Isolating Attosecond Electron Dynamics in Molecules where Nuclei Move Fast.

Capturing electronic dynamics in real time has been the ultimate goal of attosecond science since its beginning. While for atomic targets the existing measurement techniques have been thoroughly validated, in molecules there are open questions due to the inevitable copresence of moving nuclei, which are not always mere spectators of the phototriggered electron dynamics. Previous work has shown that not only can nuclear motion affect the way electrons move in a molecule, but it can also lead to contradictory interpretations depending on the chosen experimental approach. In this Letter we investigate how nuclear motion affects and eventually distorts the electronic dynamics measured by using two of the most popular attosecond techniques, reconstruction of attosecond beating by interference of two-photon transitions and attosecond streaking. Both methods are employed, in combination with ab initio theoretical calculations, to retrieve photoionization delays in the dissociative ionization of H_{2}, H_{2}→H^{+}+H+e^{-}, in the region of the Q_{1} series of autoionizing states, where nuclear motion plays a prominent role. We find that the experimental reconstruction of attosecond beating by interference of two-photon transitions results are very sensitive to bond softening around the Q_{1} threshold (27.8 eV), even at relatively low infrared (IR) intensity (I_{0}∼1.4×10^{11} W/cm^{2}), due to the long duration of the probe pulse that is inherent to this technique. Streaking, on the other hand, seems to be a better choice to isolate attosecond electron dynamics, since shorter pulses can be used, thus reducing the role of bond softening. This conclusion is supported by very good agreement between our streaking measurements and the results of accurate theoretical calculations. Additionally, the streaking technique offers the necessary energy resolution to accurately retrieve the fast-oscillating phase of the photoionization matrix elements, an essential requirement for extending this technique to even more complicated molecular targets.

Vibrationally resolved photoelectron angular distributions of ammonia.

We present a theoretical study of vibrationally resolved photoelectron angular distributions for ammonia in both laboratory and molecular frames, in the photon energy range up to 70 eV, where only valence and inner-valence ionization is possible. We focus on the band resulting from ionization of the 3a1 HOMO orbital leading to NH3+ in the electronic ground state, , for which the dominant vibrational progression corresponds to the activation of the umbrella inversion mode. We show that, at room temperature, the photoelectron angular distributions for randomly oriented molecules or molecules whose principal C3 symmetry axis is aligned along the light polarization direction are perfectly symmetric with respect to the plane that contains the intermediate D3h conformation connecting the pyramidal structures associated with the double-well potential of the umbrella inversion mode. These distributions exhibit symmetric, nearly perfect two-lobe shapes in the whole range of investigated photon energies. In contrast, for molecules where the initial vibrational state is localized in one of the two wells, a situation that can experimentally be achieved by introducing an external electric field, the molecular-frame photoelectron angular distributions (MFPADs) are in general asymmetric, but the degree of asymmetry of the two lobes dramatically changes and oscillates with photoelectron energy. We also show that, at ultracold temperatures, where all aligned molecules initially lie in the delocalized ground vibrational state, the photoelectron angular distributions are perfectly symmetric, but the two-lobe shape is only observed when the final vibrational state of the resulting NH3+ cation has even parity. When the latter vibrational state has odd parity, the angular distributions are much more involved and, at photoelectron energies of ∼10 eV, they directly reflect the bi-pyramidal geometry of the molecule in its ground vibrational state. These results suggest that, in order to obtain structural information from MFPADs in ammonia and likely in other molecules containing a similar double-well potential, one could preferably work at ultracold temperatures, which is not the case for most molecules.

Attosecond laser control of photoelectron angular distributions in XUV-induced ionization of H2.

We investigate how attosecond XUV pump/IR probe schemes can be used to exert control on the ionization dynamics of the hydrogen molecule. The aim is to play with all available experimental parameters in the problem, namely the XUV pump-IR probe delay, the energy and emission direction of the produced photo-ions, as well as combinations of them, to uncover control strategies that can lead to preferential electron ejection directions. We do so by accurately solving the time-dependent Schrödinger equation, with inclusion of both electronic and nuclear motions, as well as the coupling between them. We show that both the IR pulse and the nuclear motion can be used to break the molecular inversion symmetry, thus leading to asymmetric molecular-frame photoelectron angular distributions. The preferential electron emission direction can thus be tuned by varying the pump-probe delay, by choosing specific ranges of proton kinetic energies, or both. We expect that similar control strategies could be used in more complex molecules containing light nuclei.

Molecular fragmentation as a way to reveal early electron dynamics induced by attosecond pulses.

