Molecular Photoionization Research Articles

Direct Measurement of the Angular Dependence of the Single-Photon Ionization of Aligned N2 and CO2

By combining a state-of-the-art high-harmonic ultrafast soft X-ray source with field-free dynamic alignment, we map the angular dependence of molecular photoionization yields for the first time for a nondissociative molecule. The observed modulation in ion yield as a function of molecular alignment is attributed to the molecular frame transition dipole moment of single-photon ionization to the X, A and B states of N2(+) and CO2(+). Our data show that the transition dipoles for single-photon ionization of N2 and CO2 at 43 eV have larger perpendicular components than parallel ones. A direct comparison with published theoretical partial wave ionization cross-sections confirms these experimental observations, which are the first results to allow such comparison with theory for bound cation states. The results provide the first step toward a novel method for measuring molecular frame transition dipole matrix elements.

Near-threshold absolute photoionization cross-sections of some reaction intermediates in combustion

The use of photoionization mass spectrometry for the development of quantitative kinetic models for the complex combustion chemistry of both conventional hydrocarbon fuels and oxygenated biofuels requires near-threshold measurements of absolute photoionization cross-sections for numerous reaction intermediates. Near-threshold absolute cross-sections for molecular and dissociative photoionization for 20 stable reaction intermediates (methane, ethane, propane, n-butane, cyclopropane, methylcyclopentane, 1-butene, cis-2-butene, isobutene, 1-pentene, cyclohexene, 3,3-dimethyl-1-butene, 1,3-hexadiene, 1,3-cyclohexadiene, methyl acetate, ethyl acetate, tetrahydrofuran, propanal, 1-butyne, 2-butyne) are presented. Previously measured total photoionization cross-sections for 9 of these molecules are in good agreement with the present results. The measurements are performed with photoionization mass spectrometry (PIMS) using a monochromated VUV synchrotron light source with an energy resolution of 40 meV (fwhm) comparable to that used for flame-sampling molecular beam PIMS studies of flame chemistry and reaction kinetics.

Resonance behavior of atomic and molecular photoionization amplitudes

The behavior of the partial photoionization amplitudes with a given orbital angular momentum $l$ in the complex plane in resonances is studied. In the autoionization resonances the trajectory of the amplitude in the complex plane corresponds to a circle. With increasing photoelectron energy the amplitude moves about a circle in the counterclockwise direction. The new expressions for the partial amplitudes in the resonance are proposed which are similar to the Fano form but contain the ``partial'' profile parameters which are connected with the Fano parameter $q$ by a simple relation. In the giant dipole resonances the amplitudes in the complex plane also move about a circle in the counterclockwise direction provided the Coulomb phase is excluded from the amplitude. In the correlational resonances created by channel interactions with the giant dipole resonance the trajectories of the amplitudes acquire a loop about which the amplitudes move in the counterclockwise direction. Very similar behavior of partial photoionization amplitudes in the complex plane is demonstrated also for the dipole transitions from the $K$ shells of the ${\mathrm{N}}_{2}$ molecule in the ${\ensuremath{\sigma}}^{*}$ shape resonance.

Role of spins in molecular photoionization: Spectroscopy and dynamics of autoionizing Rydberg states of ortho-H2

A combined experimental and theoretical investigation of the role of electronic and nuclear spins in molecular photoionization is reported. Photoionization spectra of autoionizing $p$ Rydberg states belonging to series converging on the $X$ $^{2}\ensuremath{\Sigma}_{g}^{+}({v}^{+}=0,{N}^{+}=3)$ level of ortho-${\mathrm{H}}_{2}^{+}$ have been measured in the range of principal quantum number $n=50--200$ from the long-lived $H$ $^{1}\ensuremath{\Sigma}_{g}^{+}(v=0,J=3)$ level. The use of a pulsed near-Fourier-transform-limited laser with a bandwidth of less than $10\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$ resulted in a Doppler-limited linewidth of $25\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$ which sufficed to partially resolve the hyperfine structure of the Rydberg states. Below $n\ensuremath{\approx}70$, the exchange interaction between the ion core and Rydberg electrons is larger than the hyperfine interactions in the ion core and the observed levels can be understood in terms of Hund's angular momentum coupling case (d). With increasing value of $n$, the hyperfine interactions in the core lead to a mixing of singlet and triplet characters of the Rydberg states and eventually to a complete decoupling of the Rydberg electron spin from the core spins that results in distinct series converging on the hyperfine components of the ion. Several intermediate coupling cases have been identified and two of them completely characterized. Most interestingly, the total spin angular momentum has been found to be a good quantum number up to $n\ensuremath{\approx}150$ at least, i.e., far beyond the region where the ionic hyperfine structure starts dominating the coupling hierarchy. Multichannel quantum defect theory including nuclear and electron spins has been extended to treat autoionization and predict spectral intensities. The comparison with the experimental spectra has revealed a satisfactory agreement between calculated and measured line positions, linewidths, and intensities and has enabled us to extract, by extrapolation, a more accurate term value for the $H$ $^{1}\ensuremath{\Sigma}_{g}^{+}(v=0,J=3)$ level. The calculations have been used to characterize the role of hyperfine, spin-rotational, and pf interactions in rotational autoionization and have revealed a very strong dependence of the autoionization lifetimes of high Rydberg states on the value of the total angular momentum quantum number $F$.

