Time-resolved photoelectron angular distributions: concepts, applications, and directions

Time-resolved photoelectron imaging of complex resonances in molecular nitrogen

We have used the FERMI free-electron laser to perform time-resolved photoelectron imaging experiments on a complex group of resonances near 15.38 eV in the absorption spectrum of molecular nitrogen, N₂, under jet-cooled conditions. The new data complement and extend the earlier work of Fushitani et al. [Opt. Express 27, 19702-19711 (2019)], who recorded time-resolved photoelectron spectra for this same group of resonances. Time-dependent oscillations are observed in both the photoelectron yields and the photoelectron angular distributions, providing insight into the interactions among the resonant intermediate states. In addition, for most states, we observe an exponential decay of the photoelectron yield that depends on the ionic final state. This observation can be rationalized by the different lifetimes for the intermediate states contributing to a particular ionization channel. Although there are nine resonances within the group, we show that by detecting individual photoelectron final states and their angular dependence, we can identify and differentiate quantum pathways within this complex system.

Imaging large amplitude out-of-plane motion in photoexcited pentafluorobenzene using time-resolved photoelectron spectroscopy: a computational study

Excited-state dynamics of pentafluorobenzene is studied in detail for a quartic vibronic coupling model including the six b1 vibrational modes of the molecule and the two lowest excited electronic states. The study analyzes the influence of the large-amplitude out-of-plane vibrational motion on the electronic dynamics and extends to the simulation of the emerging time-resolved photoelectron spectra. The mapping of coherent non-separable electron-nuclear motion into oscillatory photoelectron signals is discussed.

Conical-intersection dynamics and ground-state chemistry probed by extreme-ultraviolet time-resolved photoelectron spectroscopy

Time-resolved photoelectron spectroscopy (TRPES) is a useful approach to elucidate the coupled electronic-nuclear quantum dynamics underlying chemical processes, but has remained limited by the use of low photon energies. Here, we demonstrate the general advantages of XUV-TRPES through an application to NO₂, one of the simplest species displaying the complexity of a non-adiabatic photochemical process. The high photon energy enables ionization from the entire geometrical configuration space, giving access to the true dynamics of the system. Specifically, the technique reveals dynamics through a conical intersection, large-amplitude motion and photodissociation in the electronic ground state. XUV-TRPES simultaneously projects the excited-state wave packet onto many final states, offering a multi-dimensional view of the coupled electronic and nuclear dynamics. Our interpretations are supported by ab initio wavepacket calculations on new global potential-energy surfaces. The presented results contribute to establish XUV-TRPES as a powerful technique providing a complete picture of ultrafast chemical dynamics from photoexcitation to the final products.

Anisotropy in Time-Resolved Photoelectron Spectroscopy in the Gas Phase

Transient absorption anisotropy is a well-established technique in time-resolved liquid phase spectroscopy. Here, we show how the technique is applied in the gas phase for time-resolved photoelectron spectroscopy and what type of additional information can be obtained as compared to other techniques. We exemplify its use by presenting results on rotational revivals in pyrazine after excitation at 324 nm and provide new insights into two recent experiments: (i) the difference between Rydberg and valence state excitation after one- and two-photon absorption in butadiene and (ii) excitation to the two lowest lying vibronic modes of the degenerate π3p Rydberg state in 1-azabicyclo[2.2.0]octane. Going forward, we expect the technique to be used on a regular basis, especially with the advent of high harmonic probe sources and liquid beam setups where other techniques to extract polarization-dependent information such as velocity map imaging cannot easily be applied.

Molecular Frame Reconstruction Using Time-Domain Photoionization Interferometry

Photoionization of molecular species is, essentially, a multipath interferometer with both experimentally controllable and intrinsic molecular characteristics. In this work, XUV photoionization of impulsively aligned molecular targets (N_{2}) is used to provide a time-domain route to "complete" photoionization experiments, in which the rotational wave packet controls the geometric part of the photoionization interferometer. The data obtained is sufficient to determine the magnitudes and phases of the ionization matrix elements for all observed channels, and to reconstruct molecular frame interferograms from lab frame measurements. In principle, this methodology provides a time-domain route to complete photoionization experiments and the molecular frame, which is generally applicable to any molecule (no prerequisites), for all energies and ionization channels.

