Time Resolved Molecular Dynamics

Abstract

The interaction of molecules with ultrashort laser pulses results in the preparation of nonstationary quantum states and may trigger photophysical and photochemical processes. As a result, measurements of molecular observables explicitly depend on time, thus reflecting the underlying dynamics. This chapter presents a theoretical description of a so-called pump-probe scheme that involves the preparation and detection of the molecular motion. As a particular example, the experimental realization of transient absorption spectroscopy is described. Utilizing this technique, a photochemical reaction proceeding differently in dependence on the solvent environment is discussed, illustrating the versatility of pump-probe measurements for investigating the dynamics of chemical reactions in real time. Further topical experimental developments in the ultrafast spectroscopy of molecular systems are outlined. These recent approaches comprise coherent two-dimensional spectroscopy, X-ray and electron diffraction, and also the possibility of quantum control with shaped laser pulses.

1 Introduction

Time-resolved experiments have been performed on a multitude of molecular systems. Applications of spectroscopic techniques that work in the time domain range from the detection of simple vibrational motion of a diatomic molecule to the direct determination of relaxation times in polyatomic molecules in a liquid environment, or the recording of isomerization processes in biomolecules. The underlying principles of these experiments are more or less the same. Here, we summarize the basic ideas of transient spectroscopy. First, the quantum-mechanical description of a so-called “pump-probe” scheme is given, where two time-delayed interactions prepare and detect molecular dynamics (Sect. 37.2). This is followed in Sect. 37.3 by a summary of experimental realizations of the pump-probe scheme. To further illustrate the latter, an example of transient absorption measurements in the liquid phase is presented in Sect. 37.4. Finally, more recent developments and additional aspects are outlined in Sect. 37.5.

There exists an extensive amount of literature on the topic of time-resolved molecular dynamics. To follow the developments over the years and keep track of the evolution of the exciting field and its latest innovations, it is instructive to consult the book series related to the biennial “International Conference on Ultrafast Phenomena” 1 ; 2 ; 3 ; 4 ; 5 ; 6 ; 7 ; 8 ; 9 ; 10 ; 11 .

2 The Principle of Time-Resolved Spectroscopy

We exemplarily look at the phenomenon of wave packets and discuss how to coherently induce and subsequently observe them with ultrashort laser pulses. Regard a molecule with Hamiltonian $\hat{H}_{0}$ so that the time-independent Schrödinger equation reads

$$\displaystyle\hat{H}_{0}\;|\psi_{n}\rangle=E_{n}\;|\psi_{n}\rangle\;.$$

(37.1)

Here, | ψ_n⟩ are the eigenstates with eigenenergies E_n. The time-dependent Schrödinger equation for a general state | ψ(t)⟩ is

$$\displaystyle i\hbar\frac{\partial}{\partial t}|\psi(t)\rangle=\hat{H}_{0}|\psi(t)\rangle\;.$$

(37.2)

If the state at the initial time t = 0 is an eigenstate, i.e., $|\psi(0)\rangle=|\psi_{n}\rangle$, the time-evolution simply reads

$$\displaystyle|\psi_{n}(t)\rangle=e^{-\frac{i}{\hbar}E_{n}t}\;|\psi_{n}\rangle\;,$$

(37.3)

and the expectation value of an operator $\hat{A}$ is time-independent

$$\displaystyle\begin{aligned}\displaystyle\langle\hat{A}\rangle(t)=\langle\psi_{n}(t)|\hat{A}|\psi_{n}(t)\rangle&\displaystyle=\langle\psi_{n}(0)|\hat{A}|\psi_{n}(0)\rangle\\ \displaystyle&\displaystyle=\langle\hat{A}\rangle(0)\;.\end{aligned}$$

(37.4)

This means that if a measurement of an observable A with associated operator $\hat{A}$ is performed on a molecule in an eigenstate, then the result of the measurement does not depend on time.