New developments in the theory of molecular K‐shell photoionization

AbstractA new version of the relaxed core Hartree–Fock approximation with a fractional charge of the molecular ion state is applied for calculations of molecular photoionization processes. The set of continuous spectrum wave functions obtained by that method is used when taking many‐electron correlations into account in the framework of the random‐phase approximation. The vibrational motion is also included into consideration. In that way, the most reliable results for the vibrationally resolved partial photoionization cross sections and the angular asymmetry parameter β for the K‐shells of CO and N2 molecules have been obtained. A good agreement with the state‐of‐the‐art experimental data is demonstrated. From our calculations it follows that the nondipole effects for the K‐shells of N2 and CO molecules are small near the ionization thresholds, in agreement with the latest experimental data. Two predictions have been made based on these calculations. One of them is the appearance of the correlational maximum in the photoionization cross section of the 1σu shell of N2 molecule near the σ* shape resonance, which is now fully confirmed by the experiment. The second prediction concerns the behavior of the nondipole parameters for the 1σg and 1σu shells of N2. According to our calculation, they oscillate in antiphase with rather large amplitudes around the unresolved values, so that after summation of the contributions of the two K‐shells, the oscillations practically disappear. This prediction does not yet have an experimental confirmation. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007

Recent advances in molecular photoionization by density functional theory based approaches

The most recent advances in the theoretical description of molecular photoionization by means of the Density Functional Theory with B-splines basis functions is reviewed. From the methodological point of view, the formalism of the Time Dependent Density Functional Theory applied to molecular continuum is considered, with a new implementation based on a non-iterative algorithm. Also, applications of the Kohn–Sham method for the calculation of dichroism in photoionization of chiral molecules and of dynamical parameters beyond the dipole approximation are considered. The methods have proved successful to accurately reproduce experimental data and to suggest reliable assignments to observed spectral features.

Evolution of photoelectron–vibrational coupling with molecular complexity

We review how electronic and vibrational degrees of freedom become coupled in molecular photoionization, and describe effects that emerge as the molecular complexity increases. Molecular photoionization is frequently influenced by the temporary trapping of the continuum electron in the field of the target molecules, which is referred to as a shape resonance, as it depends on the shape of the potential experienced by the exiting photoelectron. Such resonances couple electronic and vibrational motion, and the nature of the coupling can vary widely for polyatomic molecules. We show how vibrationally resolved photoelectron spectra acquired as a function of energy can be used to elucidate such coupling. The experiments are analysed using physically realistic and computationally tractable Schwinger variational theory, and the systems studied to date can be well understood using an independent-particle, adiabatic nuclei framework. As a result, simple and intuitive pictures emerge, even when dealing with scattering phenomena involving complex molecular targets and potentials.

Espectroscopia de fotoelétrons de limiares de átomos e moléculas

A threshold photoelectron spectrometer applied to the study of atomic and molecular threshold photoionization processes is described. The spectrometer has been used in conjunction with a toroidal grating monochromator at the National Synchrotron Radiation Laboratory (LNLS), Brazil. It can be tuned to accept threshold electrons (< 20 meV) and work with a power resolution of 716 (~18 meV at 12 eV) with a high signal/noise ratio. The performance of this apparatus and some characteristics of the TGM (Toroidal Grating Monochromator) beam line of LNLS are described and discussed by means of argon, O2 and N2 threshold photoelectron spectra.

A theoretical study on the photoionization of the valence orbitals of phosphine

We report a theoretical study on the photoionization of phosphine in the static-exchange level and frozen core approximation, using the method of continued fractions. The main subject of the present study is to investigate in which extent the Hartree-Fock description of the target applied to molecular photoionization is valid. Also, the role played by multichannel coupling is analysed. Our study shows that single-channel Hartree-Fock calculations can provide reliable results except for photon energies near the photoionization threshold.

