Molecular Frame Photoelectron Angular Distributions Research Articles

Validity of the static-exchange approximation for inner-shell photoionization of polyatomic molecules

Author(s): Marante, CA; Greenman, L; Trevisan, CS; Rescigno, TN; McCurdy, CW; Lucchese, RR | Abstract: The simple single-channel static-exchange approximation completely ignores correlation between the continuum and molecular ion electrons. In molecular systems with symmetry equivalent atoms, the single-channel approximation can seriously fail in core ionization when using delocalized orbitals to represent the core hole states. We present cross sections and molecular frame photoelectron angular distributions with both localized and delocalized core orbitals in CF4 F (1s) ionization. We show that only a full coupled-channel calculation can recover an accurate description of the physics of inner-shell photoionization when using delocalized orbitals, whereas nearly the same result can be obtained from independent single-channel static-exchange calculations when localized core orbitals are used. A grid-based variational method described here makes such single-channel calculations possible on larger systems without local-exchange approximations. Illustrative calculations on the core ionization of SF6 are presented to illustrate the power of the grid-based method.

Experimental Separation of Subcycle Ionization Bursts in Strong-Field Double Ionization of H_{2}.

We report on the unambiguous observation of the subcycle ionization bursts in sequential strong-field double ionization of H_{2} and their disentanglement in molecular frame photoelectron angular distributions. This observation was made possible by the use of few-cycle laser pulses with a known carrier-envelope phase, in combination with multiparticle coincidence momentum imaging. The approach demonstrated here will allow sampling of the intramolecular electron dynamics and the investigation of charge-state-specific Coulomb distortions on emitted electrons in polyatomic molecules.

Asymmetry of molecular frame photoelectron angular distributions in by intense two-color attosecond pulses: coherent excitation and charge migration effects

Molecular frame photoelectron angular distributions (MFPADs) are theoretically studied by intense two-color attosecond linearly polarized laser pulses. Simulations are performed on aligned from numerical solutions of corresponding time-dependent Schrödinger equations. Asymmetric MFPADs are produced by a time-delayed soft x-ray attosecond pulse in the presence of an extreme ultraviolet (XUV) pump pulse. We present the dependence of the asymmetry ratio Γ of the MFPADs on the laser parameters of the pump-probe pulses. The asymmetry ratio Γ varies with the time delay, illustrating the coherent superposition of electronic states. Altering the phase, intensity and duration of the pump pulse gives rise to a modulation of the asymmetry ratio Γ as well. Moreover, the asymmetry of the MFPADs disappears in the case of long duration probe pulses, illustrating the coherent charge migration dynamics on the attosecond time scale.

Revealing the multiorbital and excitation effects in dissociative double ionization of CO molecules with angular streaking measurement

SynopsisWe investigate the sequential double ionization dynamics for the dissociative channel C+ + O+ of CO molecules in strong circularly polarized laser fields. By using four-particle coincident measurement, the obtained ionic angular emissions and molecular frame photoelectron angular distributions of each ionization steps for various pathways reveals the significant effects of multiorbital ionization and laser-driven excitation.

Recoil-Induced Asymmetry of Nondipole Molecular Frame Photoelectron Angular Distributions in the Hard X-ray Regime.

We investigate angular emission distributions of the 1s photoelectrons of N_{2} ionized by linearly polarized synchrotron radiation at hν=40 keV. As expected, nondipole contributions cause a very strong forward-backward asymmetry in the measured emission distributions. In addition, we observe an unexpected asymmetry with respect to the polarization direction, which depends on the direction of the molecular fragmentation. In particular, photoelectrons are predominantly emitted in the direction of the forward nitrogen atom. This observation cannot be explained via asymmetries introduced by the initial bound and final continuum electronic states of the oriented molecule. The present simulations assign this asymmetry to a novel nontrivial effect of the recoil imposed to the nuclei by the fast photoelectrons and high-energy photons, which results in a propensity for the ions to break up along the axis of the recoil momentum. The results are of particular importance for the interpretation of future experiments at x-ray free electron lasers operating in the few tens of keV regime, where such nondipole and recoil effects will be essential.

