Recoil Frame Research Articles

Attosecond photoionisation time delays reveal the anisotropy of the molecular potential in the recoil frame

Photoionisation time delays carry structural and dynamical information on the target system, including electronic correlation effects in atoms and molecules and electron transport properties at interfaces. In molecules, the electrostatic potential experienced by an outgoing electron depends on the emission direction, which should thus lead to anisotropic time delays. To isolate this effect, information on the orientation of the molecule at the photoionisation instant is required. Here we show how attosecond time delays reflect the anisotropic molecular potential landscape in CF4 molecules. The variations in the measured delays can be directly related to the different heights of the potential barriers that the outgoing electrons see in the vicinity of shape resonances. Our results indicate the possibility to investigate the spatial characteristics of the molecular potential by mapping attosecond photoionisation time delays in the recoil-frame.

Attosecond interferometry of shape resonances in the recoil frame of CF4.

Shape resonances play a central role in many areas of science, but the real-time measurement of the associated many-body dynamics remains challenging. Here, we present measurements of recoil frame angle-resolved photoionization delays in the vicinity of shape resonances of CF4. This technique provides insights into the spatiotemporal photoionization dynamics of molecular shape resonances. We find delays of up to ∼600 as in the ionization out of the highest occupied molecular orbital (HOMO) with a strong dependence on the emission direction and a pronounced asymmetry along the dissociation axis. Comparison with quantum-scattering calculations traces the asymmetries to the interference of a small subset of partial waves at low kinetic energies and, additionally, to the interference of two overlapping shape resonances in the HOMO-1 channel. Our experimental and theoretical results establish a broadly applicable approach to space- and time-resolved photoionization dynamics in the molecular frame.

Spectral dependence of photoemission in multiphoton ionization of NO2 by femtosecond pulses in the 375-430 nm range.

We investigate the multiphoton ionization of NO2 using tunable (430-375 nm) femtosecond pulses and photoelectron-photoion coincidence momentum spectroscopy. In order to understand the complex electronic and nuclear photodynamics at play following absorption of three to five photons, we also report extended photoionization calculations using correlated targets and coupled channels. Exploring the multiphoton dissociative ionization (MPDI) and multiphoton ionization (MPI) processes over such a broad energy range enables us to lend further support to our work carried out around 400 nm of a femtosecond laser [S. Marggi Poullain et al., J. Phys. B: At., Mol. Opt. Phys., 2014, 47, 124024]. Two excitation energy regions are identified and discussed in terms of the proposed reaction pathways, highlighting the significant role of Rydberg states, such as the [R*(6a1)-1, 3pσ] Rydberg state, in the NO2 multiphoton excitation and photoionization. These new results support our previous assumption that different bent and linear geometries of the NO2+(X1Σg) ionic state contribute to the MPDI and MPI, consistent with the reported calculations which reveal an important vibronic coupling characterizing the photoemission. Remarkably, the strong anisotropy of the recoil frame photoelectron angular distribution (RFPAD) previously observed at 400 nm appears as a fingerprint across the whole explored photon energy range.

Diffraction effects in the Recoil-Frame Photoelectron Angular Distributions of Halomethanes

SynopsisWe have measured the Recoil Frame - Photoelectron Angular Distributions (RF-PADs) for inner-shell photoionization of CH3F, CH3I and CF3I halomethane molecules for photoelectron energies up to 300 eV detected within a 4π solid angle in the gas-phase. For high kinetic energies, the RF-PADs are dominated by diffraction effects that encode information on the molecular geometry.

