Anisotropy Parameters for Two-Color Photoionization Phases in Randomly Oriented Molecules: Theory and Experiment in Methane and Deuteromethane.

We present combined theoretical and experimental work investigating the angle-resolved phases of the photoionization process driven by a two-color field consisting of an attosecond pulse train and an infrared pulse in an ensemble of randomly oriented molecules. We derive a general form for the two-color photoelectron (and time-delay) angular distribution valid also in the case of chiral molecules and when relative polarizations of the photons contributing to the attosecond photoelectron interferometer differ. We show a comparison between the experimental data and theoretical predictions in an ensemble of methane and deuteromethane molecules, discussing the effect of nuclear dynamics on the photoionization phases. Finally, we demonstrate that the oscillating component and the phase of the two-color signal can be fitted by using complex asymmetry parameters, in perfect analogy to the atomic case.

Influence of nuclear dynamics on molecular attosecond photoelectron interferometry.

In extreme ultraviolet spectroscopy, the photoionization process occurring in a molecule due to the absorption of a single photon can trigger an ultrafast nuclear motion in the cation. Taking advantage of attosecond photoelectron interferometry, where the absorption of the extreme ultraviolet photon is accompanied by the exchange of an additional infrared quantum of light, one can investigate the influence of nuclear dynamics by monitoring the characteristics of the photoelectron spectra generated by the two-color field. Here, we show that attosecond photoelectron interferometry is sensitive to the nuclear response by measuring the two-color photoionization spectra in a mixture of methane (CH4) and deuteromethane (CD4). The effect of the different nuclear evolution in the two isotopologues manifests itself in the modification of the amplitude and contrast of the oscillations of the photoelectron peaks. Our work indicates that nuclear dynamics can affect the coherence properties of the electronic wave packet emitted by photoionization on a time scale as short as a few femtoseconds.

Excitation and fragmentation of the dielectric gas C4F7N: Electrons vs photons.

C4F7N is a promising candidate for the replacement of sulfur hexafluoride as an insulating medium, and it is important to understand the chemical changes initiated in the molecule by collision with free electrons, specifically the formation of neutral fragments. The first step of neutral fragmentation is electronic excitation, yet neither the absorption spectrum in the vacuum ultraviolet (VUV) region nor the electron energy loss spectrum have previously been reported. Here, we experimentally probed the excited states by VUV photoabsorption spectroscopy and electron energy loss spectroscopy (EELS). We found that the distribution of states populated upon electron impact with low-energy electrons is significantly different from that following photoabsorption. This difference was confirmed and interpreted with ab initio modeling of both VUV and EELS spectra. We propose here a new computational protocol for the simulation of EELS spectra combining the Born approximation with approximate forms of correlated wave functions, which allows us to calculate the (usually very expensive) scattering cross sections at a cost similar to the calculation of oscillator strengths. Finally, we perform semi-classical non-adiabatic dynamics simulations to investigate the possible neutral fragments of the molecule formed through electron-induced neutral dissociation. We show that the product distribution is highly non-statistical.

Multi-photon above threshold ionization of multi-electron atoms and molecules using the R-matrix approach.

We formulate a computationally efficient time-independent method based on the multi-electron molecular R-matrix formalism. This method is used to calculate transition matrix elements for the multi-photon ionization of atoms and molecules under the influence of a perturbative field. The method relies on the partitioning of space which allows us to calculate the infinite-range free-free dipole integrals analytically in the outer region, beyond the range of the initial bound wave function. This approach is valid for an arbitrary order, that is, any number of photons absorbed both in the bound and the continuum part of the spectrum (below- and above-threshold ionization). We calculate generalized multi-photon cross sections and angular distributions of different systems (H, He, [Formula: see text], [Formula: see text]) and validate our approach by comparison with data from the literature.

Extracting sub-cycle electronic and nuclear dynamics from high harmonic spectra.

We present a new methodology for measuring few-femtosecond electronic and nuclear dynamics in both atoms and polyatomic molecules using multidimensional high harmonic generation (HHG) spectroscopy measurements, in which the spectra are recorded as a function of the laser intensity to form a two-dimensional data set. The method is applied to xenon atoms and to benzene molecules, the latter exhibiting significant fast nuclear dynamics following ionization. We uncover the signature of the sub-cycle evolution of the returning electron flux in strong-field ionized xenon atoms, implicit in the strong field approximation but not previously observed directly. We furthermore extract the nuclear autocorrelation function in strong field ionized benzene cations, which is determined to have a decay of [Formula: see text] fs, in good agreement with the [Formula: see text] fs obtained from direct dynamics variational multi-configuration Gaussian calculations. Our method requires minimal assumptions about the system, and is applicable even to un-aligned polyatomic molecules.

Ultrafast imaging of laser-controlled non-adiabatic dynamics in NO2 from time-resolved photoelectron emission.