Time-resolved photoelectron spectroscopy of IR-driven electron dynamics in a charge transfer model system

If the adiabatic approximation is valid, electrons smoothly adapt to molecular geometry changes. In contrast, as a characteristic of diabatic dynamics, the electron density does not follow the nuclear motion. Recently, we have shown that the asymmetry in time-resolved photoelectron spectra serves as a tool to distinguish between these dynamics [Falge et al., J. Phys. Chem. Lett., 2012, 3, 2617]. Here, we investigate the influence of an additional, moderately intense infrared (IR) laser field, as often applied in attosecond time-resolved experiments, on such asymmetries. This is done using a simple model for coupled electronic-nuclear motion. We calculate time-resolved photoelectron spectra and their asymmetries and demonstrate that the spectra directly map the bound electron-nuclear dynamics. From the asymmetries, we can trace the IR field-induced population transfer and both the field-driven and intrinsic (non-)adiabatic dynamics. This holds true when considering superposition states accompanied by electronic coherences. The latter are observable in the asymmetries for sufficiently short XUV pulses to coherently probe the coupled states. It is thus documented that the asymmetry is a measure for phases in bound electron wave packets and non-adiabatic dynamics.

Time-resolved photoelectron imaging with a femtosecond vacuum-ultraviolet light source: Dynamics in the A∼/B∼- and F∼-bands of SO2

Time-resolved photoelectron imaging is demonstrated using the third harmonic of a 400-nm femtosecond laser pulse as the ionization source. The resulting 133-nm pulses are combined with 266-nm pulses to study the excited-state dynamics in the A∼/B∼- and F∼-band regions of SO₂. The photoelectron signal from the molecules excited to the A∼/B∼-band does not decay for at least several picoseconds, reflecting the population of bound states. The temporal variation of the photoelectron angular distribution (PAD) reflects the creation of a rotational wave packet in the excited state. In contrast, the photoelectron signal from molecules excited to the F∼-band decays with a time constant of 80 fs. This time constant is attributed to the motion of the excited-state wave packet out of the ionization window. The observed time-dependent PADs are consistent with the F∼ band corresponding to a Rydberg state of dominant s character. These results establish low-order harmonic generation as a promising tool for time-resolved photoelectron imaging of the excited-state dynamics of molecules, simultaneously giving access to low-lying electronic states, as well as Rydberg states, and avoiding the ionization of unexcited molecules.

Towards the analysis of attosecond dynamics in complex systems

We study from a theoretical perspective the ionization of molecules and clusters induced by irradiation of a combined two-color laser field consisting of a train of attosecond XUV pulses in the presence of an IR field.

Revealing Deactivation Pathways Hidden in Time-Resolved Photoelectron Spectra

Time-resolved photoelectron spectroscopy is commonly employed with the intention to monitor electronic excited-state dynamics occurring in a neutral molecule. With the help of theory, we show that when excited-state processes occur on similar time scales the different relaxation pathways are completely obscured in the total photoionization signal recorded in the experiment. Using non-adiabatic molecular dynamics and Dyson norms, we calculate the photoionization signal of cytosine and disentangle the transient contributions originating from the different deactivation pathways of its tautomers. In the simulations, the total signal from the relevant keto and enol tautomers can be decomposed into contributions either from the neutral electronic state populations or from the distinct mechanistic pathways across the multiple potential surfaces. The lifetimes corresponding to these contributions cannot be extracted from the experiment, thereby illustrating that new experimental setups are necessary to unravel the intricate non-adiabatic pathways occurring in polyatomic molecules after irradiation by light.

Attosecond Delays in Molecular Photoionization

We report measurements of energy-dependent photoionization delays between the two outermost valence shells of N_{2}O and H_{2}O. The combination of single-shot signal referencing with the use of different metal foils to filter the attosecond pulse train enables us to extract delays from congested spectra. Remarkably large delays up to 160 as are observed in N_{2}O, whereas the delays in H_{2}O are all smaller than 50 as in the photon-energy range of 20-40 eV. These results are interpreted by developing a theory of molecular photoionization delays. The long delays measured in N_{2}O are shown to reflect the population of molecular shape resonances that trap the photoelectron for a duration of up to ∼110 as. The unstructured continua of H_{2}O result in much smaller delays at the same photon energies. Our experimental and theoretical methods make the study of molecular attosecond photoionization dynamics accessible.