Recoil frame photoemission in multiphoton ionization of small polyatomic molecules: photodynamics of NO2 probed by 400 nm fs pulses

We report a general method for the complete analysis of the recoil frame photoelectron angular distribution (RFPAD) in n-photon dissociative ionization of small polyatomic molecules, resulting from (n − 1) bound-to-bound transitions plus one-photon ionization of a neutral excited state of the target. This method relies on the decomposition of the RFPAD in terms of the recoil frame azimuthal harmonics (RFAHs) which are the components of its Fourier expansion in ϕe, where χ and θe are the polar angles referring to the polarization axis P and the photoelectron momentum k relative to the ion fragment recoil direction, respectively, and ϕe is the azimuth of k relative to P. The RFAH expansion method is illustrated by a detailed experimental and theoretical study of one-colour multiphoton dissociative and non-dissociative ionization of the NO2 molecule of C2v symmetry induced by 400 nm fs laser pulses, which involve electronic and nuclear dynamics within the pulse duration of the order of 70 fs. The reaction mechanism proposed to account for five-photon dissociative ionization of NO2 involves the role of [R*(6a1)−1] Rydberg states populated by three-photon absorption, subsequently ionized by a fourth photon into the NO2+ (X1Σg+, v1,v2,v3) manifold involving autoionization of [R*(4b2)−1] Rydberg states, and linear versus bent geometry selective dissociation of NO2+ (X1Σg+, v1,v2,v3) by a fifth photon. The reported calculations provide a coherent picture of the experimental findings although all features are not yet well reproduced.

Geometrical effect on the issue of asymmetric C 1s photoelectron angular distributions detected in coincidence with the fragment ion pairs of CO+–O+ for CO2 molecules

We have measured C 1s photoelectron angular distributions (PADs) in coincidence with the CO+–O+ fragment ion pairs of CO2 molecules at the photoelectron energies of 85, 120 and 150 eV. The observed left–right asymmetric PADs have been well reproduced by our theoretical model taking into account the two degenerate zero-point bending vibrations. This leads to a conclusive result on the interpretation of such PADs; although it has been believed so far that they are the molecular frame, in fact they are the recoil frame.

Off-resonance photoemission dynamics studied by recoil frame F1s and C1s photoelectron angular distributions of CH3F.

F1s and C1s photoelectron angular distributions are considered for CH3F, a molecule which does not support any shape resonance. In spite of the absence of features in the photoionization cross section profile, the recoil frame photoelectron angular distributions (RFPADs) exhibits dramatic changes depending on both the photoelectron energy and polarization geometry. Time-dependent density functional theory calculations are also given to rationalize the photoionization dynamics. The RFPADs have been compared with the theoretical calculations, in order to assess the accuracy of the theoretical method and rationalize the experimental findings. The effect of finite acceptance angles for both ionic fragments and photoelectrons has been included in the calculations, as well as the effect of rotational averaging around the fragmentation axis. Excellent agreement between theory and experiment is obtained, confirming the good quality of the calculated dynamical quantities (dipole moments and phase shifts).

DELICIOUS III: A multipurpose double imaging particle coincidence spectrometer for gas phase vacuum ultraviolet photodynamics studies

We present a versatile double imaging particle coincidence spectrometer operating in fully continuous mode, named DELICIOUS III, which combines a velocity map imaging device and a modified Wiley-McLaren time of flight momentum imaging analyzer for photoelectrons and photoions, respectively. The spectrometer is installed in a permanent endstation on the DESIRS vacuum ultraviolet (VUV) beamline at the French National Synchrotron Radiation Facility SOLEIL, and is dedicated to gas phase VUV spectroscopy, photoionization, and molecular dynamics studies. DELICIOUS III is capable of recording mass-selected threshold photoelectron photoion coincidence spectra with a sub-meV resolution, and the addition of a magnifying lens inside the electron drift tube provides a sizeable improvement of the electron threshold/ion mass resolution compromise. In fast electron mode the ultimate kinetic energy resolution has been measured at ΔE/E = 4%. The ion spectrometer offers a mass resolution--full separation of adjacent masses--of 250 amu for moderate extraction fields and the addition of an electrostatic lens in the second acceleration region allows measuring the full 3D velocity vector for a given mass with an ultimate energy resolution of ΔE/E = 15%, without sacrificing the mass resolution. Hence, photoelectron images are correlated both to the mass and to the ion kinetic energy and recoil direction, to access the electron spectroscopy of size-selected species, to study the photodissociation processes of state-selected cations in detail, or to measure in certain cases photoelectron angular distributions in the ion recoil frame. The performances of DELICIOUS III are explored through several examples including the photoionization of N2, NO, and CF3.