Time-resolving and controlling coupled electronic and nuclear dynamics at conical intersections on the sub-femtosecond to few-femtosecond time scale is among the challenging goals of attosecond physics. Here we present numerical simulations of time-resolved photoelectron spectroscopy of such dynamics in NO2, where the coupled electron-nuclear motion at the 2A1/2B2 conical intersection is steered on the sub-laser-cycle time scale by a nearly single-cycle, waveform controlled mid-infrared laser pulse. For a rigorous description of the photoionization dynamics, we employ ab initio energy- and geometry-resolved photoionization matrix elements obtained with the multichannel R-matrix method, using a multiconfigurational description of the molecule and a newly developed algorithm to generate photoionization dipoles that are phase consistent on the level of both the neutral and the ionic states. We find that for sufficient molecular alignment, the time- and energy-resolved anisotropy parameters of the photoelectron angular distributions provide a particularly clear picture of both the ultrafast natural molecular dynamics at the conical intersection and its modifications by the control pulse. In particular, changes in the electronic and nuclear configurations induced by the control pulse lead to the appearance of non-vanishing odd anisotropy parameters in the photoelectron spectra. These are absent in the spectra obtained without the control pulse and therefore provide sensitive, background-free diagnostic of the control.

General theory of photoexcitation induced photoelectron circular dichroism.

The photoionization of chiral molecules prepared in a coherent superposition of excited states can give access to the underlying chiral coherent dynamics in a procedure known as photoexcitation induced photoelectron circular dichroism (PXECD). As in photoelectron circular dichroism (PECD), chirality manifests as asymmetric photoelectron emission in the forward/backward direction (relative to the laser propagation direction). However, in PXECD, the asymmetric photoemission is additionally contingent on coherence. This exclusive dependence on coherence can also be seen in a different part of the photoelectron angular distribution (PAD), where it is not contingent on the chirality of the molecule, thus allowing extension of PXECD's sensitivity to tracking coherence to non-chiral molecules. Here we present a general theory of PXECD based on angular momentum algebra and derive explicit expressions for all pertinent asymmetry parameters which arise for the arbitrary polarization of pump (which prepares the superposition of excited states) and ionizing probe pulses. The theory is developed in a way that clearly and simply separates chiral and non-chiral contributions to the PAD and also demonstrates how PXECD and PECD-type contributions, which may be distinguished by whether the pump or ionizing probe pulse enables chiral response, are mixed when arbitrary polarization is used.

Role of electronic correlations in photoionization of NO2 in the vicinity of the 2A1/2B2 conical intersection.

We present the first ab initio multi-channel photoionization calculations for NO2 in the vicinity of the 2A1/2B2 conical intersection, for a range of nuclear geometries, using our newly developed set of tools based on the ab initio multichannel R-matrix method. Electronic correlation is included in both the neutral and the scattering states of the molecule via configuration interaction. Configuration mixing is especially important around conical intersections and avoided crossings, both pertinent for NO2, and manifests itself via significant variations in photoelectron angular distributions. The method allows for a balanced and accurate description of the photoionization/photorecombination for a number of different ionic channels in a wide range of photoelectron energies up to 100 eV. Proper account of electron correlations is crucial for interpreting time-resolved signals in photoelectron spectroscopy and high harmonic generation (HHG) from polyatomic molecules.

Role of tunnel ionization in high harmonic generation from substituted benzenes.

We theoretically study high-harmonic generation in toluene, ortho-xylene and fluorobenzene driven by a 1.8 µm ultrashort pulse. We find that the chemical substitutions have a strong influence on the amplitude and phase of the emission from the highest occupied molecular orbital, despite having a small influence on the orbital itself. We show that this influence is due to the tunnel ionization step, which depends critically on the sign and amplitude of the asymptotic part of the wave function. We discuss how these effects would manifest in phase-sensitive high-harmonic generation spectroscopy experiments.

Multidimensional high harmonic spectroscopy of polyatomic molecules: detecting sub-cycle laser-driven hole dynamics upon ionization in strong mid-IR laser fields.

High harmonic generation (HHG) spectroscopy has opened up a new frontier in ultrafast science, where electronic dynamics can be measured on an attosecond time scale. The strong laser field that triggers the high harmonic response also opens multiple quantum pathways for multielectron dynamics in molecules, resulting in a complex process of multielectron rearrangement during ionization. Using combined experimental and theoretical approaches, we show how multi-dimensional HHG spectroscopy can be used to detect and follow electronic dynamics of core rearrangement on sub-laser cycle time scales. We detect the signatures of laser-driven hole dynamics upon ionization and reconstruct the relative phases and amplitudes for relevant ionization channels in a CO2 molecule on a sub-cycle time scale. Reconstruction of channel-resolved complex ionization amplitudes on attosecond time scales has been a long-standing goal of high harmonic spectroscopy. Our study brings us one step closer to fulfilling this initial promise and developing robust schemes for sub-femtosecond imaging of multielectron rearrangement in complex molecular systems.