A proposed new scheme for vibronically resolved time-dependent photoelectron spectroscopy: pump-repump-continuous wave-photoelectron spectroscopy (prp-cw-pes)

We propose a new scheme for time-resolved photoelectron spectroscopy denoted as pump-repump-continuous wave-photoelectron spectroscopy (prp-cw-pes). This scheme is comprised of two femtosecond laser (pump) pulses under cw illumination (probe). By changing the time-delay between pump and repump lasers one can manipulate the populations of vibronic levels in electronic excited states. The cw laser acts on for a long time and establishes resonance between excited states and the continuum photo-ionized states. Sharp spectra can be obtained from the resonance condition [formula: see text]. The intensities in the spectra are sensitive to the time-delay between the pump-repump pulses, but only depend on the populations of excited states, not the phase relations (coherence). As a result, each time-delayed snapshot spectrum is a weighted sum of so-called fingerprints, where a fingerprint is the vibrationally resolved photoelectron spectrum for a single vibronic excited state. The latter information can potentially be simulated reliably using vibronic models and wave packet propagation methods. In the easiest application of the experiment, different time-delays produce different spectra, for a single molecular system. This wealth of experimental data can be fitted to an, ideally small, set of theoretical fingerprints by adjusting the populations as fitting parameters. This technique might be able to distinguish between closely related molecular species. Adopting a different viewpoint, the proposed scheme can also be employed to monitor the time-dependent dynamics by changing the phase relationship between the pump and repump laser that can be viewed as a "control mechanism" employed in wave packet interferometry. Simplifications arise as the change in the spectra is due to the changing populations, not because of the coherence. In this paper, we outline the ideas behind the scheme and illustrate the ideas theoretically using simple model systems.

The effects of symmetry and rigidity on non-adiabatic dynamics in tertiary amines: a time-resolved photoelectron velocity-map imaging study of the cage-amine ABCO

The non-adiabatic relaxation dynamics of the tertiary cage-amine azabicyclo[2.2.2]octane (ABCO, also known as quinuclidine) have been investigated following 3p Rydberg excitation at 201 nm using femtosecond time-resolved photoelectron imaging (TRPEI). The aim of the study was to investigate the influence of the rigid and symmetric cage structure found in ABCO on the general non-adiabatic relaxation processes commonly seen in other tertiary aliphatic amines (TAAs). Our data is compared with TRPEI results very recently obtained for several structurally less rigid TAA systems [J. O. F. Thompson et al., Chem. Sci., 2016, 7, 1826-1839] and helps to confirm many of the previously reported findings. The experimental results for ABCO in the short-time (<1 ps) regime strongly support earlier conclusions suggesting that planarization about the N-atom is not a prerequisite for efficient 3p-3s internal conversion. Additionally, individual photoelectron peaks within our ABCO data show no temporal shifts in energy. As confirmed by our supporting quantum mechanical calculations, this demonstrates that neither internal conversion within the 3p manifold or significant conformational re-organization are possible in the ABCO system. This result therefore lends strong additional support to the active presence of such dynamical effects in other, less conformationally restricted TAA species, where photoelectron peak shifts are commonly observed. Finally, the extremely long (>1 ns) 3s Rydberg state lifetime seen in ABCO (relative to other TAA systems at similar excitation energies) serves to illustrate the large influence of symmetry and conformational rigidity on intramolecular vibrational redistribution processes previously implicated in mediating this aspect of the overall relaxation dynamics.

Calculation of photodetachment cross sections and photoelectron angular distributions of negative ions using density functional theory

Recently, the development of photoelectron velocity map imaging makes it much easier to obtain the photoelectron angular distributions (PADs) experimentally. However, explanations of PADs are only qualitative in most cases, and very limited works have been reported on how to calculate PAD of anions. In the present work, we report a method using the density-functional-theory Kohn-Sham orbitals to calculate the photodetachment cross sections and the anisotropy parameter β. The spherical average over all random molecular orientation is calculated analytically. A program which can handle both the Gaussian type orbital and the Slater type orbital has been coded. The testing calculations on Li(-), C(-), O(-), F(-), CH(-), OH(-), NH2 (-), O2 (-), and S2 (-) show that our method is an efficient way to calculate the photodetachment cross section and anisotropy parameter β for anions, thus promising for large systems.

Ultrafast internal conversion of aromatic molecules studied by photoelectron spectroscopy using Sub-20 fs laser pulses

