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Shape resonances in physics and chemistry arise from the spatial confinement of a particle by a potential barrier. In molecular photoionization, these barriers prevent the electron from escaping instantaneously, so that nuclei may move and modify the potential, thereby affecting the ionization process. By using an attosecond two-color interferometric approach in combination with high spectral resolution, we have captured the changes induced by the nuclear motion on the centrifugal barrier that sustains the well-known shape resonance in valence-ionized N$_2$. We show that despite the nuclear motion altering the bond length by only $2\%$, which leads to tiny changes in the potential barrier, the corresponding change in the ionization time can be as large as $200$ attoseconds. This result poses limits to the concept of instantaneous electronic transitions in molecules, which is at the basis of the Franck-Condon principle of molecular spectroscopy., 24 pages, 5 figures

Carbon $1s$ photoelectron spectra of CO molecules in gas phase were recorded in the tender x-ray energy range, from 2.3 to 6.9 keV. The intensity ratios of individual peaks from $\ensuremath{\nu}=0$ to 3 within the vibrational progression of the C $1s$ photoelectron spectrum were determined at the various photon energies and are shown to be strongly affected by the photoelectron recoil effect. The experimental vibrational intensity ratios are compared with theoretical predictions at different levels of accuracy. Developments of the recoil model, using generalized Franck-Condon factors, rovibrational coupling, Morse potential energy curves, and accurate angular averaging are presented and applied to the analysis of the experimental results.

Recently we reported a series of numerical simulations proving that it is possible in principle to create an electronic wave packet and subsequent electronic motion in a neutral molecule photoexcited by a UV pump pulse within a few femtoseconds. We considered the ozone molecule: for this system the electronic wave packet leads to a dissociation process. In the present work, we investigate more specifically the time-resolved photoelectron angular distribution of the ozone molecule that provides a much more detailed description of the evolution of the electronic wave packet. We thus show that this experimental technique should be able to give access to observing in real time the creation of an electronic wave packet in a neutral molecule and its impact on a chemical process., Accepted in Scientific Report

After sudden ionization of a large molecule, the positive charge can migrate throughout the system on a sub-femtosecond time scale, purely guided by electronic coherences. The possibility to actively explore the role of the electron dynamics in the photo-chemistry of bio-relevant molecules is of fundamental interest for understanding, and perhaps ultimately controlling, the processes leading to damage, mutation and, more generally, to the alteration of the biological functions of the macromolecule. Attosecond laser sources can provide the extreme time resolution required to follow this ultrafast charge flow. In this review we will present recent advances in attosecond molecular science: after a brief description of the results obtained for small molecules, recent experimental and theoretical findings on charge migration in bio-relevant molecules will be discussed, We acknowledge the support from the European Research Council under the ERC grants no. 637756 STARLIGHT, no. 227355 ELYCHE and no. 290853 XCHEM, LASERLABEUROPE (grant agreement no. 284464, European Commissions Seventh Framework Programme), European COST Action CM1204 XLIC, the Ministerio de Ciencia e Innovación project FIS2013-42002-R, European grants MC-ITN CORINF and MC-RG ATTOTREND 268284, UKs Science and Technology Facilities Council Laser Loan Scheme, the Engineering and Physical Sciences Research Council (grant EP/J007048/ 1), the Leverhulme Trust (grant RPG-2012-735), and the Northern Ireland Department of Employment and Learning

The sudden ionization of a molecule by an attosecond pulse is followed by charge redistribution on a time scale from a few femtoseconds down to hundreds of attoseconds. This ultrafast redistribution is the result of the coherent superposition of electronic continua associated with the ionization thresholds that are reached by the broadband attosecond pulse. Thus, a correct theoretical description of the time evolution of the ensuing wave packet requires the knowledge of the actual ionization amplitudes associated with all open ionization channels, a real challenge for large and medium-size molecules. Recently, the first calculation of this kind has come to light, allowing for interpretation of ultrafast electron dynamics observed in attosecond pump–probe experiments performed on the amino acid phenylalanine [Calegari et al., Science 2014, 346, 336]. However, as in most previous theoretical works, the interpretation was based on various simplifying assumptions, namely, the ionized electron was not included in the description of the cation dynamics, the nuclei were fixed at their initial position during the hole migration process, and the effect of the IR probe pulse was ignored. Here we go a step further and discuss the consequences of including these effects in the photoionization of the glycine molecule. We show that (i) the ionized electron does not affect hole dynamics beyond the first femtosecond, and (ii) nuclear dynamics has only a significant effect after approximately 8 fs, but does not destroy the coherent motion of the electronic wave packet during at least few additional tens of fs. As a first step towards understanding the role of the probe pulse, we have considered an XUV probe pulse, instead of a strong IR one, and show that such an XUV probe does not introduce significant distortions in the pump-induced dynamics, suggesting that pump–probe strategies are suitable for imaging and manipulating charge migration in complex molecules. Furthermore, we show that hole dynamics can be changed by shaping the attosecond pump pulse, thus opening the door to the control of charge dynamics in biomolecules.