Resonance effects in elastic cross sections for electron scattering on pyrimidine: Experiment and theory.

We measured differential cross sections for elastic (rotationally integrated) electron scattering on pyrimidine, both as a function of angle up to 180(∘) at electron energies of 1, 5, 10, and 20 eV and as a function of electron energy in the range 0.1-14 eV. The experimental results are compared to the results of the fixed-nuclei Schwinger variational and R-matrix theoretical methods, which reproduce satisfactorily the magnitudes and shapes of the experimental cross sections. The emphasis of the present work is on recording detailed excitation functions revealing resonances in the excitation process. Resonant structures are observed at 0.2, 0.7, and 4.35 eV and calculations for different symmetries confirm their assignment as the X̃(2)A2, Ã(2)B1, and B̃(2)B1 shape resonances. As a consequence of superposition of coherent resonant amplitudes with background scattering the B̃(2)B1 shape resonance appears as a peak, a dip, or a step function in the cross sections recorded as a function of energy at different scattering angles and this effect is satisfactorily reproduced by theory. The dip and peak contributions at different scattering angles partially compensate, making the resonance nearly invisible in the integral cross section. Vibrationally integrated cross sections were also measured at 1, 5, 10 and 20 eV and the question of whether the fixed-nuclei cross sections should be compared to vibrationally elastic or vibrationally integrated cross section is discussed.

Absolute cross sections for electronic excitation of pyrimidine by electron impact.

We measured differential cross sections for electron-impact electronic excitation of pyrimidine, both as a function of electron energy up to 18 eV, and of scattering angle up to 180°. The emphasis of the present work is on recording detailed excitation functions revealing resonances in the excitation process. The differential cross sections were summed to obtain integral cross sections. These are compared to results of R-matrix calculations, which successfully reproduce both the magnitude of the cross section and the major resonant features. Comparison of the experiment to the calculated contributions of different symmetries to the integral cross section permitted assignment of several features to specific core-excited resonances. Comparison of the resonant structure of pyrimidine with that of benzene revealed pronounced similarities and thus a dominant role of π-π(∗) excited states and resonances. Electron energy loss spectra were measured as a preparation for the cross section measurements and vibrational structure was observed for some of the triplet states. A detailed analysis of the electronic excited states of pyrimidine is also presented.

Electron scattering cross section calculations for polar molecules over a broad energy range.

We report computational integral and differential cross sections for electron scattering by two different polar molecules, HCN and pyrimidine, over a broad energy range. We employ, for low energies, either the single-centre expansion (ePOLYSCAT) or the R-matrix method, while for the higher energies we select a corrected form of the independent-atom representation (IAM-SCAR). We provide complete sets of integral electron scattering cross sections from low energies up to 10,000 eV. Our present calculated data agree well with prior experimental results.

Shape and core excited resonances in electron collisions with diazines.

We present a comprehensive ab-initio study of electron collisions with pyrazine, pyrimidine, and pyridazine. The emphasis is placed on the identification and characterization of electron resonances in these systems. We use the R-matrix method and show that analysing the time-delay reveals resonances whose signature is not visible in the eigenphase sums. In addition to the well known π∗ resonances below 5 eV, we find three core-excited shape resonances in the energy range 5.5-8.5 eV and a few Feshbach resonances in the dipolar molecules. Additionally, 11 resonances with little effect on the elastic scattering from ground state diazines (but significant effect in elastic collisions with the molecules in an excited state) are found and characterized. We correlate these resonances across the three molecules and discuss their possible correspondence to resonances described in earlier studies on uracil.

Elastic and inelastic cross sections for low-energy electron collisions with pyrimidine.

We present theoretical elastic and electronic excitation cross sections and experimental electronic excitation cross sections for electron collisions with pyrimidine. We use the R-matrix method to determine elastic integral and differential cross sections and integral inelastic cross sections for energies up to 15 eV. The experimental inelastic cross sections have been determined in the 15-50 eV impact energy range. Typically, there is quite reasonable agreement between the theoretical and experimental integral inelastic cross sections. Calculated elastic cross sections agree very well with prior results.

Elastic and inelastic low-energy electron collisions with pyrazine.

We present results of ab-initio scattering calculations for electron collisions with pyrazine using the R-matrix method, carried out at various levels of approximation. We confirm the existing experimental and theoretical understanding of the three well-known π∗ shape resonances. In addition, we find numerous core-excited resonances (above 4.8 eV) and identify their most likely parent states. We also present differential cross sections, showing high sensitivity to the scattering model chosen at low energies. We make recommendations regarding the selection of models for scattering calculations with this type of targets.