We present a theoretical study of the electron and nuclear dynamics that would arise in an attosecond two-color XUV-pump/XUV-probe experiment in glycine. In this scheme, the broadband pump pulse suddenly ionizes the molecule and creates an electronic wave packet that subsequently evolves under the influence of the nuclear motion until it is finally probed by the second XUV pulse. To describe the different steps of such an experiment, we have combined a multi-reference static-exchange scattering method with a trajectory surface hopping approach. We show that by changing the central frequency of the pump pulse, i.e., by engineering the initial electronic wave packet with the pump pulse, one can drive the cation dynamics into a specific fragmentation pathway. Reminiscence of this early electron dynamics can be observed in specific fragmentation channels (not all of them) as a function of the pump-probe delay and in time-resolved photoelectron spectra at specific photoelectron energies. The optimum conditions to visualize the initial electronic coherence in photoelectron and photo-ion spectra depend very much on the characteristics of the pump pulse as well as on the electronic structure of the molecule under study.

Selecting two-photon sequential ionization pathways in H2 through harmonic filtering.

Recent experiments in gas-phase molecules have shown the versatility of using attosecond pulse trains combined with IR femtosecond pulses to track and control excitation and ionization yields on the attosecond timescale. The interplay between electron and nuclear motions drives the light-induced transitions favoring specific reaction paths, so that the time delay between the pulses can be used as the tracking parameter or as a control knob to manipulate the molecular dynamics. Here, we present ab initio simulations on the hydrogen molecule to demonstrate that by filtering the high harmonics in an attosecond pulse train one can quench or enhance specific quantum paths thus dictating the outcome of the reaction. It is then possible to discriminate the dominant sequential processes in two-photon ionization, as for example molecular excitation followed by ionization or the other way around. More interestingly, frequency filters can be employed to steer the one- and two-photon yields to favor electron emission in a specific direction.

Attosecond Electron Dynamics in Molecules.

Advances in attosecond science have led to a wealth of important discoveries in atomic, molecular, and solid-state physics and are progressively directing their footsteps toward problems of chemical interest. Relevant technical achievements in the generation and application of extreme-ultraviolet subfemtosecond pulses, the introduction of experimental techniques able to follow in time the electron dynamics in quantum systems, and the development of sophisticated theoretical methods for the interpretation of the outcomes of such experiments have raised a continuous growing interest in attosecond phenomena, as demonstrated by the vast literature on the subject. In this review, after introducing the physical mechanisms at the basis of attosecond pulse generation and attosecond technology and describing the theoretical tools that complement experimental research in this field, we will concentrate on the application of attosecond methods to the investigation of ultrafast processes in molecules, with emphasis in molecules of chemical and biological interest. The measurement and control of electronic motion in complex molecular structures is a formidable challenge, for both theory and experiment, but will indubitably have a tremendous impact on chemistry in the years to come.

Real-Time Imaging of Ultrafast Charge Dynamics in Tetrafluoromethane from Attosecond Pump-Probe Photoelectron Spectroscopy.

A pump-probe experiment in the tetrafluoro-methane (CF4 ) molecule has been theoretically simulated, allowing one to access electron dynamics in its natural time scale: the attosecond. The chosen pump and probe pulses can be currently produced in most attosecond laboratories. In this scheme, CF4 is first ionized by an extreme UV (XUV) attosecond pulse and the charge dynamics induced in the corresponding cation is probed with a few-femtosecond visible light (VIS) pulse. We demonstrate that modulations in the calculated photoelectron spectra with the pump-probe delay reflect the dynamics of the XUV-induced electronic wave packet. In particular, from the analysis of these modulations in the interval of time delays where the pump and probe pulses do not overlap any more, one has access to the amplitudes and phases of the different components of the electronic wave packet generated by the attosecond pulse. These reflect a complex dynamics that basically consists of very fast charge fluctuations occurring all over the molecule without any preference for a particular molecular site.

Ultrafast charge dynamics in glycine induced by attosecond pulses.

The combination of attosecond pump-probe techniques with mass spectrometry methods has recently led to the first experimental demonstration of ultrafast charge dynamics in a biomolecule, the amino acid phenylalanine [Calegari et al., Science, 2014, 346, 336]. Using an extension of the static-exchange density functional theory (DFT) method, the observed dynamics was explained as resulting from the coherent superposition of ionic states produced by the broadband attosecond pulse. Here, we have used the static-exchange DFT method to investigate charge migration induced by attosecond pulses in the glycine molecule. We show that the observed dynamics follows patterns similar to those previously found in phenylalanine, namely that charge fluctuations occur all over the molecule and that they can be explained in terms of a few typical frequencies of the system. We have checked the validity of our approach by explicitly comparing with the photoelectron spectra obtained in synchrotron radiation experiments and with the charge dynamics that follows the removal of an electron from a given molecular orbital, for which fully correlated ab initio results are available in the literature. From this comparison, we conclude that our method provides an accurate description of both the coherent superposition of cationic states generated by the attosecond pulse and its subsequent time evolution. Hence, we expect that the static-exchange DFT method should perform equally well for other medium-size and large molecules, for which the use of fully correlated ab initio methods is not possible.