Double photoionisation spectra of methane, ammonia and water

Complete double photoionisation spectra of methane, ammonia and water measured by the TOF-PEPECO method are reported. The electron pair energy distributions and low quantum yields suggest that for methane and ammonia the double photoionisation is mainly direct. In addition to the direct process, water undergoes two indirect dissociative double ionisation processes, one involving autoionisation of an oxygen atom in course of, or after, dissociation. The existence of these processes explains discrepancies between previous determinations of the ionisation threshold. Results on these and related species lead to a general conclusion that molecular double photoionisation in small molecules is mainly direct, whereas the same process in complex atoms is mainly indirect.

Photoionization cross sections for reaction intermediates in hydrocarbon combustion

Previously unmeasured absolute photoionization cross sections are presented for eight common reaction intermediates found in the combustion of many simple hydrocarbons. Total photoionization cross sections recorded for 11 additional hydrocarbons are in good agreement with previous studies. The measurements are performed with photoionization mass spectrometry (PIMS), using VUV synchrotron radiation. Absolute cross sections for molecular and dissociative photoionization are determined by comparison of the photoionization efficiencies for each intermediate with that of propene, used as a calibration standard, for photon energies from 9.7 to 11.75 eV, recorded with a photon energy resolution of 50 meV(fwhm).

Violation of the Franck-Condon Principle due to Recoil Effects in High Energy Molecular Core-Level Photoionization

Carbon 1s photoelectron spectra of methane are measured over a photon energy range between 480 eV and 1200 eV. Additional components appear between the individual symmetric stretching vibrational components and are attributed to the excitations of asymmetric stretching and bending vibrations due to recoil of the high-energy photoelectron emission. This recoil effect is the evidence for the violation of the Franck-Condon principle which states that neither the positions nor the momenta of the nuclei change during the ionization event.

Time-dependent density-functional theory for molecular photoionization with noniterative algorithm and multicenter B-spline basis set: CS2 and C6H6 case studies

In this work a new direct (noniterative) algorithm to solve the time-dependent density-functional theory equations for molecular photoionization has been proposed and implemented, using a multicentric basis set expansion of B-spline functions and complete exploiting of the molecular point-group symmetry. The method has been applied to study the photoionization dynamics of CS2 and C6H6: the results confirmed the expectation of large screening effects in CS2. For C6H6 the screening effects have been found to play a minor role than in CS2, however, also in this case the quality of the final results is definitely improved. The method has proven suitable to study with confidence molecules of medium size, and there is still room for further improvement working on more elaborate treatment of the exchange-correlation functional.

Single-photon double ionization of the hydrogen molecule

We investigate the single-photon double ionization of molecular hydrogen theoretically over a wide range of photon energies. Our numerical approach is based on the half-collision picture of single-photon multiple ionization and employs a mixed quantum-classical method that splits the double ionization process into a shake-off and a knockout part. We demonstrate that this approach, which has been applied to the double photoionization of helium before, can be successfully extended to the case of molecular target systems with two separate nuclei. The treatment given here allows for both a computationally simple way of calculating molecular double photoionization in reasonable agreement with experiment and recent ab initio calculations, and a physical understanding of the results in terms of a simple quasiclassical picture.

Keldysh-type photoionization rate of large polyatomic molecules in the tunneling region

In this paper, we demonstrate a detailed derivation of general analytical expressions of photoionization rates of spatially aligned large polyatomic molecules in the tunneling photoionization region. First, the molecular Coulomb-corrected Volkov function is derived for determining the continuum state, and the position dependence of the atoms forming the molecule is explicitly included in it. Second, using the molecular Coulomb-corrected Volkov function, a Keldysh-type photoionization rate formula is derived. For this, a linear combination of atomic orbitals will be used for the initial state. The obtained photoionization rate formula shows that the molecular photoionization rate is the sum of the photoionization rates of the individual occupied orbitals of the atoms forming the molecule, which are modified by the position dependence of the atoms, and the quantum interference terms arising from the corresponding occupied orbitals of the constituent identical and different atoms. The formula explicitly indicates that the photoionization rate sensitively depends on the angle between the molecular axis and the polarization vector of the linearly polarized laser field, the internuclear distance, and the atomic ionization potential $I$ by the expression $\mathrm{exp}(2\sqrt{2mI}\stackrel{P\vec}{F}∙{\stackrel{P\vec}{R}}_{j}∕\ensuremath{\hbar}F)$. This is a clear indication of the appropriateness of the formulas derived in this work since it is consistent with the experimental and numerical results obtained so far. Using the formula, we show numerical results of photoionization rates of all-trans polyacetylene radicals. In addition, from the formula is directly drawn the conclusion that the photoionization rate corresponding to the quantum interference terms is smaller when the distance between the atoms is longer in the case of laser polarization parallel to the molecular backbone.