We describe, in detail, a basis set approach to the multichannel scattering problem. The full set of linearly independent scattering states at each prefixed energy of the continuum spectrum can be obtained via a least-squares approach. To test the algorithm in a concrete setup, we report a parallel implementation of the close-coupling method in which the final states are treated within the configuration interaction singles (CIS) approximation. The method requires, as input, a set of orthonormal orbitals, obtained from any quantum chemistry package. A one-center expansion (OCE) basis set consisting of products of radial B-splines and symmetry adapted angular functions is then used to expand the continuum electron wave function. To assess the quality of the CIS approximation, we compute total and partial cross sections and angular asymmetry parameters for the photoionization of a selection of closed-shell atoms (He, Ne, and Ar), H-2, H2O, and ethylene. Results are compared with the experimental data and with theoretical predictions obtained with time-dependent density functional theory (TDDFT). It is seen that, generally, the photoionization observables obtained at the CIS level compare well with TDDFT predictions. The same basis can be employed to describe molecular multiphoton or strong field ionization.

Photoelectron asymmetry parameters (β) of the gerade and ungerade C 2s−1 derived states of ethyne, ethene and ethane as a function of photon energy have been calculated and experimentally measured, to extend the search of interference effects on angular distributions to polyatomic molecules. The calculations cover the electron energy range from 0 to 1100 eV while the experimental measurements cover the electron energy range from 30 to 220 eV. Clear oscillations are interpreted in terms of interference of the photoelectron wave emitted from the two possible C 2s centres, or equivalently from the gerade and ungerade states associated with them. This is a microscopic analog of Young's double-slit experiment. The effect is however quite small and requires very high experimental accuracy to be detected. It is best evidenced in the behaviour of β difference between the two channels. The connection between β trends and structural parameters shows the expected inverse correlation between oscillation period and distance between the carbon atoms, but do not simply parallel the analogous behaviour found in cross sections.

The B-spline density functional method for the electronic continuum is employed to calculate the cross section and the asymmetry parameter profiles of valence and core photoionization in M@C60 (M = Be, Mg and Ca). For the valence photoionization significant differences are identified through the series and oscillations similar to those observed in the HOMO/HOMO-1 ratio in C60 have been calculated for Ca@C60. Core M 1s and Ca 2p ionizations are studied with the help of the `dipole prepared' continuum orbitals, which allows the identification of the leading mechanisms which give rise to the characteristic sharp and intense shape resonances, typical of these compounds.

The differential photoionization cross section ratio (? = 1)/(? = 0) for the symmetric stretching mode in the C 1s photoionization of CF4 was studied both theoretically and experimentally. We observed this ratio to differ from the Franck?Condon ratio and to be strongly dependent on the photon energy, even far from the photoionization threshold. The density-functional theory computations show that the ratio is significantly modulated by the diffraction of the photoelectrons by the neighbouring atoms at high photon energies. At lower energies, the interpretation of the first very strong maximum observed about 60?eV above the photoionization threshold required detailed calculations of the absolute partial cross sections, which revealed that the absolute cross section has two maxima at lower energies, which turn into one maximum in the cross section ratio because the maxima appear at slightly different energies in ? = 1 and ? = 0 cross sections. These two strong, low-energy continuum resonances originate from the trapping of the continuum wavefunction in the molecular potential of the surrounding fluorine atoms and from the outgoing electron scattering by them.

We have measured the angular correlation between the B K-VV Auger electrons of BF(3) molecules and the coincident fragment-ion pairs of BF(2)(+)-F(+). Then, we have found that the measured angular correlation patterns depending on the mutual angle between the light polarization direction and molecular orientation are affected by the anisotropic axis distribution of the molecular ensemble of BF(3)(+) reflecting the anisotropic nature of photon-molecule interaction. In this context, we have pointed out generally that for coincidence experiments, so-called molecular frame Auger electron angular distributions are realized only if the axis distribution of the molecular ion ensemble is isotropic.