Assume now that the state of the molecule at time t = 0 is a superposition of eigenstates so that

$$\displaystyle|\psi\rangle=\sum_{n}c_{n}\;|\psi_{n}\rangle\;,$$

(37.5)

with coefficients c_n. Such superposition states are called wave packets, and their time dependence is given by

$$\displaystyle|\psi(t)\rangle=\sum_{n}c_{n}\;e^{-\frac{i}{\hbar}E_{n}t}\;|\psi_{n}\rangle\;.$$

(37.6)

Taking the expectation value of $\hat{A}$ with respect to this state, we find that it now depends on time

$$\displaystyle\langle\hat{A}\rangle(t)=\sum_{m}\sum_{n}c_{m}^{*}\;c_{n}\;e^{i\Updelta_{mn}t}\;\langle\psi_{m}|\hat{A}|\psi_{n}\rangle\;,$$

(37.7)

with $\Updelta_{mn}=(E_{m}-E_{n})/\hbar$. The time-dependence is contained in the phase factors that result in characteristic oscillations with frequencies determined by the energy differences between the molecular eigenenergies.

The obvious principle evolving from the above considerations is that a time-dependent experiment may reflect the induced dynamics, if we prepare the system in a superposition state. This is possible if it is subject to a time-dependent perturbation which, as we here are concerned with spectroscopic measurements, is a laser field. The time-dependent Schrödinger equation is then

$$\displaystyle i\hbar\frac{\partial}{\partial t}|\psi(t)\rangle=\left(\hat{H}_{0}+\hat{W}_{1}(t)\right)\;|\psi(t)\rangle\;,$$

(37.8)

with the molecule–field interaction $\hat{W}_{1}(t)$, which starts at the reference time t = 0. Writing the state vector as

$$\displaystyle|\psi(t)\rangle=\sum_{n}b_{n}(t)\;e^{-\frac{i}{\hbar}E_{n}t}\;|\psi_{n}\rangle\;,$$

(37.9)

with time-dependent coefficients b_n(t), the Schrödinger equation can, by projection, be transformed to a coupled system of linear differential equations for the coefficients, which reads

$$\displaystyle i\hbar\frac{\partial}{\partial t}b_{m}(t)=\sum_{n}b_{n}(t)\;e^{i\Updelta_{mn}t}\;\langle\psi_{m}|\hat{W}_{1}(t)|\psi_{n}\rangle\;.$$

(37.10)

In order to find conditions for the preparation of wave packets, we regard the situation where the time-dependent interaction results in photon absorption. Inserting the explicit form of the electric dipole interaction we have

$$\displaystyle\hat{W}_{1}(t)=-\frac{1}{2}\hat{\mu}\;f_{1}(t)\;e^{-i\omega_{1}t}\;,$$

(37.11)

where $\hat{\mu}$ is the projection of the dipole operator on the polarization vector of the electric field, ω₁ the frequency of the laser pulse (commonly referred to as the pump pulse), and f₁(t) is an envelope function. Then Eq. (37.10) takes the form

$$\displaystyle i\hbar\frac{\partial}{\partial t}b_{m}(t)=-\frac{1}{2}\sum_{n}\langle\psi_{m}|\hat{\mu}|\psi_{n}\rangle\;b_{n}(t)\;f_{1}(t)\;e^{i(\Updelta_{mn}-\omega_{1})t}\;.$$

(37.12)

The coefficients b_m(t) become time-independent when the interaction is over ($b_{m}(t)=\overline{b}_{m}$), and we have

$$\displaystyle\overline{b}_{m}=b_{m}(0)+\frac{1}{i\hbar}\sum_{n}\langle\psi_{m}|\hat{\mu}|\psi_{n}\rangle\;I_{mn}(1)\;,$$

(37.13)

with the integrals

$$\displaystyle I_{mn}(1)=-\frac{1}{2}\int\limits_{0}^{\infty}dt\;b_{n}(t)\,f_{1}(t)\;e^{i(\Updelta_{mn}-\omega_{1})t}\;,$$