A refocusing modified velocity map imaging electron/ion spectrometer adapted to synchrotron radiation studies

We present a modified velocity map imaging (VMI) spectrometer to be used in angle-resolved molecular photoionization studies in the gas phase with synchrotron radiation (SR) in the VUV/soft x-ray range. The main modifications as compared to the original design of Eppink and Parker [A. T. J. B. Eppink and D. H. Parker, Rev. Sci. Instrum. 68, 3477 (1997)] are an open repeller which allows the VMI spectrometer to be coupled to an independent dispersive electrostatic analyzer for combined operation in coincidence mode experiments, and the introduction of a coupled double Einzel lens in the flight tube in order to collect the full 4π solid angle for higher kinetic energy particles. The length and position of the lenses have been optimized by a genetic algorithm to obtain the maximum kinetic energy possible without compromising the energy resolution. Ray-tracing simulations and SR experiments show that the lenses can increase the kinetic energy bandwidth by a factor of up to 2.5. Furthermore, a remarkable improvement in the radial focusing of the particles’ momenta can be achieved when the lens array is operated in optimum fashion. The accuracy in the determination of the angular parameters, already satisfactory in the original VMI design, is not compromised by the lens operation. Experimentally, we succeeded in collecting 4π electrons with 14eV kinetic energy and 6% relative energy resolution with a detector of 36mm effective diameter, despite the larger ionization volume given by the SR as compared to laser multiphoton experiments. We predict that, by changing to a detector diameter of 70mm and reducing the focal length by a third, particles with energies up to 200eV could be collected by applying 10kV to the repeller electrode.

‘Molecular photography’: velocity–map imaging of chemical events

Every chemical reaction bears its own unique fingerprint, embodied in the kinetic energy, angular distribution and rotational and vibrational motion of the newly formed reaction products. These quantities reflect the forces acting during the chemical reaction, and their measurement often provides unparalleled insight into the basic physics governing chemical reactivity. One experimental technique that has truly captured the imagination of the reaction-dynamics community is velocity-map ion imaging, which provides a visual 'snapshot' of the complete product scattering distribution in a single measurement. Originally developed to study gas-phase photodissociation, the technique is now routinely being applied to bimolecular processes, particularly inelastic and reactive scattering. This article will review recent developments in the field, using examples from studies of a range of chemical processes.

Electron propagator theory calculations of molecular photoionization cross sections: the first-row hydrides.

Together with ionization potentials, cross sections provide valuable information for the interpretation of photoelectron spectra. We have developed a program to perform ab initio calculations of photoionization cross sections within the electric dipole approximation using electron propagator theory. Applications to the first-row hydrides CH(4), NH(3), H(2)O, and HF, using several approximations for the propagator self-energy and the plane-wave and orthogonalized-plane-wave approximations to represent the photoelectron, as well as comparison to experimental data, are presented. This program is implemented within the quantum chemistry package GAUSSIAN.

Many-body effects and new phenomena in atomic and molecular photoionization

The interplay between theory and experiment has stimulated the uncovering and understanding of a broad range of new phenomena in atomic and molecular photoabsorption processes, brought about by the advent of third-generation synchrotron light sources, on the experimental side, and vastly enhanced computing power on the theoretical. Among the examples of the new physics explored are nondipole effects in atoms and molecules at very low photon energies (tens or hundreds of eV) and the influence of many-body correlations on them, core level photodetachment of negative ions and the structure engendered by the photoelectron emerging through the charge cloud of the outer, loosely bound electrons, and the photoionization of confined atoms and ions trapped, e.g., in a C 60 cage, and the modifications to the photoionization cross section resulting from the confinement.

Many-body effects in molecular photoionization in intense laser fields; time-dependent Hartree-Fock simulations.

The time evolution of the reduced single electron density matrix for eight electrons in a one-dimensional finite box potential driven by an intense laser field is calculated by numerically integrating the time-dependent Hartree-Fock equations. We study the effects of the Coulomb interaction, field intensity, and frequency on the time profile of the ionization process. Our computed saturation ionization intensity (Isat) is in good agreement with experimental results for decatetraene [Ivanov et al. J. Chem. Phys. 117, 1575 (2002)].