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.

Water Solvent Reorganization upon Ultrafast Resonant Stimulated X-ray Raman Excitation of a Metalloporphyrin Dimer.

We propose an X-ray Raman pump-X-ray diffraction probe scheme to follow solvation dynamics upon charge migration in a solute molecule. The X-ray Raman pump selectively prepares a valence electronic wavepacket in the solute, while the probe provides information about the entire molecular ensemble. A combination of molecular dynamics and ab initio quantum chemistry simulations is applied to a Zn-Ni porphyrin dimer in water. Using time-resolved X-ray diffraction and pair distribution functions, we extracted solvation shell dynamics.

Quantum Interferometric Pathway Selectivity in Difference-Frequency-Generation Spectroscopy.

Even-order spectroscopies such as sum-frequency generation (SFG) and difference-frequency generation (DFG) can serve as direct probes of molecular chirality. Such signals are usually given by the sum of several interaction pathways that carry different information about matter. Here we focus on DFG, involving impulsive optical-optical-IR interactions, where the last IR pulse probes vibrational transitions in the ground or excited electronic state manifolds, depending on the interaction pathway. Spectroscopy with classical light can use phase matching to select the two pathways. In this theoretical study, we propose a novel quantum interferometric protocol that uses entangled photons to isolate individual pathways. This additional selectivity originates from engineering the state of light using a Zou-Wang-Mandel interferometer combined with coincidence detection.

Time-resolved enantiomer-exchange probed by using the orbital angular momentum of X-ray light.

Molecular chirality, a geometric property of utmost importance in biochemistry, is now being investigated in the time-domain. Ultrafast chiral techniques can probe the formation or disappearance of stereogenic centers in molecules. The element-sensitivity of X-rays adds the capability to probe chiral nuclear dynamics locally within the molecular system. However, the implementation of ultrafast techniques for measuring transient chirality remains a challenge because of the intrinsic weakness of chiral-sensitive signals based on circularly polarized light. We propose a novel approach for probing the enantiomeric dynamics by using the orbital angular momentum (OAM) of X-ray light, which can directly monitor the real-time chirality of molecules. Our simulations probe the oscillations in excited chiral formamide on different potential energy surfaces and demonstrate that using the X-ray OAM can increase the measured asymmetry ratio. Moreover, combining the OAM and SAM (spin angular momentum) provides stronger dichroic signals than linearly polarized light, and offers a powerful scheme for chiral discrimination.

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.

Attosecond Monitoring of Nonadiabatic Molecular Dynamics by Transient X-ray Transmission Spectroscopy.

Tracing the evolution of molecular coherences can provide a direct, unambiguous probe of nonadiabatic molecular processes, such as the passage through conical intersections of electronic states. Two techniques, attosecond transient absorption spectroscopy (ATAS) and Transient Redistribution of Ultrafast Electronic Coherences in Attosecond Raman Signals (TRUECARS), have been used or proposed for monitoring nonadiabatic molecular dynamics. Both techniques employ the transmission of a weak attosecond extreme-ultraviolet or X-ray probe to interrogate the molecule at controllable time delays with respect to an optical pump, thereby extracting dynamical information from transient spectral features. The connection between these techniques has not been firmly established yet. In this theoretical study, we provide a unified description of both transient transmission techniques, establishing their relationship as limits of the same pump-probe spectroscopy technique for different pulse parameter regimes. We demonstrate this by quantum dynamical simulations of thiophenol photodissociation and show how complementary coherence information can be revealed by the two techniques.

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.

Ultrafast Energy Transfer from Photoexcited Tryptophan to the Haem in Cytochrome c.

We report femtosecond Fe K-edge absorption (XAS) and nonresonant X-ray emission (XES) spectra of ferric cytochrome C (Cyt c) upon excitation of the haem (>300 nm) or mixed excitation of the haem and tryptophan (<300 nm). The XAS and XES transients obtained in both excitation energy ranges show no evidence for electron transfer processes between photoexcited tryptophan (Trp) and the haem, but rather an ultrafast energy transfer, in agreement with previous ultrafast optical fluorescence and transient absorption studies. The reported (J. Phys. Chem. B 2011, 115 (46), 13723-13730) decay times of Trp fluorescence in ferrous (∼350 fs) and ferric (∼700 fs) Cyt c are among the shortest ever reported for Trp in a protein. The observed time scales cannot be rationalized in terms of Förster or Dexter energy transfer mechanisms and call for a more thorough theoretical investigation.

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 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.

Coupled Electronic and Nuclear Motions during Azobenzene Photoisomerization Monitored by Ultrafast Electron Diffraction.

Ultrafast electron diffraction is a powerful technique that can resolve molecular structures with femtosecond and angstrom resolutions. We demonstrate theoretically how it can be used to monitor conical intersection dynamics in molecules. Specific contributions to the signal are identified which vanish in the absence of vibronic coherence and offer a direct window into conical intersection paths. A special focus is on hybrid scattering from nuclei and electrons, a process that is unique to electron (rather than X-ray) diffraction and monitors the strongly coupled nuclear and electronic motions in the vicinity of conical intersections. An application is made to the cis to trans isomerization of azobenzene, computed with exact quantum dynamics wavepacket propagation in a reactive two-dimensional nuclear space.

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.

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.

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.

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.

Signatures of electronic and nuclear coherences in ultrafast molecular x-ray and electron diffraction.

Femtosecond x-ray and electron diffraction hold promise to image the evolving structures of single molecules. We present a unified quantum-electrodynamical formulation of diffraction signals, based on the exact many-body nuclear + electronic wavefunction that can be extracted from quantum chemistry simulations. This gives a framework for analyzing various approximate molecular dynamics simulations. We show that the complete description of ultrafast diffraction signals contains interesting contributions involving mixed elastic and inelastic scattered photons that are usually masked by other larger contributions and are neglected. These terms include overlaps of nuclear wavepackets between different electronic states that provide an electronic decoherence mechanism and are important for the time-resolved imaging of conical intersections.

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.

Spin cascade and doming in ferric hemes: Femtosecond X-ray absorption and X-ray emission studies.

The structure-function relationship is at the heart of biology, and major protein deformations are correlated to specific functions. For ferrous heme proteins, doming is associated with the respiratory function in hemoglobin and myoglobins. Cytochrome c (Cyt c) has evolved to become an important electron-transfer protein in humans. In its ferrous form, it undergoes ligand release and doming upon photoexcitation, but its ferric form does not release the distal ligand, while the return to the ground state has been attributed to thermal relaxation. Here, by combining femtosecond Fe Kα and Kß X-ray emission spectroscopy (XES) with Fe K-edge X-ray absorption near-edge structure (XANES), we demonstrate that the photocycle of ferric Cyt c is entirely due to a cascade among excited spin states of the iron ion, causing the ferric heme to undergo doming, which we identify. We also argue that this pattern is common to a wide diversity of ferric heme proteins, raising the question of the biological relevance of doming in such proteins.