Molecular interferometer to decode attosecond electron-nuclear dynamics.

Understanding the coupled electronic and nuclear dynamics in molecules by using pump-probe schemes requires not only the use of short enough laser pulses but also wavelengths and intensities that do not modify the intrinsic behavior of the system. In this respect, extreme UV pulses of few-femtosecond and attosecond durations have been recognized as the ideal tool because their short wavelengths ensure a negligible distortion of the molecular potential. In this work, we propose the use of two twin extreme UV pulses to create a molecular interferometer from direct and sequential two-photon ionization processes that leave the molecule in the same final state. We theoretically demonstrate that such a scheme allows for a complete identification of both electronic and nuclear phases in the wave packet generated by the pump pulse. We also show that although total ionization yields reveal entangled electronic and nuclear dynamics in the bound states, doubly differential yields (differential in both electronic and nuclear energies) exhibit in addition the dynamics of autoionization, i.e., of electron correlation in the ionization continuum. Visualization of such dynamics is possible by varying the time delay between the pump and the probe pulses.

Attosecond vacuum UV coherent control of molecular dynamics.

High harmonic light sources make it possible to access attosecond timescales, thus opening up the prospect of manipulating electronic wave packets for steering molecular dynamics. However, two decades after the birth of attosecond physics, the concept of attosecond chemistry has not yet been realized; this is because excitation and manipulation of molecular orbitals requires precisely controlled attosecond waveforms in the deep UV, which have not yet been synthesized. Here, we present a unique approach using attosecond vacuum UV pulse-trains to coherently excite and control the outcome of a simple chemical reaction in a deuterium molecule in a non-Born-Oppenheimer regime. By controlling the interfering pathways of electron wave packets in the excited neutral and singly ionized molecule, we unambiguously show that we can switch the excited electronic state on attosecond timescales, coherently guide the nuclear wave packets to dictate the way a neutral molecule vibrates, and steer and manipulate the ionization and dissociation channels. Furthermore, through advanced theory, we succeed in rigorously modeling multiscale electron and nuclear quantum control in a molecule. The observed richness and complexity of the dynamics, even in this very simplest of molecules, is both remarkable and daunting, and presents intriguing new possibilities for bridging the gap between attosecond physics and attochemistry.

Decoherence, control and attosecond probing of XUV-induced charge migration in biomolecules. A theoretical outlook.

The sudden ionization of a molecule by an attosecond pulse is followed by charge redistribution on a time scale from a few femtoseconds down to hundreds of attoseconds. This ultrafast redistribution is the result of the coherent superposition of electronic continua associated with the ionization thresholds that are reached by the broadband attosecond pulse. Thus, a correct theoretical description of the time evolution of the ensuing wave packet requires the knowledge of the actual ionization amplitudes associated with all open ionization channels, a real challenge for large and medium-size molecules. Recently, the first calculation of this kind has come to light, allowing for interpretation of ultrafast electron dynamics observed in attosecond pump-probe experiments performed on the amino acid phenylalanine [Calegari et al., Science 2014, 346, 336]. However, as in most previous theoretical works, the interpretation was based on various simplifying assumptions, namely, the ionized electron was not included in the description of the cation dynamics, the nuclei were fixed at their initial position during the hole migration process, and the effect of the IR probe pulse was ignored. Here we go a step further and discuss the consequences of including these effects in the photoionization of the glycine molecule. We show that (i) the ionized electron does not affect hole dynamics beyond the first femtosecond, and (ii) nuclear dynamics has only a significant effect after approximately 8 fs, but does not destroy the coherent motion of the electronic wave packet during at least few additional tens of fs. As a first step towards understanding the role of the probe pulse, we have considered an XUV probe pulse, instead of a strong IR one, and show that such an XUV probe does not introduce significant distortions in the pump-induced dynamics, suggesting that pump-probe strategies are suitable for imaging and manipulating charge migration in complex molecules. Furthermore, we show that hole dynamics can be changed by shaping the attosecond pump pulse, thus opening the door to the control of charge dynamics in biomolecules.

Crystal structure of inhibitor of growth 4 (ING4) dimerization domain reveals functional organization of ING family of chromatin-binding proteins.