Recoil-frame photoelectron angular distributions probing inner-valence dissociative ionization of carbon monoxide

Dissociative photoionization of carbon monoxide with angle resolved photoelectron-photoion fragment detection has yielded recoil frame photoelectron angular distributions. Comparisons with accurate photoionization calculations have lead to the identification of the inner-valence ion states and estimates of their predissociative lifetimes.

Recoil frame photoelectron angular distributions in core O 1s ionization of H2CO

Recoil frame photoelectron angular distributions (RFPADs) from core O 1s ionization of H2CO are studied theoretically and experimentally. Time-dependent density functional theory calculations are performed to elucidate the ionization dynamics. The effect of averaging around the fragmentation axis is considered to explain differences between molecular frame and recoil frame angular distributions. Convolution by acceptance angles is also considered for the comparison between theory and experiment. The shape resonance to the virtual valence σ* (C–O) is properly reproduced by the calculations. In addition, it is found that the shape resonance plays a major role in assessing the RFPADs for light polarization parallel to the fragmentation axis.

Valence and inner-valence shell dissociative photoionization of CO in the 26–33 eV range. II. Molecular-frame and recoil-frame photoelectron angular distributions

Experimental and theoretical results for molecular-frame photoemission are presented for inner-valence shell photoionization of the CO molecule induced by linearly and circularly polarized light. The experimental recoil frame photoelectron angular distributions (RFPADs) obtained from dissociative photoionization measurements where the velocities of the ionic fragment and photoelectron were detected in coincidence, are compared to RFPADs computed using the multichannel Schwinger configuration interaction method. The formalism for including a finite lifetime of the predissociative ion state is presented for the case of general elliptically polarized light, to obtain the RFPAD rather than the molecular frame photoelectron angular distribution (MFPAD), which would be obtained with the assumption of instantaneous dissociation. We have considered photoionization of CO for the photon energies of 26.0 eV, 29.5 eV, and 32.5 eV. A comparison of experimental and theoretical RFPADs allows us to identify the ionic states detected in the experimental studies. In addition to previously identified states, we found evidence for the 2 (2)Δ state with an ionization potential of 25.3 eV and (2)Σ(+) states with ionization potentials near 32.5 eV. A comparison of the experimental and theoretical RFPADs permits us to estimate predissociative lifetimes of 0.25-1 ps for some of the ion states. Consideration of the MFPADs of a series of (2)Π ion states indicates the importance of inter-channel coupling at low photoelectron kinetic energy and the limitations of a single-channel analysis based on the corresponding Dyson orbitals.

Recoil frame photoelectron angular distributions of BF3: A sensitive probe of the shape resonance in the F 1s continuum

Recoil frame photoelectron angular distributions (RFPADs) of BF(3) molecules are presented over the energy region of the shape resonance in the F 1s continuum. Time-dependent density functional theory calculations are also given to understand the shape resonance dynamics. The RFPADs have been compared with the theoretical calculations. It is found that the RFPADs calculated by the localized core-hole model are in better agreement with the experimental, compared with those by the delocalized core hole. Dipole matrix elements and dipole prepared continuum wavefunctions show that the shape resonance in the F 1s ionization continuum of BF(3) is induced by p-partial waves as previously reported by Swanson et al. [J. Chem. Phys. 75, 619 (1981)]. However, due to the couplings with the other partial waves the feature characteristic of the p-partial waves has not been observed in the RFPADs.

Photofragment angular momentum distributions in the molecular frame. II. Single state dissociation, multiple state interference, and nonaxial recoil in photodissociation of polyatomic molecules