(37.14)

where the argument (1) refers to the properties of the pump pulse. In general, several of the coefficients will be nonzero so that, after the interaction, the state vector is a wave packet

$$\displaystyle|\psi(t)\rangle=\sum_{n}\overline{b}_{n}\;e^{-\frac{i}{\hbar}E_{n}t}\;|\psi_{n}\rangle\;.$$

(37.15)

The characteristic timescales for the molecular motion are determined by the energy differences

$$\displaystyle T_{mn}=\left|\frac{2\pi}{\Updelta_{mn}}\right|\;,$$

(37.16)

where the longest oscillation period T_max is obtained for the smallest energy separation between two eigenstates. If the pulse duration T_p1 is longer than T_max, and the excitation of the molecule is resonant with a single transition, i.e., $\Updelta_{m_{r}n_{r}}-\omega_{1}=0$, then, due to the oscillating phase factors, only one integral I_mn(1) is nonzero. This means that, for longer interaction times, a single eigenstate rather than a linear combination of states is excited. Thus, the condition for the preparation of wave packets is that the pulse duration is smaller than, or in the order of, the longest characteristic timescale for the molecular motion, i.e., $T_{p,1}<T_{\max}$. Typical, oscillation periods for the vibrational motion of molecules are in the femtosecond range, so that time-resolved experiments need ultrashort pulses in the femtosecond regime. The same applies to the fastest photochemical reactions, which, for direct dissociations, take place on the sub-100-fs timescale. On the other hand, rotational periods are in the order of picoseconds (and longer), so they can be resolved with ps laser pulses.

Having prepared a wave packet with the pump interaction at the reference time t = 0, the question is how to detect its motion. This is realized in perturbing the system, at a defined delay time T, with another laser pulse (the probe pulse). Restricting the discussion to a second photon absorption, the interaction energy is as in Eq. (37.11), but the pulse envelope f₂(t) starts at the delay time, and the frequency ω₂ may be different. The wave packet at time T is now written as

$$\displaystyle|\psi(t^{\prime})\rangle=\sum_{n}d_{n}(t^{\prime})\;e^{-\frac{i}{\hbar}E_{n}(t^{\prime}+T)}\;|\psi_{n}\rangle\;,$$

(37.17)

where $d_{n}(0)=\overline{b}_{n}$, and the new time variable starts at t^′ = 0. Following the same procedure as above, one arrives at the coupled equations

$$\displaystyle\begin{aligned}\displaystyle i\hbar\frac{\partial}{\partial t^{\prime}}d_{m}(t^{\prime})&\displaystyle=-\frac{1}{2}\sum_{n}\langle\psi_{m}|\hat{\mu}|\psi_{n}\rangle\\ \displaystyle&\displaystyle\quad\times d_{n}(t^{\prime})f_{2}(t^{\prime})\;e^{i(\Updelta_{mn}-\omega_{2})t^{\prime}}e^{i\Updelta_{mn}T}\;.\end{aligned}$$

(37.18)

We may integrate this equation and regard times after the interaction when the coefficients become time-independent, so that

$$\displaystyle\overline{d}_{m}=d_{m}(0)+\frac{1}{i\hbar}\sum_{n}\langle\psi_{m}|\hat{\mu}|\psi_{n}\rangle\;I_{mn}(2)\;e^{i\Updelta_{mn}T}\;,$$

(37.19)

where

$$\displaystyle I_{mn}(2)=-\frac{1}{2}\int\limits_{0}^{\infty}dt^{\prime}\;d_{n}(t^{\prime})\,f_{2}(t^{\prime})\;e^{i(\Updelta_{mn}-\omega_{2})t^{\prime}}\;.$$

(37.20)

Regarding the quantity I_mn(2) we see again that for a pulse being substantially longer than the oscillations times T_mn, the probe laser couples only levels that are in resonance with its frequency ω₂.

If we now regard the wave packet after the two laser interactions [Eq. (37.17) with $d_{n}(t^{\prime})=\overline{d}_{n}$], the expectation value of an operator $\hat{A}$ depends not only on the propagation time t^′ but also on the delay time between the pump pulse and the probe pulse. This scheme is readily extended to experiments that involve more than two interactions. For example, in a third-order photon echo experiment, three pulses are delayed to each other. Then the expectation value of the dipole operator, which is the third-order polarization, depends on two delay times τ , T and on the propagation (or detection) time t^′.

