Manipulating ultrafast even-order nonlinear chiral responses of L-tryptophan by polarization pulse shaping.

Molecular chirality has long been monitored in the frequency domain in the ultraviolet, visible, and infrared regimes. Recently developed time-domain approaches can detect time-dependent chiral dynamics by enhancing intrinsically weak chiral signals. Even-order nonlinear signals in chiral molecules have gained attention thanks to their existence in the electric dipole approximation, without relying on the weaker higher-order multipole interactions. We illustrate the optimization of temporal polarization pulse-shaping in various frequency ranges (infrared/optical and optical/X ray) to enhance chiral nonlinear signals. These signals can be recast as an overlap integral of matter and field pseudoscalars which contain the relevant chiral information. Simulations are carried out for second- and fourth-order nonlinear spectroscopies in L-tryptophan.

Ultrafast X-Ray Probes of Elementary Molecular Events.

Elementary events that determine photochemical outcomes and molecular functionalities happen on the femtosecond and subfemtosecond timescales. Among the most ubiquitous events are the nonadiabatic dynamics taking place at conical intersections. These facilitate ultrafast, nonradiative transitions between electronic states in molecules that can outcompete slower relaxation mechanisms such as fluorescence. The rise of ultrafast X-ray sources, which provide intense light pulses with ever-shorter durations and larger observation bandwidths, has fundamentally revolutionized our spectroscopic capabilities to detect conical intersections. Recent theoretical studies have demonstrated an entirely new signature emerging once a molecule traverses a conical intersection, giving detailed insights into the coupled nuclear and electronic motions that underlie, facilitate, and ultimately determine the ultrafast molecular dynamics. Following a summary of current sources and experiments, we survey these techniques and provide a unified overview of their capabilities. We discuss their potential to dramatically increase our understanding of ultrafast photochemistry.

Molecular Chirality and Its Monitoring by Ultrafast X-ray Pulses.

Major advances in X-ray sources including the development of circularly polarized and orbital angular momentum pulses make it possible to probe matter chirality at unprecedented energy regimes and with Ångström and femtosecond spatiotemporal resolutions. We survey the theory of stationary and time-resolved nonlinear chiral measurements that can be carried out in the X-ray regime using tabletop X-ray sources or large scale (XFEL, synchrotron) facilities. A variety of possible signals and their information content are discussed.

Imaging conical intersection dynamics during azobenzene photoisomerization by ultrafast X-ray diffraction.

X-ray diffraction is routinely used for structure determination of stationary molecular samples. Modern X-ray photon sources, e.g., from free-electron lasers, enable us to add temporal resolution to these scattering events, thereby providing a movie of atomic motions. We simulate and decipher the various contributions to the X-ray diffraction pattern for the femtosecond isomerization of azobenzene, a textbook photochemical process. A wealth of information is encoded besides real-time monitoring of the molecular charge density for the cis to trans isomerization. In particular, vibronic coherences emerge at the conical intersection, contributing to the total diffraction signal by mixed elastic and inelastic photon scattering. They cause distinct phase modulations in momentum space, which directly reflect the real-space phase modulation of the electronic transition density during the nonadiabatic passage. To overcome the masking by the intense elastic scattering contributions from the electronic populations in the total diffraction signal, we discuss how this information can be retrieved, e.g., by employing very hard X-rays to record large scattering momentum transfers.

Unveiling the spatial distribution of molecular coherences at conical intersections by covariance X-ray diffraction signals.

The outcomes and timescales of molecular nonadiabatic dynamics are decisively impacted by the quantum coherences generated at localized molecular regions. In time-resolved X-ray diffraction imaging, these coherences create distinct signatures via inelastic photon scattering, but they are buried under much stronger background elastic features. Here, we exploit the rich dynamical information encoded in the inelastic patterns, which we reveal by frequency-dispersed covariance ultrafast powder X-ray diffraction of stochastic X-ray free-electron laser pulses. This is demonstrated for the photoisomerization of azobenzene involving the passage through a conical intersection, where the nuclear wave packet branches and explores different quantum pathways. Snapshots of the coherence dynamics are obtained at high frequency shifts, not accessible with conventional diffraction measurements. These provide access to the timing and to the confined spatial distribution of the valence electrons directly involved in the conical intersection passage. This study can be extended to full three-dimensional imaging of conical intersections with ultrafast X-ray and electron diffraction.