We present an a(q) (k)(s) polarization-parameter model to describe product angular momentum polarization from the one-photon photodissociation of polyatomic molecules in the molecular frame. We make the approximation that the final photofragment recoil direction is unique and described by the molecular frame polar coordinates (alpha,phi(i)), for which the axial recoil approximation is a special case (e.g., alpha=0). This approximation allows the separation of geometrical and dynamical factors, in particular, the expression of the experimental sensitivities to each of the a(q) (k)(s) in terms of the molecular frame polar angles (chi(i),phi(i)) of the transition dipole moment mu(i). This separation is applied to the linearly polarized photodissociation of polyatomic molecules (asymmetric, symmetric, and spherical top molecules are discussed) and to all dissociation mechanisms that satisfy our recoil approximation, including those with nonaxial recoil and multiple state interference, giving important insight into the geometrical properties of the photodissociation mechanism. For example, we demonstrate that the ratio of polarization parameters A(0) (k)(aniso)/A(0) (k)(iso)=beta (where beta is the spatial anisotropy parameter) is an indication that the dynamics can be explained by a single dissociative state. We also show that for asymmetric top photodissociation, the sensitivity to the a(1) (k)(s) parameters, which can arise either from single-surface or multiple-surface interference mechanisms, is nonzero only for components of the transition dipole moments within the v-d plane of the recoil frame.

Cross sections and asymmetry parameters for photoionization from ground and triplet excited states of nitromethane

Total cross sections and asymmetry parameters for single-photon ionization from the highest-occupied molecular orbitals of the X1 Á, 1 3Á́ and 2 Á́ states of CH3NO2 are computed within the single-channel, frozen-core Hartree-Fock approximation. Results are presented for photon energies between 0.5 and 20 eV and are compared to previous theoretical and experimental results wherever possible. One-electron resonant processes in the ionization channels are studied through the use of a local model potential. Computed molecular frame and recoil frame photoelectron angular distributions are also reported.

Molecular frame photoemission in multiphoton ionization of small molecules induced by linearly and circularly polarized light

We report results for one-color multiphoton dissociative ionization (MPDI) of NO2 induced by linearly (P) and circularly (k, ê) polarized femtosecond (fs) pulses centered at 400 nm. The experiments were performed by combining the use of 1 kHz femtosecond laser sources (SLIC, Saclay) and the electron-ion vector correlation method. The recoil frame photoelectron angular distributions (RFPADs), derived from the analysis of the (Ve, VNO+) velocity vector correlation, are analyzed using a new formalism. It generalizes the expression of the MFPADs for one-photon photoionization of linear molecules, and models the reaction as n−1 bound-to-bound transitions and ionization induced by the nth photon. The polar and azimuthal angle dependences of the RFPAD are characterized. We illustrate the discussion by the RFPADs measured for a MPDI process induced by five-photon absorption.

Recoil frame photoemission in inner-shell photoionization of small polyatomic molecules

Going from a diatomic to a polyatomic linear or non-linear molecule, the description of molecular frame photoemission in photoionization of molecules involves a function of increasing complexity. Using the electron-ion Vector Correlation method, which provides the emission velocity vectors of the emitted charged particles in a dissociative photoionization reaction, generally gives access to Recoil Frame Photoelectron Angular Distributions (RFPADs). We report results for site selected inner-shell photoionization of the N2O molecule induced by elliptically polarized light, where the primary ionization reaction leads to the production of several fragmentation channels. Ion fragment kinetic energy release distributions as well as RFPADs are reported for selected two ion-channels containing the complete parent molecule. Experimental results are compared with recent multi-channel Schwinger configuration interaction (MCSCI) ab initio calculations at the level of the RFPADs. The link with the original computed molecular frame photoelectron angular distributions (MFPADs) is discussed.

Molecular frame and recoil frame angular distributions in dissociative photoionization of small molecules

Photoelectron angular distributions in the dipole approximation can be written with respect to several different reference frames. A brief review of the molecular frame and recoil frame are given. Experimentally, one approach for obtaining such angular distributions is through angle-resolved coincidence measurements of dissociative ionization. If the system dissociates into two heavy fragments, then the recoil frame angular distribution can be measured. Computed molecular frame and recoil frame photoelectron angular distributions are compared to experimental data for the Cl 2p ionization of CH3Cl.