As described in the previous sections, the preparation of wave packets and the detection of their motion are essential to time-resolved spectroscopy 12 ; 13 ; 14 . If regarded in coordinate space, the probability density of a wave packet changes as a function of time. As an example, we regard a one-dimensional, coupled electron-nuclear motion. The employed model of this reduced dimensionality dynamics is such that the nuclear motion can be described with the Born–Oppenheimer approximation 15 . Then, the nuclear probability density moves in a bound-state potential, and the electronic density follows the nuclear dynamics. This is illustrated in the left-hand panels of Fig. 37.1. The densities move towards larger distances R, and upon reflection at the outer potential wall, the motion is reversed. The right-hand panels illustrate another case where the bound-state potential curve exhibits a potential barrier at R = 0, and the mean energy of the electron-nuclear wave packet is in the order of the barrier height. Then, a splitting occurs where the densities are partly reflected at the barrier.

Fig. 37.1

Wave packet bound-state motion. From the solution of the time-dependent Schrödinger equation for a simplified one-dimensional electron-nuclear motion, the nuclear (ρ_N(R , t)) and electronic (ρ_el(r , t)) probability densities are obtained. The motion proceeds adiabatically, so that the electronic density follows the nuclear geometry changes. Left-hand panels: the nuclear wave packet moves in a bound-state potential outward until it is reflected at a potential wall. The electronic density adapts adiabatically to the nuclear motion. Right-hand panels: the nuclear density is partly reflected at a potential barrier, and the same applies to the electronic density. The data was originally discussed in 15

One-dimensional wave packet motion has been studied extensively using pump-probe fluorescence 16 ; 17 . Later, other techniques like pump-probe ionization 18 ; 19 or time-resolved CARS spectroscopy 20 were applied. A beautiful example is the detection of vibrational motion in the Na₂ molecule via time-resolved photoelectron spectroscopy. Following theoretical studies 21 ; 22 , it was documented that the time-dependent probability density of nuclear wave packets can be directly mapped onto the energy dependence of the photoelectron spectra 23 ; 24 ; 25 .

3 Pump-Probe Scheme

The pump-probe scheme outlined above can be realized in various ways. In the majority of experiments on ultrafast dynamics, the time resolution is obtained by employing two laser pulses: the first one (termed pump pulse) interacts with the sample and starts the process to be studied, whereas after a well-defined, adjustable delay time T, a second laser pulse (called probe pulse) interacts and thereby monitors the time evolution induced by the pump pulse 26 ; 27 ; 28 . In order to detect signals as a function of T, different detection schemes have been realized and depend on the sample that is investigated. Nonoptical detection may record the amount of ions or electrons generated by the probe pulse, e.g., from a molecular beam, a liquid microjet, a surface, or its adsorbate in a vacuum chamber system; optical detection may comprise the emission intensity from a higher-lying state reached by the probe pulse (laser-induced fluorescence) or the degree of attenuation of the probe pulse (transient absorption).

Generally, the signal detected reflects the temporal evolution of the system as induced by the pump pulse. In the case of wave packet dynamics, an oscillatory behavior can be detected, because the wave packet's spatial distribution varies with time (Fig. 37.1), and properties like the ionization cross section or the absorption coefficient are, thereby, transiently modulated. Beyond coherent effects, many processes can cause signal changes on an ultrafast timescale, among them relaxation and solvation, or actual reactions originating from the state reached by the pump pulse, e.g., photodissociation, energy or charge transfer, photoisomerization, rearrangement and other geometrical changes, intersystem crossing and quenching, and very often a combination of several of these processes.