X-ray and Optical Circular Dichroism as Local and Global Ultrafast Chiral Probes of [12]Helicene Racemization.

Chirality is a fundamental molecular property that plays a crucial role in biophysics and drug design. Optical circular dichroism (OCD) is a well-established chiral spectroscopic probe in the UV-visible regime. Chirality is most commonly associated with a localized chiral center. However, some compounds such as helicenes (Figure 1) are chiral due to their screwlike global structure. In these highly conjugated systems, some electric and magnetic allowed transitions are distributed across the entire molecule, and OCD thus probes the global molecular chirality. Recent advances in X-ray sources, in particular the control of their polarization and spatial profiles, have enabled X-ray circular dichroism (XCD), which, in contrast to OCD, can exploit the localized and element-specific nature of X-ray electronic transitions. XCD therefore is more sensitive to local structures, and the chirality probed with it can be referred to as local. During the racemization of helicene, between opposite helical structures, the screw handedness can flip locally, making the molecule globally achiral while retaining a local handedness. Here, we use the racemization mechanism of [12]helicene as a model to demonstrate the capabilities of OCD and XCD as time-dependent probes for global and local chiralities, respectively. Our simulations demonstrate that XCD provides an excellent spectroscopic probe for the time-dependent local chirality of molecules.

Time-Evolving Chirality Loss in Molecular Photodissociation Monitored by X-ray Circular Dichroism Spectroscopy.

The ultrafast photoinduced chirality loss of 2-iodobutane is studied theoretically by time- and frequency-resolved X-ray circular dichroism (TRXCD) spectroscopy. Following an optical excitation, the iodine atom dissociates from the chiral center, which we capture by quantum non-adiabatic molecular dynamics simulations. At variable time delays after the pump, the resonant X-ray pulse selectively probes the iodine and carbon atom involved in the chiral dissociation through a selected core-to-valence transition. The TRXCD signal at the iodine L1 edge accurately captures the timing of C-I photodissociation and thereby chirality loss, c.a 70 fs. The strong electric dipole-electric quadrupole (ED-EQ) response makes this signal particularly sensitive to vibronic coherence at the high X-ray regime. At the carbon K-edges, the signals monitor the molecular chirality of the 2-butyl radical photoproduct and the spin state of the iodine atom. The ED-EQ response is masked under the strong electric dipole-magnetic dipole response, making this signal intuitive for the electronic population. The evolution of the core electronic states and its chiral sensitivity is discussed. Overall, the element-specific TRXCD signal provides a detailed picture of molecular dynamics and offers a unique sensitive window into the time-dependent chirality of molecules.

Direct Monitoring of Conical Intersection Passage via Electronic Coherences in Twisted X-Ray Diffraction.

Quantum coherences in electronic motions play a critical role in determining the pathways and outcomes of virtually all photophysical and photochemical molecular processes. However, the direct observation of electronic coherences in the vicinity of conical intersections remains a formidable challenge. We propose a novel time-resolved twisted x-ray diffraction technique that can directly monitor the electronic coherences created as the molecule passes through a conical intersection. We show that the contribution of electronic populations to this signal is canceled out when using twisted x-ray beams that carry a light orbital angular momentum, providing a direct measurement of transient electronic coherences in gas-phase molecules.

Molecular Structure and Modeling of Water-Air and Ice-Air Interfaces Monitored by Sum-Frequency Generation.

