Time-resolved photoelectron angular distributions as a probe of intramolecular dynamics: Connecting the molecular frame and the laboratory frame

Observation of Nondipole-Induced Asymmetry in the Angular Emission Distribution of Photoelectrons from Fixed-in-Space CO Molecules

We investigate experimentally and theoretically the C and O 1s photoionization of fixed-in-space CO molecules at a photon energy of 905 eV. We find a significant dependence of the photoelectron angular distributions on the direction of propagation of the ionizing radiation. It results from an interplay of nondipole effects, on one hand, and molecular effects, on the other. The nondipole effects lead to an increase of the emission probability in the forward direction along the light propagation, and the photoelectron wave being scattered by the molecular potential gives rise to a strong peak in the direction of the atom neighboring the emitter site. These effects can either conspire or extenuate each other, depending on the photoelectron emission direction and molecular orientation in space.

A laboratory frame density matrix for ultrafast quantum molecular dynamics

In most cases, the ultrafast dynamics of resonantly excited molecules are considered and almost always computed in the molecular frame, while experiments are carried out in the laboratory frame. Here, we provide a formalism in terms of a lab frame density matrix, which connects quantum dynamics in the molecular frame to those in the laboratory frame, providing a transparent link between computation and measurement. The formalism reveals that in any such experiment, the molecular frame dynamics vary for molecules in different orientations and that certain coherences, which are potentially experimentally accessible, are rejected by the orientation-averaged reduced vibronic density matrix. Instead, molecular angular distribution moments are introduced as a more accurate representation of experimentally accessible information. Furthermore, the formalism provides a clear definition of a molecular frame quantum tomography and specifies the requirements to perform such a measurement enabling the experimental imaging of molecular frame vibronic dynamics. Successful completion of such a measurement fully characterizes the molecular frame quantum dynamics for a molecule at any orientation in the laboratory frame.

A geometric approach to decoding molecular structure and dynamics from photoionization of isotropic samples

We propose a geometric approach to the description and analysis of photoelectron angular distributions resulting from isotropic samples in the case of few-photon ionization by electric fields of arbitrary polarization. This approach formulates the standard photoionization observables - the b_l,m expansion coefficients of the photoelectron angular distribution, in terms of geometrical properties of the vector field D⃑(k⃑) ≡ 〈k⃑|d⃑|0〉 describing the electronic transition from a bound state |0〉 into a scattering state |k⃑〉 - the photoionization transition dipole. Besides revealing selection rules for the enantio-sensitivity of b_l,m coefficients in multiphoton ionization, our approach yields very compact expressions for both chiral and achiral molecules revealing how the molecular rotational invariants couple to the rotational invariants of the setup defined by the electric field polarization and the arrangement of photoelectron detectors. We apply this approach to one-photon ionization and find that the forward-backward asymmetry parameter b_1,0, emerging exclusively in chiral molecules and encoded in the field B⃑(k⃑) ≡ iD⃑*(k⃑) × D⃑(k⃑), is sensitive only to the components of D⃑(k⃑) perpendicular to k⃑, while the regular asymmetry parameter b_2,0 emerging in chiral and achiral molecules is sensitive only to the component of D⃑(k⃑) parallel to k⃑. Next, we analyze resonantly enhanced two-photon ionization and show that b_0,0 and b_1,0 can be written in terms of an effectively stretched D⃑(k⃑), and how b_1,0 and b_3,0 can be used to probe B⃑(k⃑).

Time-resolved photoelectron spectroscopy: the continuing evolution of a mature technique

Time-resolved photoelectron spectroscopy (TRPES) has become one of the most widespread techniques for probing nonadiabatic dynamics in the excited electronic states of molecules. Furthermore, the complementary development of ab initio approaches for the simulation of TRPES signals has enabled the interpretation of these transient spectra in terms of underlying coupled electronic-nuclear dynamics. In this perspective, we discuss the current state-of-the-art approaches, including efforts to push femtosecond pulses into vacuum ultraviolet and soft X-ray regimes as well as the utilization of novel polarizations to use time-resolved optical activity as a probe of nonadiabatic dynamics. We close this perspective with a forward-looking prospectus on the new areas of application for this technique.