There are also ultrafast techniques that do not incorporate two laser pulses interacting with the sample. In fluorescence upconversion as well as in fluorescence Kerr gating, the emitted light from a sample excited by the pump pulse is strobed by a second laser pulse (often called the gate pulse) in a nonlinear process. Since the delay time between the pump (and thus the fluorescence) and the gate pulse is again adjustable in a well-defined fashion, the temporal emission profile is obtained. Great advances have also been achieved by an ultrashort pump pulse in combination with streak cameras or time-correlated single-photon counting, yet the best time resolution can be achieved in the nonlinear approaches with very short laser pulses 27 .

In the past decades, laser sources have been perpetually improved. In the visible spectral domain, pulse durations of 20 fs are routinely employed; soft X-rays even allow the generation of attosecond pulses. The accessible spectral range has been continuously extended as well, so that pump-induced dynamics can be performed or probed with pulses from the far-infrared 29 or from the X-ray regime (Sect. 37.5.2), and basically all spectral regions in between.

4 Transient Absorption in the Liquid Phase

Chemical reaction dynamics in solution can be elucidated with ultrafast transient absorption spectroscopy in a unique fashion. A schematic experimental implementation is shown in Fig. 37.2a. The spectrally resolved intensity of the probe beam is measured as a function of the pump-probe delay T. To separate the transient from stationary absorption signals, the difference in optical density is determined from two measurements, one with and one without the pump pulse, respectively

$$\displaystyle\Updelta OD(\lambda_{\mathrm{probe}},T)=-\log_{10}\left[\frac{I_{\mathrm{pumped}}(\lambda_{\mathrm{probe}},T)}{I_{\mathrm{unpumped}}(\lambda_{\mathrm{probe}})}\right]\;;$$

(37.21)

ΔOD is positive if the probe encounters absorbing species that were not there in the absence of the pump pulse, i.e., excited reactants or products, whereas it is negative for stimulated emission from excited species or in case of the ground-state bleach caused by a reduced number of reactants in the ground state.

Fig. 37.2

Three ultrafast liquid-phase spectroscopy approaches (plotted with lenses and a minimal amount of optics for simplicity). a Transient absorption: a spectrometer determines the probe spectrum for different values of the pump-probe delay T. b Coherent 2-D spectroscopy in pump-probe geometry. The spectrometer measures the probe spectrum for each combination of pump-probe delay T and the delay τ of a phase-stable pump-pulse pair, here generated by a liquid-crystal display (LCD) pulse shaper in a folded zero-dispersion compressor setup. Subsequent Fourier transformation with respect to τ yields 2-D spectra for each value of T. c Coherent 2-D spectroscopy in boxcars geometry: the phase-stable pump pulses and the probe pulse traverse the sample from different directions, a local oscillator heterodynes the signal field emitted. Thus, the spectrometer measures the interference of the signal field and the local oscillator for each combination of T and τ

As an example, the photodynamics of Ph₂CN₂ (diphenyldiazomethane) in different solvent environments are shown in Fig. 37.3. Upon excitation at T = 0 with a pump pulse centered at 285 nm, N₂ is photolyzed off, and a reactive carbene ¹Ph₂C is formed, which is initially in a singlet configuration. The singlet absorption is observed around 355 nm (labeled S in Fig. 37.3). In the aprotic solvent MeCN (acetonitrile), ¹Ph₂C (S) will turn into a triplet ³Ph₂C (T) within several hundred ps. In the presence of the protic solvent MeOH (methanol), a benzhydryl cation Ph₂CH⁺ (B) or a hydrogen-bonded complex ¹Ph₂C⋯HOMe (C) can be formed, depending on whether or not the close-by MeOH molecule is part of a hydrogen-bond network with other MeOH molecules, respectively. Both B and C react on to an ether that does not absorb in the covered spectral range. As can be seen in Fig. 37.3, the signal of the benzhydryl cation B is the most pronounced and decays the most rapidly in the absence of MeCN. Thus, these exemplary data sets emphasize that transient absorption is a powerful tool to reveal the different reaction pathways and the characteristic time scales of chemical reactions in solution.