Here we present a comparative computational study of the photoionization of furan from the ground and the two lowest-lying excited electronic states. The study aims to assess the quality of the computational methods currently employed for treating bound and continuum states in photoionization. For the ionization from the ground electronic state, we show that the Dyson orbital approach combined with an accurate solution of the continuum one particle wave functions in a multicenter B-spline basis, at the density functional theory (DFT) level, provides cross sections and asymmetry parameters in excellent agreement with experimental data. On the contrary, when the Dyson orbitals approach is combined with the Coulomb and orthogonalized Coulomb treatments of the continuum, the results are qualitatively different. In excited electronic states, three electronic structure methods, TDDFT, ADC(2), and CASSCF, have been used for the computation of the Dyson orbitals, while the continuum was treated at the B-spline/DFT level. We show that photoionization observables are sensitive probes of the nature of the excited states as well as of the quality of excited state wave functions. This paves the way for applications in more complex situations such as time resolved photoionization spectroscopy.

This is an author-created, un-copyedited version of an article published in Journal of physics B: atomic molecular and optical physics. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at http://dx.doi.org/10.1088/0953-4075/45/19/194008, Vibrationally resolved photoelectron angular distributions from randomly oriented and fixed-in-space N 2 and CO molecules have been evaluated by using an extension of the static-exchange density functional theory that includes the nuclear motion. Both K-shell and valence-shell photoionization have been considered. Comparison with the experimental data, only available for randomly oriented molecules, is very good. Our predictions for molecular-frame photoelectron angular distributions of N 2 show the signature of electron confinement and coherent two-centre interferences as those previously found in H 2. For CO, they exhibit diffraction patterns associated with the scattering of the ejected electron by the neighbouring atomic centre. The conclusions reported in this work suggest that vibrationally resolved photoelectron angular distributions can be a useful instrument to determine structure parameters in these simple molecules, We thank Mare Nostrum BSC, Cineca and CCC-UAM for allocation of computer time. Work supported by the MICINN project Nos. FIS2010-15127, ACI2008-0777 and CSD 2007-00010 (Spain), the ERA-Chemistry project PIM2010EEC-00751, the European COST Action CM0702, the Marie Curie ITN CORINF, and the XCHEM Advanced Grant 290853 of the European Research Council

Photoelectron distributions of the polarized $2{p}^{5}3d$ Rydberg states of neon have been studied with a newly built velocity map imaging analyzer. The atoms were polarized by absorption of synchrotron radiation and ionized by an infrared laser. The asymmetry parameters ${\ensuremath{\beta}}_{2}$ and ${\ensuremath{\beta}}_{4}$ characterizing two-photon resonant ionization have been extracted from the measured images and compared with the results of a quantum defect treatment. To achieve a good theoretical description of the data, it is necessary to take into account the dependence of the dipole transition matrix elements and phases of the partial waves on the angular momentum quantum numbers pertaining to various continuum channels.

Photoionization dynamics of the RNA base Uracil is studied in the framework of Density Functional Theory (DFT). The photoionization calculations take advantage of a newly developed parallel version of a multicentric approach to the calculation of the electronic continuum spectrum which uses a set of B-spline radial basis functions and a Kohn-Sham density functional hamiltonian. Both valence and core ionizations are considered. Scattering resonances in selected single-particle ionization channels are classified by the symmetry of the resonant state and the peak energy position in the photoelectron kinetic energy scale; the present results highlight once more the site specificity of core ionization processes. We further suggest that the resonant structures previously characterized in low-energy electron collision experiments are partly shifted below threshold by the photoionization processes. A critical evaluation of the theoretical results providing a guide for future experimental work on similar biosystems.

Contributions of the first-order nondipole terms to the photoelectron angular distributions from randomly oriented nitrogen molecules have been calculated in the framework of density functional theory and by employing a single centre expansion for the bound and continuum wavefunctions. Both valence and inner-shell ionizations have been considered in a photon energy range from threshold up to 2000 eV. Our results agree reasonably with calculations based on the random phase approximation and with the experimental data available. Our results for core ionizations confirm the most recent experimental finding of rather small nondipole effects in the near-threshold range. However, nondipole terms turn out to be quite large, even at the threshold, when individual contributions from the 1 sigma(-1)(g) and 1 sigma(-1)(u) ionization channels are considered. Strong interference effects leading to high-energy oscillations in the dipole and nondipole asymmetry parameters are satisfactorily explained within the Cohen-Fano model.

A comparison between the results of different configuration interaction excitation levels, up to SDTQ/4h-3p for the ground and ionised states, has been performed on LiH and Li2. Strong correlation effects are found in the latter molecule. The qualitative relevance of the lowest approximation, 1 det/2h-1p, is pointed out as well as its limitations. Such a calculation on LiF shows the absence of similar effects. Available experimental data are discussed in the context of the present results.