Basic studies toward ultrafast soft x-ray photoelectron diffraction; its application to probing local structure in iodobenzene molecules

Ultrafast x-ray photoelectron diffraction (UXPD) for free molecules has a promising potential to probe the local structures of the molecules in an element-specific fashion. Our UXPD scheme consists of three steps: (1) near-infrared laser (NIR) with ns pulse duration aligns sample molecules, (2) ultra-violet laser with fs pulse duration pumps the aligned molecules, and (3) soft x-ray free-electron laser (SXFEL) with fs pulse duration probes the molecules by measuring x-ray photoelectron diffraction (XPD) profiles. Employing steps of (1) and (3), we have measured I 3d XPD profiles from ground state iodobenzene aligned by the NIR laser with the SXFEL. Then, we have intensively calculated I 3d XPD profiles with density functional theory, taking degrees of alignments of the molecules into account, to extract a distance between C and I atoms in iodobenzene from the experimental I 3d XPD profiles. Although we have failed to determine the distance from the comparison between the experimental and theoretical results, we have succeeded in concluding that the degeneracies of the initial state eliminate the sensitivity on molecular structure in the I 3d XPD profiles. Thus, the observation of fine structures in the XPD profiles could be expected, if a nondegenerate molecular orbital is selected for a probe of UXPD. Finally, we have summarized our criteria to perform UXPD successfully: (1) to use SXFEL, (2) to prepare sample molecules with the degree of alignment higher than 0.8, and (3) to select a photoemission process from a nondegenerate inner-shell orbital of sample molecules.

Trends in angle-resolved molecular photoelectron spectroscopy

In this perspective article, main trends of angle-resolved molecular photoelectron spectroscopy in the laboratory up to the molecular frame, in different regimes of light-matter interactions, are highlighted with emphasis on foundations and most recent applications.

Fourfold Differential Photoelectron Circular Dichroism

We report on a joint experimental and theoretical study of photoelectron circular dichroism (PECD) in methyloxirane. By detecting O 1s photoelectrons in coincidence with fragment ions, we deduce the molecule's orientation and photoelectron emission direction in the laboratory frame. Thereby, we retrieve a fourfold differential PECD clearly beyond 50%. This strong chiral asymmetry is reproduced by ab initio electronic structure calculations. Providing such a pronounced contrast makes PECD of fixed-in-space chiral molecules an even more sensitive tool for chiral recognition in the gas phase.

Perfect control of photoelectron anisotropy for randomly oriented ensembles of molecules by XUV REMPI and polarization shaping

We report two schemes to generate perfect anisotropy in the photoelectron angular distribution of a randomly oriented ensemble of polyatomic molecules. In order to exert full control over the anisotropy of photoelectron emission, we exploit interferences between single-photon pathways and a manifold of resonantly enhanced two-photon pathways. These are shown to outperform nonsequential (ω, 2ω) bichromatic phase control for the example of CHFClBr molecules. We are able to optimize pulses that yield anisotropic photoelectron emission thanks to a very efficient calculation of photoelectron momentum distributions. This is accomplished by combining elements of quantum chemistry, variational scattering theory, and time-dependent perturbation theory.

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

Imaging and controlling the ultrafast conical intersection dynamics in NO₂ using the latest advances in attosecond and light-synthesizer technology.

Accessing the molecular frame through strong-field alignment of distributions of gas phase molecules

A rationale for creating highly aligned distributions of molecules is that it enables vector properties referenced to molecule-fixed axes (the molecular frame) to be determined. In the present work, the degree of alignment that is necessary for this to be achieved in practice is explored. Alignment is commonly parametrized in experiments by a single parameter, [Formula: see text], which is insufficient to enable predictive calculations to be performed. Here, it is shown that, if the full distribution of molecular axes takes a Gaussian form, this single parameter can be used to determine the complete set of alignment moments needed to characterize the distribution. In order to demonstrate the degree of alignment that is required to approach the molecular frame, the alignment moments corresponding to a few chosen values of [Formula: see text] are used to project a model molecular frame photoelectron angular distribution into the laboratory frame. These calculations show that [Formula: see text] needs to approach 0.9 in order to avoid significant blurring to be caused by averaging.This article is part of the theme issue 'Modern theoretical chemistry'.