Fig. 37.3

Transient absorption maps of Ph₂CN₂ in binary solvent mixtures of MeCN and MeOH. Note the logarithmic ordinate for T values beyond 2 ps in the left panel. The data was originally discussed in 30 , and graphs are adapted therefrom

5 Further Implementations

The arsenal of ultrafast experimental techniques is increasing at an incredible speed. Besides extending to new spectral regions and lower pulse durations, the nonlinearity of the light–matter interaction and also the number of laser pulses employed are adapted to unravel previously unexplored photophysical and photochemical aspects. In the following, a few of these recent developments are outlined.

5.1 Coherent Two-Dimensional Spectroscopy

While in a transient absorption experiment, molecules are excited with a wavenumber $\tilde{\nu}_{\mathrm{pump}}$ and probed with $\tilde{\nu}_{\mathrm{probe}}$ (note that often frequency or wavenumber rather than wavelength is used for data presentation) after a delay time T, a transient absorption map as in Fig. 37.3 is a representation of the system response as a function of the latter two quantities only. To gain information on the role of the pump wavenumber, the spectral position of the pump pulse can be tuned, and each time a transient absorption map is recorded (Fig. 37.4a). However, the spectral bandwidth of the pump pulse limits the spectral resolution along $\tilde{\nu}_{\mathrm{pump}}$. This can be overcome by splitting the pump pulse into a phase-stable pulse pair whose delay τ is scanned (e.g. by a pulse shaper as in Fig. 37.2b), a subsequent Fourier transform of the detected signal with respect to τ yields the dependence on $\tilde{\nu}_{\mathrm{pump}}$. Hence, for each delay time T, which can be varied as well to capture the full dynamics, the information is spread along two frequency axes (Fig. 37.4b), thereby allowing in an intuitive way the identification of couplings, transfer processes, or generally how a pumped species interacts with or turns into a probed one. This technique of coherent two-dimensional (2-D) spectroscopy 31 ; 32 ; 33 ; 34 ; 35 ; 36 ; 37 can be understood as an optical analogue of recording frequency-correlation spectra in 2-D nuclear magnetic resonance.

Fig. 37.4

Ultrafast spectroscopy data for the molecule 6-nitro-1^′ , 3^′ , 3^′-trimethylspiro[2H-1-benzopyran-2 , 2^′-indoline] (6-nitro-BIPS). By transient absorption with different central pump wavenumbers $\tilde{\nu}_{\mathrm{pump}}^{\mathrm{central}}$ (a), the dynamics can be investigated in a 3-D space with dimensions representing the central pump wavenumber, the pump-probe delay time T, and the probe wavenumber. 2-D spectroscopy (b) measurements can span the same 3-D space but without the disadvantage of a spectral blurring along the pump wavenumber axis as present in transient absorption as a consequence of the pump pulse's spectral width. The graphs are adapted from 37

Many different implementations of 2-D spectroscopy exist, all with pros and cons, the most versatile but possibly also experimentally most challenging being the boxcars geometry (Fig. 37.2c), where the three pulses all come from different directions, and the desired signal from the sample is emitted in yet another direction. With the help of an adequate local oscillator, that is a further pulse that together with the signal field impinges upon the detector, the signal field can be fully retrieved in both amplitude and phase, and thus the system's response to the interacting fields is fully accessible.

2-D spectroscopy is successfully applied in many spectral ranges, from THz 38 to ultraviolet 39 ; 40 ; 41 ; 42 ; 43 . In 2-D infrared spectroscopy, vibrations are labeled by the pump event, and subsequent processes (coupling between vibrational modes, spectral diffusion, relaxation, chemical exchange, …) are monitored, making it a versatile tool for assessing molecular structure and associated dynamics 34 ; 35 ; 44 . 2-D electronic spectroscopy correlates electronic transitions and has proven to be particularly powerful for unraveling electronic couplings and exciton dynamics in light-harvesting systems 45 ; 46 and has opened the door to tackle the pressing question as to which extent coherent phenomena affect functionality in chemical or biological systems 46 .

