Intramolecular photoelectron diffraction in the gas phase

Attosecond Intramolecular Scattering and Vibronic Delays

We study the temporal and vibrational signature of the universal nuclear recoil associated with the electron emission and intramolecular scattering that accompanies the photoelectric effect. We illustrate these phenomena in the photoionization of the CO molecule from the C-1s orbital using an analytical model that reproduces the entangled character of the nuclear and electronic motion in this process. We show that the photoelectron emission delay can be decomposed into its localization and resonant-confinement components. Photoionization by a broadband x-ray pulse results in a coherent vibrational ionic state delayed compared to the classical sudden-photoemission limit.

Probing gaseous molecular structure by molecular-frame photoelectron angular distributions

Carbon 1s photoelectron angular distributions of an iodomethane molecule were measured relative to the recoil-frame determined by the momentum correlation between I⁺ and CH₃ ⁺ at photoelectron energies of 3, 6.1, and 12 eV. The energy dependent behavior of the recoil-frame photoelectron angular distributions is reproduced reasonably well by the time-dependent density functional theory with B-spline methods. We discuss potential applications of the fully differential photoelectron angular distribution measurements in the molecular frame to three-dimensional molecular structural determinations identifying the directions and lengths of the bonds.

Energy-Dependent Relative Cross Sections in Carbon 1s Photoionization: Separation of Direct Shake and Inelastic Scattering Effects in Single Molecules

We demonstrate that the possibility of monitoring relative photoionization cross sections over a large photon energy range allows us to study and disentangle shake processes and intramolecular inelastic scattering effects. In this gas-phase study, relative intensities of the carbon 1s photoelectron lines from chemically inequivalent carbon atoms in the same molecule have been measured as a function of the incident photon energy in the range of 300-6000 eV. We present relative cross sections for the chemically shifted carbon 1s lines in the photoelectron spectra of ethyl trifluoroacetate (the "ESCA" molecule). The results are compared with those of methyl trifluoroacetate and S-ethyl trifluorothioacetate as well as a series of chloro-substituted ethanes and 2-butyne. In the soft X-ray energy range, the cross sections show an extended X-ray absorption fine structure type of wiggles, as was previously observed for a series of chloroethanes. The oscillations are damped in the hard X-ray energy range, but deviations of cross-section ratios from stoichiometry persist, even at high energies. The current findings are supported by theoretical calculations based on a multiple scattering model. The use of soft and tender X-rays provides a more complete picture of the dominant processes accompanying photoionization. Such processes reduce the main photoelectron line intensities by 20-60%. Using both energy ranges enabled us to discern the process of intramolecular inelastic scattering of the outgoing electron, whose significance is otherwise difficult to assess for isolated molecules. This effect relates to the notion of the inelastic mean free path commonly used in photoemission studies of clusters and condensed matter.

Full-dimensional theoretical description of vibrationally resolved valence-shell photoionization of H2O

We have performed a full-dimensional theoretical study of vibrationally resolved photoelectron emission from the valence shell of the water molecule by using an extension of the static-exchange density functional theory that accounts for ionization as well as for vibrational motion in the symmetric stretching, antisymmetric stretching, and bending modes. At variance with previous studies performed in centrosymmetric molecules, where vibrationally resolved spectra are mostly dominated by the symmetric stretching mode, in the present case, all three modes contribute to the calculated spectra, including intermode couplings. We have found that diffraction of the ejected electron by the various atomic centers is barely visible in the ratios between vibrationally resolved photoelectron spectra corresponding to different vibrational states of the remaining H2O+ cation (the so-called v-ratios), in contrast to the prominent oscillations observed in K-shell ionization of centrosymmetric molecules, including those that only contain hydrogen atoms around the central atoms, e.g., CH4. To validate the conclusions of our work, we have carried out synchrotron radiation experiments at the SOLEIL synchrotron and determined photoelectron spectra and v-ratios for H2O in a wide range of photon energies, from threshold up to 150 eV. The agreement with the theoretical predictions is good.

Onset of ionic coherence and ultrafast charge dynamics in attosecond molecular ionisation

Here is presented a fully ab initio theoretical framework for simulating the correlated many-electron dynamics occurring during and emerging from molecular ionisation by attosecond laser pulses. This is based on the time-dependent (TD) version of the B-spline restricted correlation space (RCS)-algebraic diagrammatic construction (ADC) method, with the full description of the photoelectron and inclusion of electron correlation effects, such as shakeup processes and inter-channel couplings. The nature of the ultrafast charge dynamics in the molecular ion is elucidated by quantitatively predicting the degree of electronic coherence and eigenstate content of the prepared molecular cationic state, beyond the commonly used sudden approximation. The results presented here for the acetylene and ethylene molecules show that even in the high photon energy regime the simulated hole dynamics is quantitatively different from the prediction of the sudden approximation. Moreover, for high-bandwidth ionising pulse, the residual interaction between the cation, in highly-excited shake-up states, and the emitted slow photoelectron gives rise to a loss of coherence in the ionic system which can persist for the first few femtoseconds after ionisation.