From a glass of water to glaciers in Antarctica, water-air and ice-air interfaces are abundant on Earth. Molecular-level structure and dynamics at these interfaces are key for understanding many chemical/physical/atmospheric processes including the slipperiness of ice surfaces, the surface tension of water, and evaporation/sublimation of water. Sum-frequency generation (SFG) spectroscopy is a powerful tool to probe the molecular-level structure of these interfaces because SFG can specifically probe the topmost interfacial water molecules separately from the bulk and is sensitive to molecular conformation. Nevertheless, experimental SFG has several limitations. For example, SFG cannot provide information on the depth of the interface and how the orientation of the molecules varies with distance from the surface. By combining the SFG spectroscopy with simulation techniques, one can directly compare the experimental data with the simulated SFG spectra, allowing us to unveil the molecular-level structure of water-air and ice-air interfaces. Here, we present an overview of the different simulation protocols available for SFG spectra calculations. We systematically compare the SFG spectra computed with different approaches, revealing the advantages and disadvantages of the different methods. Furthermore, we account for the findings through combined SFG experiments and simulations and provide future challenges for SFG experiments and simulations at different aqueous interfaces.

Imaging electron-density fluctuations by multidimensional X-ray photon-coincidence diffraction.

The ultrafast spontaneous electron-density fluctuation dynamics in molecules is studied theoretically by off-resonant multiple X-ray diffraction events. The time- and wavevector-resolved photon-coincidence signals give an image of electron-density fluctuations expressed through the four-point correlation function of the charge density in momentum space. A Fourier transform of the signal provides a real-space image of the multipoint charge-density correlation functions, which reveal snapshots of the evolving electron density in between the diffraction events. The proposed technique is illustrated by ab initio simulations of the momentum- and real-space inelastic scattering signals from a linear cyanotetracetylene molecule.

Diffractive Imaging of Conical Intersections Amplified by Resonant Infrared Fields.

The fate of virtually all photochemical reactions is determined by conical intersections. These are energetically degenerate regions of molecular potential energy surfaces that strongly couple electronic states, thereby enabling fast relaxation channels. Their direct spectroscopic detection relies on weak features that are often buried beneath stronger, less interesting contributions. For azobenzene photoisomerization, a textbook photochemical reaction, we demonstrate how a resonant infrared field can be employed during the conical intersection passage to significantly enhance its coherence signatures in time-resolved X-ray diffraction while leaving the product yield intact. This transition-state amplification holds promise to bring signals of conical intersections above the detection threshold.

Femtosecond X-ray spectroscopy of haem proteins.

We discuss our recently reported femtosecond (fs) X-ray emission spectroscopy results on the ligand dissociation and recombination in nitrosylmyoglobin (MbNO) in the context of previous studies on ferrous haem proteins. We also present a preliminary account of femtosecond X-ray absorption studies on MbNO, pointing to the presence of more than one species formed upon photolysis.

Monitoring molecular nonadiabatic dynamics with femtosecond X-ray diffraction.

Ultrafast time-resolved X-ray scattering, made possible by free-electron laser sources, provides a wealth of information about electronic and nuclear dynamical processes in molecules. The technique provides stroboscopic snapshots of the time-dependent electronic charge density traditionally used in structure determination and reflects the interplay of elastic and inelastic processes, nonadiabatic dynamics, and electronic populations and coherences. The various contributions to ultrafast off-resonant diffraction from populations and coherences of molecules in crystals, in the gas phase, or from single molecules are surveyed for core-resonant and off-resonant diffraction. Single-molecule [Formula: see text] scaling and two-molecule [Formula: see text] scaling contributions, where N is the number of active molecules, are compared. Simulations are presented for the excited-state nonadiabatic dynamics of the electron harpooning at the avoided crossing in NaF. We show how a class of multiple diffraction signals from a single molecule can reveal charge-density fluctuations through multidimensional correlation functions of the charge density.

Monitoring aromatic ring-currents in Mg-porphyrin by time-resolved circular dichroism.

Time-resolved circular dichroism signals (TRCD) in the X-ray regime can directly probe the magnitude and the direction of ring currents in molecules. The electronic ring currents in Mg-porphyrin, generated by a coherent superposition of electronic states induced by a circularly polarized UV pulse, are tracked by a time-delayed circularly polarized attosecond X-ray pulse. The signals are calculated using the minimal coupling Hamiltonian, which directly makes use of transition current densities. The TRCD signals obtained from the left and right circularly polarized light pump have opposite signs, revealing the direction of the ring current. Molecular aromaticity and its role in photochemical reactions such as ring opening or closure can be studied using this technique.