5.2 Ultrafast Dynamics Studied with X-Ray and Electron Pulses

In recent years, ultrashort pulses have been extended into the X-ray regime 47 ; 48 ; 49 ; 50 ; 51 ; 52 . Laboratory-based sources often rely on a laser-induced plasma or a high-harmonic-generation (HHG) process. In the latter, photons at odd multiples of the initial laser frequency are generated in a strong-field nonlinear effect up to a spectral cutoff region, so that the radiation comprises coherent soft X-rays, which even allow the formation of attosecond pulses. Pump-probe schemes involving these soft X-rays opened a new way for unraveling nuclear and electron dynamics in atoms but also in molecules, both for gas-phase samples and in the condensed phase, providing insight into processes like charge transfer, ring opening, and photofragmentation 51 ; 52 ; 53 . Many of these experiments make use of a high photon-energy pump pulse in order to prepare core-excited states such that the following dynamics could be detected with a time-delayed optical probe pulse. In a second scenario, a visible or UV pump pulse initiates a chemical reaction that is followed by a time-delayed X-ray pulse, which is then able to selectively excite core levels of the atoms involved in the process and thereby track the transient changes due to structural dynamics. This requires femtosecond hard X-ray pulses, as are available from storage rings with electron-bunch slicing and more recently from X-ray free-electron lasers (XFELs) delivering high-intensity hard X-ray pulses with durations of a few fs. Hard X-ray pulses have helped to elucidate structural changes after photoexcitation, e.g., in iron complexes that exhibit rapid spin-crossover processes: for [Fe^II(bpy)₃]²⁺, absorption changes near the K-edge of Fe disclose bond lengthening after spin-crossover 48 , resonant inelastic X-ray scattering applied to Fe(CO)₅ in an ethanol jet can separate triplet and ligation reaction channels on sub-ps time scales after photolysis of one CO 54 .

These soft and hard X-ray approaches provide insight into structural dynamics not accessible in a similar fashion with ultrafast techniques in more conventional spectral regimes. A further example is the ring-opening reaction of 1,3-cyclohexadiene to 1,3,5-hexatriene, which has been extensively studied both with ultrafast spectroscopy and dynamics simulations (as e.g., summarized in 55 ). The reaction dynamics could also be investigated by X-ray core ionization from an XFEL 56 , the temporal evolution of the valence electronic structure was explored by soft X-rays near the carbon K-edge generated by HHG 57 , while fs X-ray scattering in combination with calculated reaction trajectories provide real-space images of transient structures in this electrocyclic reaction 58 .

The latter study is an example of a time-resolved X-ray diffraction experiment, an area that strongly benefits from recent advances in XFELs 49 ; 50 . Instead of using electromagnetic waves, a complementary approach with pulses of electrons (ultrafast electron diffraction) has been developed, with high sensitivity and spatiotemporal resolution so that structural dynamics are followed in real time 59 ; 60 . These powerful techniques provide an auspicious perspective for resolving structural dynamics with unprecedented possibilities, probing changes in molecular geometry rather than in energy.

5.3 Dynamics and Control

As has been discussed throughout this chapter, molecular motion can be traced with the help of time-resolved spectroscopy. It is also possible to go one step ahead and use laser pulses to control molecular motion. For a long time, the field of “quantum control” has been dominated by theoretical work, see the textbooks 61 ; 62 ; 25 . However, the technical advances in laser technology have led to experimental realizations of proposed theoretical schemes. Employing sophisticated devices to modify the amplitude, phase, and/or polarization state of the laser pulses in a well-defined way 63 , e.g., pulse shapers 64 as in Fig. 37.2b, the outcome of a chemical reaction can be influenced by specifically tailored light pulses. For the determination of the latter, feedback algorithms can be employed 65 . The range of photochemical reactions for which such an approach was demonstrated spans from molecular dimers in the gas phase via reactions on surfaces, organic molecules in solution, processes in solids, to large biological systems relevant in photosynthesis. It is worthwhile taking a look at one of the reviews 66 ; 67 ; 68 ; 69 ; 70 summarizing the accomplishments with quantum control approaches.