Symmetry breaking in the body-fixed electron emission pattern due to electron-retroaction in the photodissociation of H2+ and D2+ close to threshold

Author(s): Heck, S; Gatton, A; Larsen, KA; Iskandar, W; Champenois, EG; Strom, R; Landers, A; Reedy, D; Dailey, C; Williams, JB; Severt, T; Jochim, B; Ben-Itzhak, I; Moshammer, R; Dorner, R; Slaughter, DS; Weber, T | Abstract: We present an experimental investigation of symmetry breaking of H2 and D2 molecules after single photoionization due to the Coulomb field of the emitted slow electron interacting with the parent cation during dissociation. The experiments were carried out by measuring the three-dimensional momentum vectors of the photoelectron and recoiling ion in coincidence using a reaction microscope. For photon energies close to threshold, the low-energy photoelectron influences the dissociation process, which results in an asymmetric molecular frame photoelectron angular distribution. This can be explained by the retroaction of the Coulomb field of the photoelectron on its parent ion and has been recently experimentally demonstrated by M. Waitz et al. [Phys. Rev. Lett. 116, 043001 (2016)PRLTAO0031-900710.1103/PhysRevLett.116.043001], confirming theoretical predictions by V. V. Serov and A. S. Kheifets [Phys. Rev. A 89, 031402(R) (2014)PLRAAN1050-294710.1103/PhysRevA.89.031402]. High-momentum resolution and a new series of photon energies just above the dissociation threshold enable the observation of a strong influence of the electron energy and nuclear kinetic energy on the electron localization process for energies below ∼100 meV, which so far has neither been observed nor discussed by theory. Exploring the limitations of the retroaction mechanism at our lowest photon energy, we are able to single out a sensitive testbed and present data of non-Born-Oppenheimer dynamics of the simplest molecular system for future benchmark computational treatments.

Dissociative photoionization of NO across a shape resonance in the XUV range using circularly polarized synchrotron radiation.

We report benchmark results for dissociative photoionization (DPI) spectroscopy and dynamics of the NO molecule in the region of the σ* shape resonance in the ionization leading to the NO+(c3Π) ionic state. The experimental study combines well characterized extreme ultraviolet (XUV) circularly polarized synchrotron radiation, delivered at the DESIRS beamline (SOLEIL), with ion-electron coincidence 3D momentum spectroscopy. The measured (N+, e) kinetic energy correlation diagrams reported at four discrete photon energies in the extended 23-33 eV energy range allow for resolving the different active DPI reactions and underline the importance of spectrally resolved studies using synchrotron radiation in the context of time-resolved studies where photoionization is induced by broadband XUV attosecond pulses. In the dominant DPI reaction which leads to the NO+(c3Π) ionic state, photoionization dynamics across the σ* shape resonance are probed by molecular frame photoelectron angular distributions where the parallel and perpendicular transitions are highlighted, as well as the circular dichroism CDAD(θe) in the molecular frame. The latter also constitute benchmark references for molecular polarimetry. The measured dynamical parameters are well described by multichannel Schwinger configuration interaction calculations. Similar results are obtained for the DPI spectroscopy of highly excited NO+ electronic states populated in the explored XUV photon energy range.

The effect of elliptical polarization in MSXα calculations of the molecular-frame photoelectron angular distributions of CO C(1s) ionization

We present a theoretical investigation of the molecular-frame photoelectron angular distribution (MF-PAD) resulting from the inner-shell photoionization of fixed-in-space CO molecules with elliptically polarized light. The MSXα output program, originally written for linearly polarized light, was changed in order to calculate the MF-PAD for circularly and elliptically polarized light. The calculations were made for CO C(1s) inner-shell photoionization for 3, 10, and 30 eV kinetic energy electrons. The MF-PADs were calculated from 0° angle of ellipticity (equivalent to linear polarized light parallel to the molecular axis) in steps of 5° (corresponding to different types of elliptical light) up to 90° (equivalent to linear polarized light perpendicular to the molecular axis).

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

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

Strong-field ionization of diatomic molecules in orthogonally polarized two-color fields

We study the control of ionization dynamics of aligned ${\mathrm{N}}_{2}$ and ${\mathrm{O}}_{2}$ molecules in orthogonally polarized two-color (OTC) fields and calculate the photoelectron momentum distributions of molecules by solving the time-dependent Schr\odinger equation and with a semiclassical model. In contrast with that of atoms in the OTC field, we show that the photoelectron momentum distribution is essentially dependent on the molecular outmost orbital, the alignment angle, and the phase of the OTC field. We illustrate the controlling of the molecular frame photoelectron angular distributions and the temporal and spatial double-slit interference effect for strong-field ionization of ${\mathrm{N}}_{2}$ molecules. For ${\mathrm{O}}_{2}$ molecules, it is shown that the ionization wave packets are splitting. The temporal and spatial double-slit interference effect is always present for ${\mathrm{O}}_{2}$, which is not able to be turned off using the OTC field. This work would have implications for probing molecular structures with a two-color synthesized laser field.