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.

Retrieving transient conformational molecular structure information from inner-shell photoionization of laser-aligned molecules

We discuss a scheme to retrieve transient conformational molecular structure information using photoelectron angular distributions (PADs) that have averaged over partial alignments of isolated molecules. The photoelectron is pulled out from a localized inner-shell molecular orbital by an X-ray photon. We show that a transient change in the atomic positions from their equilibrium will lead to a sensitive change in the alignment-averaged PADs, which can be measured and used to retrieve the former. Exploiting the experimental convenience of changing the photon polarization direction, we show that it is advantageous to use PADs obtained from multiple photon polarization directions. A simple single-scattering model is proposed and benchmarked to describe the photoionization process and to do the retrieval using a multiple-parameter fitting method.

Photoelectron wave function in photoionization: plane wave or Coulomb wave?

The calculation of absolute total cross sections requires accurate wave functions of the photoelectron and of the initial and final states of the system. The essential information contained in the latter two can be condensed into a Dyson orbital. We employ correlated Dyson orbitals and test approximate treatments of the photoelectron wave function, that is, plane and Coulomb waves, by comparing computed and experimental photoionization and photodetachment spectra. We find that in anions, a plane wave treatment of the photoelectron provides a good description of photodetachment spectra. For photoionization of neutral atoms or molecules with one heavy atom, the photoelectron wave function must be treated as a Coulomb wave to account for the interaction of the photoelectron with the +1 charge of the ionized core. For larger molecules, the best agreement with experiment is often achieved by using a Coulomb wave with a partial (effective) charge smaller than unity. This likely derives from the fact that the effective charge at the centroid of the Dyson orbital, which serves as the origin of the spherical wave expansion, is smaller than the total charge of a polyatomic cation. The results suggest that accurate molecular photoionization cross sections can be computed with a modified central potential model that accounts for the nonspherical charge distribution of the core by adjusting the charge in the center of the expansion.

Photoelectron angular distributions from liquid water: effects of electron scattering

Photoelectron angular distributions (PADs) from the liquid-water surface and from bulk liquid water are reported for water oxygen-1s ionization. Although less so than for the gas phase, the measured PADs from the liquid are remarkably anisotropic, even at electron kinetic energies lower than 100 eV, when elastic scattering cross sections for the outgoing electrons with other water molecules are large. The PADs reveal that theoretical estimates of the inelastic mean free path are likely too long at low kinetic energies, and hence the electron probing depth in water, near threshold ionization, appears to be considerably smaller than so far assumed.

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.

Time-energy mapping of photoelectron angular distribution: application to photoionization stereodynamics of nitric oxide

The time-energy mapping of the photoionization integral cross section and laboratory-frame photoelectron angular distribution is used to study photoionization stereodynamics of a diatomic molecule. The general theoretical formalism [Y. Suzuki and T. Suzuki, Mol. Phys., 2007, 105, 1675] is simplified for application to a diatomic molecule, and a high-resolution photoelectron imaging apparatus is used to determine the transition dipole moments and phase shifts of photoelectron partial waves in near-threshold and non-dissociative photoionization of NO from the A(2)Σ(+) state. The transition dipoles and phase shifts thus determined are in reasonable agreement with those by state-to-state photoionization experiment and Schwinger variational calculations. The difference of the phase shifts from those expected from the quantum defects of Rydberg states suggests occurrence of weak hybridization of different l-waves, in addition to the well-known s-d super complex. The circular dichroism in photoelectron angular distribution is also simulated from our results.

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.