This article describes our recent experimental studies on internal conversion via a conical intersection using photoelectron spectroscopy. Ultrafast S2(ππ*)-S1(nπ*) internal conversion in pyrazine is observed in real time using sub-20 fs deep ultraviolet pulses (264 and 198 nm). While the photoelectron kinetic energy distribution does not exhibit a clear signature of internal conversion, the photoelectron angular anisotropy unambiguously reveals the sudden change of electron configuration upon internal conversion. An explanation is presented as to why these two observables have different sensitivities to internal conversion. The 198 nm probe photon energy is insufficient for covering the entire Franck-Condon envelopes upon photoionization from S2/S1 to D1/D0. A vacuum ultraviolet free electron laser (SCSS) producing 161 nm radiation is employed to solve this problem, while its pulse-to-pulse timing jitter limits the time resolution to about 1 ps. The S2-S1 internal conversion is revisited using the sub-20 fs 159 nm pulse created by filamentation four-wave mixing. Conical intersections between D1(π-1) and D0(n-1) and also between the Rydberg state with a D1 ion core and that with a D0 ion core of pyrazine are studied by He(I) photoelectron spectroscopy, pulsed field ionization photoelectron spectroscopy and one-color resonance-enhanced multiphoton ionization spectroscopy. Finally, ultrafast S2(ππ*)-S1(ππ*) internal conversion in benzene and toluene are compared with pyrazine.

Photodetachment anisotropy for mixed s-p states: 8/3 and other fractions

An approximate model for analytical prediction of photoelectron angular distributions in anion photodetachment from mixed s-p states is presented. Considering the dipole-allowed s, p, and d free-electron partial waves, the model describes photodetachment anisotropy in terms of the fractional p character of the initial orbital and the A and B coefficients describing the relative intensities of the p → d to p → s and s → p to p → s channels, respectively. The model represents an extension of the central-potential model to an intermediate regime encompassing varying degrees of s and p contributions to the initial bound orbital. This description is applicable to a broad class of hybrid molecular orbitals, particularly those localized predominantly on a single atom. Under the additional assumption of hydrogenic or Slater-type orbitals, the B/A ratio in photodetachment from a mixed 2s-2p state is shown to equal 8/3. Corresponding fractions are derived for other ns-np mixing cases. The predictions of the model are tested on several anion systems, including NH(2)(-) and CCl(2)(-). The quantitative discrepancies in the latter case are attributed to the breakdown of the central-atom approximation and a mechanism for corresponding corrections is indicated.

Fingerprints of Adiabatic versus Diabatic Vibronic Dynamics in the Asymmetry of Photoelectron Momentum Distributions

When the Born-Oppenheimer approximation is valid, electrons adiabatically follow the nuclear motion in molecules. For strong nonadiabatic coupling between electronic states, one encounters a diabatic motion where the electrons remain local and do not adapt to molecular geometry changes. We show that the mentioned limiting cases are reflected differently in the asymmetry of time-resolved photoelectron momentum distributions. Whereas for adiabatic dynamics, the asymmetry directly maps the time-dependent average nuclear momentum, in the diabatic case, the asymmetry is determined by a nonclassical interference effect arising from the mixing of wave function components in different electronic states, which is present at times nonadiabatic transitions take place.

Photoelectron angular distributions in negative-ion photodetachment from mixed sp states

We describe an approach for constructing analytical models for the energy-dependence of photoelectron angular distributions in the one-electron, non-relativistic approximation. We construct such a model for electron emission from an orbital described as a superposition of s- and p-type functions, using linearly polarized light. In the limits of pure s or pure p electron photodetachment or photoionization, the model correctly reproduces the familiar Cooper-Zare formula. The model predictions are compared to experimental results for strongly solvated H(-) and NH(2)(-), corresponding to predominantly s and predominantly p character parent states, respectively.

Time-resolved photoelectron spectroscopy: from wavepackets to observables

Time-resolved photoelectron spectroscopy (TRPES) is a powerful tool for the study of intramolecular dynamics, particularly excited state non-adiabatic dynamics in polyatomic molecules. Depending on the problem at hand, different levels of TRPES measurements can be performed: time-resolved photoelectron yield; time- and energy-resolved photoelectron yield; time-, energy-, and angle-resolved photoelectron yield. In this pedagogical overview, a conceptual framework for time-resolved photoionization measurements is presented, together with discussion of relevant theory for the different aspects of TRPES. Simple models are used to illustrate the theory, and key concepts are further amplified by experimental examples. These examples are chosen to show the application of TRPES to the investigation of a range of problems in the excited state dynamics of molecules: from the simplest vibrational wavepacket on a single potential energy surface; to disentangling intrinsically coupled electronic and nuclear motions; to identifying the electronic character of the intermediate states involved in non-adiabatic dynamics by angle-resolved measurements in the molecular frame, the most complete measurement.

Time-resolved photoelectron imaging of S2 → S1 internal conversion in benzene and toluene

Ultrafast internal conversion of benzene and toluene from the S(2) states was studied by time-resolved photoelectron imaging with a time resolution of 22 fs. Time-energy maps of the photoelectron intensity and the angular anisotropy were generated from a series of photoelectron images. The photoelectron kinetic energy distribution exhibits a rapid energy shift and intensity revival, which indicates nuclear motion on the S(2) adiabatic surface, while the ultrafast evolution of the angular anisotropy revealed a change in the electronic character of the S(2) adiabatic surface. From their decay profiles of the total photoelectron intensity, the time constants of 48 ± 4 and 62 ± 4 fs were determined for the population decay from the S(2) states in benzene and toluene, respectively.