Communication: Strong laser alignment of solvent-solute aggregates in the gas-phase

Strong quasi-adiabatic laser alignment of the indole-water-dimer clusters, an amino-acid chromophore bound to a single water molecule through a hydrogen bond, was experimentally realized. The alignment was visualized through ion and electron imaging following strong-field ionization. Molecular-frame photoelectron angular distributions showed a clear suppression of the electron yield in the plane of the ionizing laser's polarization, which was analyzed as strong alignment of the molecular cluster with ⟨cos2 θ2D⟩ ≥ 0.9.

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'.

Imaging of strong field dissociative single and double ionization channels of N2O

In this paper, we study single and double ionizations of N2O in a short elliptically polarized 800 nm laser pulse using the COLTRIMS technique. The molecular-frame photoelectron angular distribution and the ion sum-momentum distribution of single and double ionizations of N2O molecules are reported for the single ionization dissociative channel NO[Formula: see text] + N and the double ionization dissociative channel NO[Formula: see text] + N[Formula: see text]. The ionizations of multiple orbitals for the two studied dissociative channels were identified via studying the orientation dependent ionization rates for their KERs. The results show that the shape of the ionizing orbitals governs the single and double ionization processes of N2O.

Orientation dependence in multichannel dissociative ionization of OCS molecules

With 800-nm, 25-fs elliptically polarized ionization pulses, we observe molecular frame photoelectron angular distributions (MF-PADs) correlated with different dissociative ionization channels: ${\mathrm{OCS}}^{+}\ensuremath{\rightarrow}{\mathrm{S}}^{+}$+CO, ${\mathrm{CO}}^{+}$+S, ${\mathrm{CS}}^{+}$+O, and ${\mathrm{O}}^{+}$+CS. We find that the asymmetry in the MF-PAD depends on the specific dissociation channel and the laser intensities. For the dissociation channel leading to the production of ${\mathrm{O}}^{+}$, the OCS molecules are more likely to be ionized when the electric field points toward the O atom, while for other dissociation channels, they are more likely to be ionized when the electric field points toward the S atom.

Calculation of photoionization differential cross sections using complex Gauss-type orbitals.

Accurate theoretical calculation of photoelectron angular distributions for general molecules is becoming an important tool to image various chemical reactions in real time. We show in this article that not only photoionization total cross sections but also photoelectron angular distributions can be accurately calculated using complex Gauss-type orbital (cGTO) basis functions. Our method can be easily combined with existing quantum chemistry techniques including electron correlation effects, and applied to various molecules. The so-called two-potential formula is applied to represent the transition dipole moment from an initial bound state to a final continuum state in the molecular coordinate frame. The two required continuum functions, the zeroth-order final continuum state and the first-order wave function induced by the photon field, have been variationally obtained using the complex basis function method with a mixture of appropriate cGTOs and conventional real Gauss-type orbitals (GTOs) to represent the continuum orbitals as well as the remaining bound orbitals. The complex orbital exponents of the cGTOs are optimized by fitting to the outgoing Coulomb functions. The efficiency of the current method is demonstrated through the calculations of the asymmetry parameters and molecular-frame photoelectron angular distributions of H2+ and H2. In the calculations of H2, the static exchange and random phase approximations are employed, and the dependence of the results on the basis functions is discussed. © 2017 Wiley Periodicals, Inc.

Ultrafast molecular photoionization by two-color orthogonally polarized ultraviolet laser pulses: Effects of relative pulse phases

We present molecular photoionization by two-color 2ω1=ω2 orthogonally polarized ultraviolet laser pulses. Simulations are performed on aligned H2+ by numerically solving time-dependent Schrödinger equations. Two ionization processes with one ω2 photon interfering with two ω1 photon absorption are studied at different molecular alignments. Molecular frame photoelectron momentum and angular distributions exhibit asymmetries which are functions of the relative pulse phase. For resonant excitation processes by the ω1 pulse, symmetric distributions are obtained. An attosecond ionization model is adopted to describe the ultrafast ionization dynamics. The dependence of the ionization asymmetry on the molecular alignment allows to further monitor interference effects on orbital symmetry.