Restricted Correlation Space B-Spline ADC Approach to Molecular Ionization: Theory and Applications to Total Photoionization Cross-Sections

Herein is presented a new approach to the ab initio algebraic diagrammatic construction (ADC) schemes for the polarization propagator, which is explicitly designed to accurately and efficiently describe molecular ionization. The restricted correlation space (RCS) version of the ADC methods up to second order of perturbation theory is derived via the intermediate state representation (ISR) and implemented in the multicenter B-spline basis set for the electronic continuum. Remarkably a general close-coupling structure of the RCS-ADC many-electron wave function, connecting the N-particle to the ( N - 1)-particle ADC intermediate states, emerges naturally as a nontrivial result of the RCS ansatz. Moreover, the introduced RCS-ADC schemes prove to be particularly manageable from a computational point of view, overcoming the practical limitations of the conventional ADC approaches. The quality of the new RCS-ADC( n) approaches is verified by performing a series of total photoionization cross-section calculations on a test set of molecules. The excellent agreement of the results with existing accurate benchmarks demonstrates that the RCS versions of the ADC schemes are optimal and quantitatively accurate methods for studying multichannel molecular photoionization.

Probing molecular bond-length using molecular-frame photoelectron angular distributions

The molecular-frame photoelectron angular distributions (MFPADs) in O 1s photoemission from CO₂ molecule were measured. Patterns due to photoelectron diffractions were observed in the MFPADs. The polarization-averaged MFPADs were compared with theoretical calculation and were found to be useful in determining the molecular bond-length, which is a component to determine molecular structures.

Energy Transfer into Molecular Vibrations and Rotations by Recoil in Inner-Shell Photoemission

A mixture of CF_{4} and CO gases is used to study photoelectron recoil effects extending into the tender x-ray region. In CF_{4}, the vibrational envelope of the C 1s photoelectron spectrum becomes fully dominated by the recoil-induced excitations, revealing vibrational modes hidden from Franck-Condon excitations. In CO, using CF_{4} as an accurate energy calibrant, we determine the partitioning of the recoil-induced internal excitation energy between rotational and vibrational excitation. The observed rotational recoil energy is 2.88(28) times larger than the observed vibrational recoil energy, well in excess of the ratio of 2 predicted by the basic recoil model. The experiment is, however, in good agreement with the value of 2.68 if energy transfer via Coriolis coupling is included.

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.

Reconstruction of the time-dependent electronic wave packet arising from molecular autoionization

Autoionizing resonances are paradigmatic examples of two-path wave interferences between direct photoionization, which takes a few attoseconds, and ionization via quasi-bound states, which takes much longer. Time-resolving the evolution of these interferences has been a long-standing goal, achieved recently in the helium atom owing to progress in attosecond technologies. However, already for the hydrogen molecule, similar time imaging has remained beyond reach due to the complex interplay between fast nuclear and electronic motions. We show how vibrationally resolved photoelectron spectra of H₂ allow one to reconstruct the associated subfemtosecond autoionization dynamics by using the ultrafast nuclear dynamics as an internal clock, thus forgoing ultrashort pulses. Our procedure should be general for autoionization dynamics in molecules containing light nuclei, which are ubiquitous in chemistry and biology.

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.

Photoelectron diffraction in methane probed via vibrationally resolved inner-valence photoionization cross-section ratios

Vibrationally resolved photoionization of the 2a1 orbital in methane has been studied both experimentally and theoretically, over a wide range of photon energies (40-475 eV). A vibrational progression associated with the symmetric stretch mode of the 2a1(-1) single-hole state was observed in the experimental photoelectron spectra. Individual vibrational sub-states of the spectra were found to be best modeled by asymmetric line-shapes with linewidths gradually increasing with the vibrational quantum number. This indicates the occurrence of a pre-dissociation process for the involved ionic state, discussed here in detail. Finally, diffraction patterns were observed in the vibrational branching ratios for the first three vibrational sub-states ("v-ratios") of the experimental photoelectron spectra. They are found to be in excellent qualitative agreement with those obtained from ab initio models. Compared with previous studies of the 1a1(-1) core-shell photoionization of methane, the period of oscillation of the v-ratios is found to be very different and the phases are of opposite signs. This suggests a strong interplay between the electron diffraction and interference effects inside the molecular potential.

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.

Synchrotron-radiation-based soft X-ray electron spectroscopy applied to structural and chemical characterization of isolated species, from molecules to nanoparticles

With its extended tunability from the IR to hard X-rays and the exceptional spectral brightness offered by the 3rd generation storage rings, synchrotron radiation (SR) is an invaluable investigation tool. Major methodological developments are now available, and are applied to simple, isolated atoms and molecules (which can be often modeled ab initio) and are then extended to the investigation of more and more complex species, up to soft and hard condensed matter. The present article highlights, with a few examples, the most recent achievements in SR-based soft X-ray electron spectroscopy applied to the structural characterization of isolated species of increasing complexity, from molecules and clusters to nanoparticles. Special attention is devoted to very high resolution studies of single molecules revealing electron diffraction and interference effects, as well as detailed information about their potential energy surfaces. These achievements are only possible based on the new opportunities offered by the most advanced SR facilities.