Photoelectron angular distributions from autoionizing 4s¹4p⁶6p¹ states in atomic krypton probed with femtosecond time resolution

Photoelectron angular distributions (PADs) are obtained for a pair of 4s(1)4p(6)6p(1) (a singlet and a triplet) autoionizing states in atomic krypton. A high-order harmonic pulse is used to excite the pair of states and a time-delayed 801 nm ionization pulse probes the PADs to the final 4s(1)4p(6) continuum with femtosecond time resolution. The ejected electrons are detected with velocity map imaging to retrieve the time-resolved photoelectron spectrum and PADs. The PAD for the triplet state is inherently separable by virtue of its longer autoionization lifetime. Measuring the total signal over time allows for the PADs to be extracted for both the singlet state and the triplet state. Anisotropy parameters for the triplet state are measured to be β(2)=0.55 ± 0.17 and β(4)=-0.01 ± 0.10, while the singlet state yields β(2)=2.19 ± 0.18 and β(4)=1.84 ± 0.14. For the singlet state, the ratio of radial transition dipole matrix elements, X, of outgoing S to D partial waves and total phase shift difference between these waves, Δ, are determined to be X=0.56 ± 0.08 and Δ=2.19 ± 0.11 rad. The continuum quantum defect difference between the S and D electron partial waves is determined to be -0.15 ± 0.03 for the singlet state. Based on previous analyses, the triplet state is expected to have anisotropy parameters independent of electron kinetic energy and equal to β(2)=5∕7 and β(4)=-12∕7. Deviations from the predicted values are thought to be a result of state mixing by spin-orbit and configuration interactions in the intermediate and final states; theoretical calculations are required to quantify these effects.

Determining partial differential cross sections for low-energy electron photodetachment involving conical intersections using the solution of a Lippmann-Schwinger equation constructed with standard electronic structure techniques

A method for obtaining partial differential cross sections for low energy electron photodetachment in which the electronic states of the residual molecule are strongly coupled by conical intersections is reported. The method is based on the iterative solution to a Lippmann-Schwinger equation, using a zeroth order Hamiltonian consisting of the bound nonadiabatically coupled residual molecule and a free electron. The solution to the Lippmann-Schwinger equation involves only standard electronic structure techniques and a standard three-dimensional free particle Green's function quadrature for which fast techniques exist. The transition dipole moment for electron photodetachment, is a sum of matrix elements each involving one nonorthogonal orbital obtained from the solution to the Lippmann-Schwinger equation. An expression for the electron photodetachment transition dipole matrix element in terms of Dyson orbitals, which does not make the usual orthogonality assumptions, is derived.

Real-time visualization of the dynamic evolution of CS2 4d and 6s Rydberg wave packet components

The dynamic evolution of CS2 4d and 6s Rydberg wave packet components has been experimentally visualized via femtosecond time-resolved photoelectron imaging coupled with time-resolved mass spectroscopy. The temporal evolution of the four components of the prepared Rydberg wave packet is directly observed as time-dependent changes of the intensities of different parts in the main photoelectron peak. Furthermore, time-resolved photoelectron angular distributions (PADs) clearly reflect the different component characters of 4d and 6s molecular orbitals. The lifetime of Rydberg wave packets is determined to be about 830fs and their decay is attributed to predissociation. Our results suggest the possibility of directly visualizing and determining the amplitudes and relative phases of different electronic and vibrational wave packet components in polyatomic molecules.

Ultrafast relaxation dynamics observed through time-resolved photoelectron angular distributions

Time-resolved photoelectron imaging of the 7,7,8,8-tetracyanoquinodimethane (TCNQ) radical anion is presented. Photoelectron angular distributions (PADs) are qualitatively analyzed in terms of the simple s-p model that is based on symmetry arguments. The internal conversion dynamics from the first excited state (1(2)B(3u)) to the ground state ((2)B(2g)) may be observed through temporal changes in the PADs of the spectrally overlapping photoelectron features arising from photodetachment of the ground state and the excited state. A formulism for extracting the population dynamics from the β(2) anisotropy parameter of overlapping spectroscopic features is presented. This is used to extract the lifetime of the first excited state, which is in good agreement with that observed in the time-resolved photoelectron spectra.