Enhanced second harmonic generation of gold nanostars: optimizing multipolar radiation to improve nonlinear properties.

We report a detailed investigation on the second harmonic generation (SHG) emission from single 150 nm diameter non-centrosymmetric gold nanoparticles. Polarization-resolved analysis together with scanning electron microscopy images shows that these nanostructures exhibit a unique polarization-sensitive SHG that depends strongly on the particle's shape. An analytical approach based on multipolar analysis is introduced to link SHG properties to the nanoparticles' shape. Those multipolar modes can be probed using polarization-resolved SHG. This multipolar analysis offers a physical picture of the relation between shape (size, symmetries, defects, etc.) and nonlinear polarized optical efficiency.

Imaging of transition charge densities involving carbon core excitations by all X-ray sum-frequency generation.

X-ray diffraction signals from the time-evolving molecular charge density induced by selective core excitation of chemically inequivalent carbon atoms are calculated. A narrowband X-ray pulse selectively excites the carbon K-edge of the -CH3 or -CH2F groups in fluoroethane (CH3-CH2F). Each excitation creates a distinct core coherence which depends on the character of the electronic transition. Direct propagation of the reduced single-electron density matrix, using real-time time-dependent density functional theory, provides the time-evolving charge density following interactions with external fields. The interplay between partially filled valence molecular orbitals upon core excitation induces characteristic femtosecond charge migration which depends on the core-valence coherence, and is monitored by the sum-frequency generation diffraction signal. This article is part of the theme issue 'Measurement of ultrafast electronic and structural dynamics with X-rays'.

X-Ray Sum Frequency Diffraction for Direct Imaging of Ultrafast Electron Dynamics.

X-ray diffraction from molecules in the ground state produces an image of their charge density, and time-resolved x-ray diffraction can thus monitor the motion of the nuclei. However, the density change of excited valence electrons upon optical excitation can barely be monitored with regular diffraction techniques due to the overwhelming background contribution of the core electrons. We present a nonlinear x-ray technique made possible by novel free electron laser sources, which provides a spatial electron density image of valence electron excitations. The technique, sum frequency generation carried out with a visible pump and a broadband x-ray diffraction pulse, yields snapshots of the transition charge densities, which represent the electron density variations upon optical excitation. The technique is illustrated by ab initio simulations of transition charge density imaging for the optically induced electronic dynamics in a donor or acceptor substituted stilbene.

Linear and nonlinear frequency- and time-domain spectroscopy with multiple frequency combs.

Two techniques that employ equally spaced trains of optical pulses to map an optical high frequency into a low frequency modulation of the signal that can be detected in real time are compared. The development of phase-stable optical frequency combs has opened up new avenues to metrology and spectroscopy. The ability to generate a series of frequency spikes with precisely controlled separation permits a fast, highly accurate sampling of the material response. Recently, pairs of frequency combs with slightly different repetition rates have been utilized to down-convert material susceptibilities from the optical to microwave regime where they can be recorded in real time. We show how this one-dimensional dual comb technique can be extended to multiple dimensions by using several combs. We demonstrate how nonlinear susceptibilities can be quickly acquired using this technique. In a second class of techniques, sequences of ultrafast mode locked laser pulses are used to recover pathways of interactions contributing to nonlinear susceptibilities by using a photo-acoustic modulation varying along the sequences. We show that these techniques can be viewed as a time-domain analog of the multiple frequency comb scheme.

Monitoring Nonadiabatic Electron-Nuclear Dynamics in Molecules by Attosecond Streaking of Photoelectrons.

Streaking of photoelectrons has long been used for the temporal characterization of attosecond extreme ultraviolet pulses. When the time-resolved photoelectrons originate from a coherent superposition of electronic states, they carry additional phase information, which can be retrieved by the streaking technique. In this contribution we extend the streaking formalism to include coupled electron and nuclear dynamics in molecules as well as initial coherences. We demonstrate how streaked photoelectrons offer a novel tool for monitoring nonadiabatic dynamics as it occurs in the vicinity of conical intersections and avoided crossings. Streaking can provide high time resolution direct signatures of electronic coherences, which affect many primary photochemical and biological events.