Vibronic coupling in the superoxide anion: the vibrational dependence of the photoelectron angular distribution

We present a comprehensive photoelectron imaging study of the O(2)(X  (3)Σ(g)(-),v(')=0-6)←O(2)(-)(X  (2)Π(g),v(")=0) and O(2)(a (1)Δ(g),v(')=0-4)←O(2)(-)(X  (2)Π(g),v(")=0) photodetachment bands at wavelengths between 900 and 455 nm, examining the effect of vibronic coupling on the photoelectron angular distribution (PAD). This work extends the v(')=1-4 data for detachment into the ground electronic state, presented in a recent communication [R. Mabbs, F. Mbaiwa, J. Wei, M. Van Duzor, S. T. Gibson, S. J. Cavanagh, and B. R. Lewis, Phys. Rev. A 82, 011401(R) (2010)]. Measured vibronic intensities are compared to Franck-Condon predictions and used as supporting evidence of vibronic coupling. The results are analyzed within the context of the one-electron, zero core contribution (ZCC) model [R. M. Stehman and S. B. Woo, Phys. Rev. A 23, 2866 (1981)]. For both bands, the photoelectron anisotropy parameter variation with electron kinetic energy, β(E), displays the characteristics of photodetachment from a d-like orbital, consistent with the π(g)(∗) 2p highest occupied molecular orbital of O(2)(-). However, differences exist between the β(E) trends for detachment into different vibrational levels of the X  (3)Σ(g)(-) and a (1)Δ(g) electronic states of O(2). The ZCC model invokes vibrational channel specific "detachment orbitals" and attributes this behavior to coupling of the electronic and nuclear motion in the parent anion. The spatial extent of the model detachment orbital is dependent on the final state of O(2): the higher the neutral vibrational excitation, the larger the electron binding energy. Although vibronic coupling is ignored in most theoretical treatments of PADs in the direct photodetachment of molecular anions, the present findings clearly show that it can be important. These results represent a benchmark data set for a relatively simple system, upon which to base rigorous tests of more sophisticated models.

Femtosecond time-resolved photoelectron imaging

Femtosecond time-resolved photoelectron imaging (TRPEI) is a variant of time-resolved photoelectron spectroscopy used in the study of gas-phase photoinduced dynamics. A new observable, time-dependent photoionization-differential cross section provides useful information on wave-packet motions, electronic dephasing, and photoionization dynamics. This review describes fundamental issues and the most recent works involving TRPEI.

Observation of a simple vibrational wavepacket in a polyatomic molecule via time-resolved photoelectron velocity-map imaging: A prototype for time-resolved IVR studies

We have prepared a coherent superposition of the two components of a Fermi resonance in the S1 state of toluene at approximately 460 cm(-1) with a approximately 1 ps laser pulse and monitored time-resolved photoelectron velocity-map images. The photoelectron intensities oscillate with time in a manner that depends on their kinetic energy, even though full vibrational resolution in the cation is not achieved. Analysis of the time-dependent photoelectron spectra enables information on the composition of the S1 wavepacket to be deduced. Such an experiment, in which a whole set of partially dispersed cation vibrational states are detected simultaneously, suggests an efficient method of studying intramolecular vibrational energy redistribution processes in excited states.

Mapping rotational coherences onto time-resolved photoelectron imaging observables

We explore the information content of time-resolved photoelectron imaging, a potentially powerful pump-probe technique whose popularity has been rapidly growing in recent years. To that end, we identify a mapping of the alignment properties of time-evolving wave packets onto the moments of the photoelectron images and investigate its origin and consequences theoretically and numerically.

Field-free three dimensional molecular axis alignment

We investigate strategies for field-free three dimensional molecular axis alignment using strong nonresonant laser fields under experimentally realistic conditions. Using the polarizabilites and rotational constants of an asymmetric top rotor molecule (ethene, C2H4), we consider three different methods for axis alignment of a Boltzmann distribution of rotors at 4 K. Specifically, we compare the use of impulsive kick laser pulses having both linear and elliptical polarization to the use of elliptically polarized switched laser pulses. We show that an enhanced degree of field-free three dimensional alignment of ground vibronic state molecules obtains from the use of two orthogonally polarized, time-separated laser pulses.