Monitoring non-adiabatic dynamics in CS2 with time- and energy-resolved photoelectron spectra of wavepackets

We report results from a novel fully ab initio method for simulating the time-resolved photoelectron angular distributions around conical intersections in CS2. The technique employs wavepacket densities obtained with the multiple spawning method in conjunction with geometry- and energy-dependent photoionization matrix elements. The robust agreement of the calculated molecular-frame photoelectron angular distributions with measured values for CS2 demonstrates that this approach can successfully illuminate, and disentangle, the underlying coupled nuclear and electronic dynamics around conical intersections in polyatomic molecules.

Monitoring coherent electron wave packet excitation dynamics by two-color attosecond laser pulses.

We propose a method to monitor coherent electron wave packet (CEWP) excitation dynamics with two-color attosecond laser pulses. Simulations are performed on aligned H2+ by numerically solving the three-dimensional time-dependent Schrödinger equation with combinations of a resonant linearly polarized λl= 100/70 nm pump pulse and a circularly polarized λc=5 nm attosecond probe pulse. It is found that time dependent diffraction patterns in molecular frame photoelectron angular distributions (MFPADs) produced by the circular probe pulse exhibit sensitivity to the molecular alignments and time-dependent geometry of the CEWPs during and after the coherent excitation between the ground and excited states induced by the linear pump pulse. The time dependent MFPADs are described by an ultrafast diffraction model for the ionization of the bound CEWPs.

Effects of molecular rotation after ionization and prior to fragmentation on observed recoil-frame photoelectron angular distributions in the dissociative photoionization of nonlinear molecules

Experimental angle-resolved photoelectron-photoion coincidence experiments measure photoelectron angular distributions (PADs) in dissociative photoionization (DPI) in the reference frame provided by the momenta of the emitted heavy fragments. By extension of the nomenclature used with DPI of diatomic molecules, we refer to such a PAD as a recoil-frame PAD (RFPAD). When the dissociation is fast compared to molecular rotational and bending motions, the emission directions of the heavy fragments can be used to determine the orientation of the bonds that are broken in the DPI at the time of the ionization, which is known as the axial-recoil approximation (ARA). When the ARA is valid, the RFPADs correspond to molecular-frame photoelectron angular distributions (MFPADs) when the momenta of a sufficient number of the heavy fragments are determined. When only two fragments are formed, the experiment cannot measure the orientation of the fragments about the recoil axes so that the resulting measured PAD is an azimuthally averaged RFPAD (AA-RFPAD). In this study we consider how the breakdown of the ARA due to rotation will modify the observed RFPADs for DPI processes in nonlinear molecules for ionization by light of arbitrary polarization. This model is applied to the core C $1s$ DPI of ${\mathrm{CH}}_{4}$, with the results compared to experimental measurements and previous theoretical calculations done within the ARA. The published results indicate that there is a breakdown in the ARA for two-fragment events where the heavy-fragment kinetic energy release was less than 9 eV. Including the breakdown of the ARA due to rotation in our calculations gives very good agreement with the experimental AA-RFPAD, leading to an estimate of upper bounds on the predissociative lifetimes as a function of the kinetic energy release of the intermediate ion states formed in the DPI process.

Interference asymmetry of molecular frame photoelectron angular distributions in bichromatic UV ionization processes

We investigate molecular photoionization by ultrafast bichromatic linearly polarized UV laser pulses at frequencies perpendicular to the internuclear axis R involving π orbital excitation. Results from numerical solutions of time dependent Schrödinger equations for aligned show that molecular frame photoelectron angular distributions (MFPADs) exhibit signatures of asymmetry perpendicular to the molecular symmetry axis, arising from interference of coherent electron wave packets created by respectively one and two-photon absorption. A resonant excitation process between the ground state and the excited state is triggered by the pulse. The asymmetry of MFPADs varies periodically with pulse intensity I0 and duration T, which we attribute to coherent resonant Rabi oscillations in electronic state population. A perturbative model is adopted to qualitatively describe and analyze these effects in both resonant and nonresonant photoionization processes.