Circular dichroism in molecular frame photoemission

The paper reports on a comparative experimental and theoretical study of circular dichroism in electron angular distribution (CDAD) in the molecular frame (MF) of linear molecules photoionized by circularly or elliptically polarized light. The CDAD is derived from the analysis of the complete molecular frame angular distribution (MFPAD) I(χ,θe,φe ), where χ is the orientation of the molecule with respect to the light propagation axis and (θe,φe ) the electron emission direction in the MF, using the vector correlation method. The CDAD is quantified by the θe dependence of the left–right emission asymmetry maximum in the plane perpendicular to the light propagation axis k, for a space fixed molecule orthogonal to k. The experimental results for selected valence shell photoionization (PI) reactions in NO, O2, N2O compare very well with the multichannel Schwinger configuration interaction (MCSCI) ab initio calculations. Combined with a simple model of the ionization process, including the partial-wave composition of the initial state and phase shifts estimated from quantum defects for the various scattering partial-waves, these results provide the basis for a general discussion of the circular dichroism effect. This study enables one to disentangle the influence of the (spσ, pπ…) initial valence shell ionized orbital and that of the scattering dynamics on some fingerprint properties of the CDAD. On the other hand, the CDAD for sσ K-shell is purely assigned to a final state scattering effect. This analysis will be extended to PI of non-linear molecules where the circular dichroism characterizes recoil frame photoelectron angular distributions (RFPADs).

Molecular frame and recoil frame photoelectron angular distributions from dissociative photoionization of NO2

The authors report measured and computed molecular frame photoelectron angular distributions (MFPADs) and recoil frame photoelectron angular distributions (RFPADs) for the single photon ionization of the nonlinear molecule NO2 leading to the (1a2)-1 b 3A2 and (4a1)-1 3A1 states of NO2+. Experimentally, the RFPADs were obtained using the vector correlation approach applied to the dissociative photoionization (DPI) involving these molecular ionic states. The polar and azimuthal angle dependences of the photoelectron angular distributions are measured relative to the reference frame provided by the ion recoil axis and direction of polarization of the linearly polarized light. Experimental results are reported for the photon excitation energies hnu=14.4 and 22.0 eV. Theoretically the authors give expressions for both the MFPAD and the RFPAD. They show that the functional form in the recoil frame, where an average over the azimuthal dependence of the molecular fragments about the recoil direction is made, is identical to that they have earlier found for the DPI experiments performed on linear molecules. MFPADs were then computed using single-center expansion techniques within the fixed-nuclei frozen-core Hartree-Fock approximation. The computed cross sections for ionization to the (1a2)-1 b 3A2 state show a strong propensity for ionization with the polarization of the light perpendicular to the plane of the molecule, whereas the ionization to the (4a1)-1 3A1 state of the ion is of similar intensity for all orientations of the polarization of the light in the molecular frame. These qualitative features of the MFPAD are also evident in the RFPAD. The RFPAD for ionization leading to the (1a2)-1 b 3A2 state is strongly peaked in the perpendicular orientation, whereas the RFPAD for ionization leading to the (4a2)-1 3A1 state is much more nearly isotropic. Comparison between experimental and theoretical RFPADs indicates that the recoil angle for NO+ fragments is approximately 50 degrees relative to the symmetry axis of the initial C2v symmetry of the NO2 molecule in the ionization leading to the (1a2)-1 b 3A2 state and the recoil angle is approximately 120 degrees for the O+ fragment for ionization leading to the (4a1)-1 3A1 state.

Photoemission in the molecular frame induced by soft X-ray elliptically polarized light

A new step for complete experiments in photoionization (PI) of linear molecules is achieved when the electron-ion vector correlation method, based on imaging and time-of-flight resolved electron-ion coincidence techniques, is combined with the use of elliptically polarized light. The molecular frame photoelectron angular distributions (MFPADs), as well as the s 1 and s 2 Stokes parameters characterizing the polarization state of the light, can be derived from a single experiment performed with undefined elliptically polarized light. Using this method, we report and discuss MFPADs for site selective K-shell ionization of the NO and N 2O linear molecules in the region of the N 1s and O 1s shape resonances. A large molecular frame circular dichroism is observed, well predicted by the multi-channel Schwinger configuration interaction calculations reported for PI of NO. We also present recent experimental results for PI of non-linear molecules like CH 3Cl measured above the Cl 2p and C 1s ionization thresholds: the recoil frame photoelectron angular distributions (RFPADs) obtained by the vector correlation method may be influenced both by the molecular frame photoemission pattern and the fragmentation process.