Photoelectron kinetic energy dependence in near threshold ionization of NO from A state studied by time-resolved photoelectron imaging

Photoelectron angular distributions in the laboratory frame (LF-PADs) from the A((2)sigma(+)) state of NO molecule were measured by femtosecond time-resolved photoelectron imaging with (1 + 1(')) resonance enhanced multiphoton ionization via the A state. High-precision measurements of the anisotropy parameters of LF-PADs were performed for the photoelectron kinetic energy from 0.03 to 1.05 eV as a function of the pump-probe delay time. The revival feature of the rotational wave packet on the A state was clearly observed in the time dependence of the photoelectron anisotropy parameters. By approximating the phase shifts of the photoelectron partial waves by the quantum defects in the high-lying Rydberg states using the multichannel quantum defect theory, the energy-dependent photoionization transition dipole moments were determined, for the first time, from time-dependent LF-PADs measured by time-resolved photoelectron spectroscopy.

Reevaluation of the use of photoelectron angular distributions as a probe of dynamical processes: strong dependence of such distributions from s1 paradifluorobenzene on photoelectron kinetic energy

Photoelectron angular distributions (PADs) have been measured following the excitation of the S1 origin band in paradifluorobenzene using a range of ionizing wavelengths and for resolved ion vibrational states. The PADs show a dramatic sensitivity to the photoelectron kinetic energy over an energy range of at least 1 eV from threshold, and almost no sensitivity to any prepared intermediate state alignment. This has important consequences for those studies of intramolecular dynamics that use PADs. We suggest that the observed behavior is caused by a shape resonance in the continuum.

Photoelectron angular distributions

Angle-resolved photoelectron spectroscopy has been performed for more than 70 years in various guises, but recently its potential to help solve in detail problems in the photoionization dynamics and intramolecular dynamics of gas-phase molecules has been recognized. One key development has been the design of experiments in appropriate geometries to extract information that pertains to the molecular frame, another has been the development of imaging spectrometers, and a third is the use of ultrafast lasers to cause photoionization. In this review, which is aimed at experimentalists, simple expressions for photoelectron angular distributions (PADs) in various experimental geometries are given and their applications explained.

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

The use of photoelectron angular distributions (PADs) as a probe in short-pulse, pump-probe scenarios is reviewed. We focus on concepts, on the insight that can be gained through theoretical analysis, on applications, and on future opportunities. Time-resolved PADs are sensitive to both the time-evolving rotational composition of wavepackets and their time-evolving electronic symmetry. The former feature renders this observable a potential probe of molecular structure, intensity effects, and rotational perturbations. The latter feature renders the PAD a potential probe of radiationless transitions.

Photoelectron imaging on time-dependent molecular alignment created by a femtosecond laser pulse

Rotational wave packet revivals on an excited electronic state have been measured by femtosecond time-resolved photoelectron imaging for the first time. The first full revival at 82 ps of S1 (n,pi*) pyrazine was clearly observed in the time dependencies of the photoelectron intensity and the photoelectron angular distribution (PAD). The PAD, measured for laser aligned pyrazine, clearly reflects the different characters of pi* and 3s molecular orbitals.

Coincidence spectroscopy

The application of coincidence techniques to the study of the reaction dynamics of isolated molecules is reviewed. Coincidence spectroscopy is a powerful approach for carrying out a number of measurements. At its most basic level, coincidence techniques can identify the source of a specific signal, as in the well-known photoelectron-photoion coincidence approach used for several years. By carrying out coincidence experiments in an increasingly differential manner, correlated energy and angular distributions of reaction products may be recorded. Completely energy- and angle-resolved measurements of photoelectrons and ionic or neutral products can reveal molecular-frame photoelectron and photofragment angular distributions and aid in the characterization of dissociative states of molecules and ions. Recent work in this area is reviewed, including examples from studies of dissociative photodetachment, dissociative photoionization, time-resolved studies of dissociative photoionization, and three-body dissociation processes.