The protein ING4 binds to histone H3 trimethylated at Lys-4 (H3K4me3) through its C-terminal plant homeodomain, thus recruiting the HBO1 histone acetyltransferase complex to target promoters. The structure of the plant homeodomain finger bound to an H3K4me3 peptide has been described, as well as the disorder and flexibility in the ING4 central region. We report the crystal structure of the ING4 N-terminal domain, which shows an antiparallel coiled-coil homodimer with each protomer folded into a helix-loop-helix structure. This arrangement suggests that ING4 can bind simultaneously two histone tails on the same or different nucleosomes. Dimerization has a direct impact on ING4 tumor suppressor activity because monomeric mutants lose the ability to induce apoptosis after genotoxic stress. Homology modeling based on the ING4 structure suggests that other ING dimers may also exist.

Electron localization involving doubly excited states in broadband extreme ultraviolet ionization of H2.

Dissociative single ionization of H(2) induced by extreme ultraviolet photons from an attosecond pulse train has been studied in a kinematically complete experiment. Depending on the electron kinetic energy and the alignment of the molecule with respect to the laser polarization axis, we observe pronounced asymmetries in the relative emission directions of the photoelectron and the H(+) ion. The energy-dependent asymmetry pattern is explained by a semiclassical model and further validated by fully quantum mechanical calculations, both in very good agreement with the experiment.

Two-pulse control of large-amplitude vibrations in H2(+).

A laser-adiabatic manipulation of the bond (LAMB) scheme using moderately intense fields is proposed to induce and control large-amplitude oscillations in nuclear wave packets. The present scheme involves an ultrashort UV pump pulse to initially create a wave packet in an excited electronic state of the hydrogen molecular ion and a low-frequency control pulse, which is switched on after a given time, leading to controllable vibrational trapping. The choice of H2(+) as the target exploits the larger dipole values that molecular ions present as the internuclear distance increases. The amplitude and oscillation period of the wave packet is tuned by the field parameters of the control pulse, and more importantly, significant dissociation and ionization losses are prevented by keeping the laser intensities below hundreds of Terawatts. Our numerical simulations, based on the solution of the time-dependent Schrödinger equation, show that this control of the bond length is achieved in a wide range of moderate intensities and for relatively long pulse durations, from tens to hundreds of femtoseconds.

Autoionization of molecular hydrogen: where do the Fano lineshapes go?

Atomic autoionization following photoabsorption is a typical example of quantum interferences governed by electron-electron correlation. Coherence between direct photoionization and autoionization paths results in "Fano profiles", widely explored in atoms in the last 60 years. The advent of femto- and attosecond laser technology made time-resolved images of the delayed electron ejection in autoionization accessible, leading to the reemergence of such studies in atomic systems. The counterpart molecular phenomena show the richness, as well as the complexity, added by nuclear motion, which may proceed on similar time scales. However, Fano profiles are usually absent in measured molecular photoionization cross sections and an unequivocal parametrization of molecular autoionization signatures, similar to that introduced by Fano in atoms [U. Fano, Phys. Rev. 1961, 124, 1866] has not yet been achieved. In this work we introduce a simple semiclassical model that accounts for all the features observed in H2 photoionization and demonstrate that the interference structures observed in dissociative ionization spectra are almost exclusively due to the phase accumulated in the nuclear motion. Furthermore, we show that the temporal build-up of these structures in the energy-differential cross sections is also determined by nuclear motion. We validate our models by comparing with full-dimensional ab initio calculations solving the time-dependent Schrödinger equation.

Ultrafast coherent control of giant oscillating molecular dipoles in the presence of static electric fields.

We propose a scheme to generate electric dipole moments in homonuclear molecular cations by creating, with an ultrashort pump pulse, a quantum superposition of vibrational states on electronic states strongly perturbed by very strong static electric fields. By field-induced molecular stabilization, the dipoles can reach values as large as 50 Debyes and oscillate on a time-scale comparable to that of the slow vibrational motion. We show that both the electric field and the pump pulse parameters can be used to control the amplitude and period of the oscillation, while preventing the molecule from ionizing or dissociating.

Attosecond delays between dissociative and non-dissociative ionization of polyatomic molecules.

The interplay between electronic and nuclear motions in molecules is a central concept in molecular science. To what extent it influences attosecond photoionization delays is an important, still unresolved question. Here, we apply attosecond electron-ion coincidence spectroscopy and advanced calculations that include both electronic and nuclear motions to study the photoionization dynamics of CH4 and CD4 molecules. These molecules are known to feature some of the fastest nuclear dynamics following photoionization. Remarkably, we find no measurable delay between the photoionization of CH4 and CD4, neither experimentally nor theoretically. However, we measure and calculate delays of up to 20 as between the dissociative and non-dissociative photoionization of the highest-occupied molecular orbitals of both molecules. Experiment and theory are in quantitative agreement. These results show that, in the absence of resonances, even the fastest nuclear motion does not substantially influence photoionization delays, but identify a previously unknown signature of nuclear motion in dissociative-ionization channels. These findings have important consequences for the design and interpretation of attosecond chronoscopy in molecules, clusters, and liquids.