynamics takes place on an isolated repulsive potential energy surface (similar to Fig. 3). The simplicity of this system has made HOD the “hydrogen atom” in the field of laser-controlled selective bond breakage [65]. The dynamics can be described within a well established two-degree of freedom model - on high quality potential energy surfaces for the ground as well as the first excited state - where bending and overall rotation are neglected. Furthermore, a realistic transition dipole moment surface is available for the transition between the two electronic states. Starting with HOD in its vibrational ground state, it has been found that the branching ratio OD/OH always is larger than 1.9 for weak-field excitation within the first absorption band. For a cw laser, the branching ratio depends quite strongly on frequency but it can be shown that the branching ratio always is larger than 1.9 using any form of UV-pulse shaping. Turning to the strong-field limit the optimized laser pulse shape is calculated via optimal control theory with the objective of making the OD/OH branching ratio smaller than 1.9. This objective is sought by maximizing population in the D+OH channel. It is found that it is possible to obtain the desired result provided high laser intensities are employed (peak intensities higher than ∼ 10 TW/cm2 ) [65]. The optimized laser pulse can roughly speaking be described as consisting of three pulses. The first pulse excites HOD out of its vibrational ground state into the excited electronic state. The second pulse “dumps” part of this wave packet back into the electronic ground state, and a non-stationary vibrational state is created in the electronic ground state involving combinations of O-H and O-D stretches. Finally, the third pulse excites HOD out of this non-stationary vibrational state into the excited electronic state. The overall mechanism can be described as a “pump-dump-pump” sequence. This mechanism is related to the pump-dump idea suggest by Tannor and Rice [36]. Alternatively, as suggested some time ago [54], one can replace the optimized UV-pulse by an intense IR laser and an ultrashort UV pulse. An intense IR pulse can induce vibrational motion in the molecule and the ul-

trashort UV pulse is fired when the wave packet has an optimal position and/or momentum, see Fig. 3. As another considerably more complicated system, we consider the photofragmentation of CH2 BrCl: ½ Br + CH2 Cl CH2 BrCl + coherent light −→ (13) CH2 Br + Cl within the second absorption band [66]. The dynamics includes non-adiabatic transitions between the first and second excited electronic states. Within the framework of a description based on the three lowest electronic states and for weak-field excitation out of the vibrational ground, it has been found that the Br/Cl branching ratio cannot be made smaller than 0.4 by simple wavelength tuning. Thus, the question is whether pump and dump of wave packets between these electronic states could lead to branching ratios beyond what is obtainable in the weakfield limit [66]. To simplify the calculations, CH2 BrCl was treated as a pseudo-triatomic molecule, composed of Cl, CH2 , and Br. Realistic values for the transition dipole moments between the ground and the two excited electronic states were employed. Application of optimal control theory, with the objective of maximizing the population in the CH2 Br + Cl channel, leads to a Br/Cl branching ratio smaller than 0.4. The central frequency of the laser pulse is centered around 170 nm. The required laser intensities are, however, very high > 200 TW/cm2 . This is, in part, due to small values of the transition dipole moments. The intensities are so high that ionization (which was not explicitly included in the calculation) will play an important role. Again, a key point in the mechanism is the creation of a non-stationary vibrational state in the electronic ground state, and overall a pump-dump-pump type mechanism can be identified. It should be noticed that in the two examples discussed above, the target state was chosen such that a high selectivity as well as a high yield was sought. It might perhaps be possible to reduce the intensities somewhat if the requirement of a high yield is relaxed. The two illustrations above suggest that it is not always straightforward to beat the branching ratio obtained in the weak-field limit. Furthermore, some methodological/numerical problems were identified. Thus, with the present computational resources the application of optimal control algorithms is limited to low-dimensional systems. In fact, due to slow convergence, the calculation was not feasible when the real coordinate dependent transition dipole moment surfaces of CH2 BrCl were used [66]. Both of the above examples are outside the frequency range of current pulse shaping experiments. The control of bond-selective photochemistry in Eq. (13) has been studied experimentally [67] using a phase-modulated 800 nm pulse. However, at the chosen pulse intensity of 50 TW/cm2 , the fragments were found in ionized form. The mechanism clearly involves nonresonant multiphoton excitations, since access even to the first excited electronic

state requires more than two photons at a wavelength of 800 nm. Such multiphoton mechanisms may play an important role in many current pulse shaping experiments [68]. In the strong-field regime, it is a theoretical challenge to include and suppress undesired ionization. For a simple one-dimensional model atom it was recently demonstrated, for a fixed pulse energy and duration, that pulse shape optimization via optimal control theory can lead to significant suppression of ionization [69].

IV.

DETECTION OF CHEMICAL DYNAMICS

The detection/probing of non-stationary states has typically been accomplished via time-resolved spectroscopy [3, 70, 71]. For example, for the interpretation of UV-spectroscopy, a detailed knowledge of the molecular electronic states is required. From the relation between electronic energy levels and internuclear positions, it is then possible to determine the internuclear positions at a given time, i.e., to obtain a snapshot of the instantaneous structure. Spectroscopy gives a local, and for x-ray spectroscopy even an element specific, snapshot of the molecular structure [70]. Time-resolved detection via electron or x-ray diffraction gives a global snapshot of the molecular structure since scattering/diffraction takes place from all parts of the molecular structure. No knowledge of molecular energy levels is required in order to interpret diffraction signals. Thus, time-resolved diffraction gives a more direct reflection of structural dynamics. The interpretation of diffraction signals is, however, still far from being trivial. In relatively simple situations, say diffraction from a shortlived intermediate, one may compare the theoretically calculated signal based on a structural model with the experimental signal and the discrepancy between the experimental and theoretical signal can then be minimized by optimizing the structure model. This standard iterative procedure is more difficult when a distribution of structures contribute to the signal. Furthermore, with sufficiently high time-resolution, the “classical cartoon” of a chemical reaction pictured with well defined internuclear distances, at a given time, is a simplification of the real situation. In the transformation of matter between various minima on a multidimensional potential energy surface, dynamic non-equilibrium structures will show up, i.e., at a given time a distribution of internuclear distances will be observed due to wave packet spreading. In the future, when such non-equilibrium structures can be extracted from experiments, it might give us new insights concerning reaction mechanisms. The holy grail of diffraction techniques is inversion. That is, the mathematical procedure which will allow us to go directly from the experimental diffraction signal to the instantaneous molecular structure. For a diatomic

molecule, an exact inversion procedure is available [72– 74]. From the isotropic part of experimental scattering signal S(q, tp ) as a function of the scattering vector q at time tp , one can recover the wave packet associated with the internuclear (radial) distance r: Z

∞

dq q 2 j2 (qr)

0

S(q, tp ) ˆex (tp )u0 (r)|2 /r2 (14) = |U Af1 (q)f2 (q)

where j2 is a spherical Bessel function, A is a constant, and f1 (q) and f2 (q) are the atomic form factors. Thus, ˆex (tp )u0 (r) is obthe time-dependent radial density U tained from the transformation in Eq. (14) [73]. The possible generalization to the femtosecond dynamics of polyatomic molecules is a pending scientific question. The precise elucidation of dynamics in condensed phases, e.g., involving solvents is a major challenge. We are now entering a new era of time-resolved xray diffraction. A number of large scale free electron laser (XFEL) sources are under construction or have just opened. These sources can deliver intense x-ray pulse with a duration of less than 100 fs. From an experimental point of view it is, however, a challenge to obtain the required femtosecond time resolution, in particular, in related to the precise timing of the pump laser and the x-ray pulse. The first results from XFEL’s have been published, e.g., reporting the observation of CO desorption from Ru(0001) via x-ray spectroscopy [75]. Time-resolved electron diffraction has already proved to be a highly successful technique at the picosecond timescale where, e.g., shortlived intermediates in organic photochemistry have been detected [70]. Recent interesting developments in the generation of electron pulses can take this technique into the femtosecond and even subfemtosecond timescale. This might ultimately lead to the investigation of non-stationary electron densities in molecule [76].

V.

CONCLUSIONS/OUTLOOK

In this Perspective we have discussed some selected topics within femtochemistry. Impressive results have been obtained within this young field of chemical physics but some areas are still at the proof-of-principle stage. The challenges and pending scientific questions which we have discussed include: (i) the study of unimolecular and, in particular, bimolecular reactions in the electronic ground state, (ii) structural dynamics, in particular, the general inversion problem, e.g., how to go from experimental diffraction data to molecular structure, a question which is of current interest with the massive investments in XFEL’s. In the discussion we had special emphasis on laser control of chemical dynamics. Photoassociation, the laser-assisted formation of chemical bonds from atoms

or molecular fragments is an emerging and challenging field. For unimolecular reactions we discussed the potential of weak-field as well as strong-field control. The weak-field excitation out of a single stationary state has attracted renewed attention, e.g., concerning the possibilities of laser phase control at intermediate times after the pulse has decayed but before the “long-time limit” is reached. For strong-field control we discussed, in particular, some realistic theoretical implementations of “pumpdump” control. It was shown that in order to control branching ratios in photofragmentation, beyond what is obtainable in the weak-field limit, very strong fields are required. Thus, the suppression of ionization becomes an important issue. Clearly, further advancements in laser technology

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Femtochemistry; non-stationary states; laser control

A

UV-pulse

A A

B

B

C A

C A

B

B C

C

B

+ C