Vibrationally resolved valence-shell photoionization spectra of H 2 , N 2 and CO have been measured in the photon energy range 20-300 eV using third-generation synchrotron radiation. Young's double-slit interferences lead to oscillations in the corresponding vibrational ratios, showing that the molecules behave as two-center electron-wave emitters and that the associated interferences leave their trace in the angle-integrated photoionization cross section. In contrast to previous work, the oscillations are directly observable in the experiment, thereby removing any possible ambiguity related to the introduction of external parameters or fitting functions. A straightforward extension of an original idea proposed by Cohen and Fano [Cohen HD, Fano U (1966) photoelectron spectroscopy | molecular spectroscopy | molecular ionization | density functional theory | quantum chemistry T he recognition of wave-particle duality, resolving centuries of scientific debate, is nowadays considered as a milestone in the development of Quantum Mechanics. This revolutionary concept has been repeatedly demonstrated in variations of Young's double-slit experiment, where a beam of massive particles, from electrons (1) to fullerenes (2), with momentum p e , passing through two slits separated by a distance comparable to their associated de Broglie wavelength (λ e ¼ h∕p e ) displays temporal and spatial coherence evidenced through interferogram fringes (3). In the 1960's, Cohen and Fano (4) conjectured the possibility to realize the double-slit experiment on the microscopic length scale by photoionizing a diatomic molecule, where the source of free electrons is delocalized over two atomic centers. A sketch of the interference expected from the coherent emission of the two centers is shown in Fig. 1.Coherence is observable when the electron-wave length λ e is of the order of R e , or equivalently, when the photon energy hν is of the order of I p þ h 2 ∕ð2m e R 2 e Þ, where R e is the internuclear distance at equilibrium, m e is the electron mass, and I p is the vertical ionization potential. These energies correspond to incoming photons of a few hundred eV, i.e., to vacuum or extreme ultraviolet radiation. Fingerprints of this coherent emission can be found in the total photoionization cross section, which in the case of a homonuclear diatomic molecule is approximately given by the formulawhere σ 0 is an atomic photoionization cross section (for an effective charge Z eff ) and k e ¼ 2π∕λ e is the electron-wave vector. The oscillatory term within brackets quantifies the interference effect (hereafter called Cohen-Fano, CF, interference). The beauty of such a simple expression is that it is proportional to the very general intensity pattern produced by two dipole antennas separated by a distance R e that radiate coherently (5). Eq. 1 is obtained by assuming that the ionized molecular orbital ψ can be expressed by a linear combination of atomic orbitals (LCAO):where 1s A and 1s B are identical 1s atomic orbitals centered on atoms A and B of...

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 N2. 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.

Current techniques based on x-ray or electron diffraction are successfully employed for structure determination in condensed matter but are sometimes limited when applied to low density media such as the gas phase. Here we show that vibrationally resolved photoelectron spectroscopy based on x rays generated by third generation synchrotron light sources can be used to infer the structure of isolated molecules in a simple and efficient way. In particular, we show that vibrational ratios obtained from inner shell C 1s photoelectron spectroscopy of isolated methane molecules exhibit pronounced oscillations that are the fingerprints of electron diffraction by the surrounding atomic centers, thus providing the necessary information for the determination of the molecular geometry.

We report unambiguous experimental and theoretical evidence of intramolecular photoelectron diffraction in the collective vibrational excitation that accompanies high-energy photoionization of gas-phase CF 4 , BF 3 , and CH 4 from the 1s orbital of the central atom. We show that the ratios between vibrationally resolved photoionization cross sections (v-ratios) exhibit pronounced oscillations as a function of photon energy, which is the fingerprint of electron diffraction by the surrounding atomic centers. This interpretation is supported by the excellent agreement between first-principles static-exchange and time-dependent density functional theory calculations and high resolution measurements, as well as by qualitative agreement at high energies with a model in which atomic displacements are treated to first order of perturbation theory. The latter model allows us to rationalize the results for all the v-ratios in terms of a generalized v-ratio, which contains information on the structure of the above three molecules and the corresponding molecular cations. A fit of the measured v-ratios to a simple formula based on this model suggests that the method could be used to obtain structural information of both neutral and ionic molecular species.

We report the first evidence for double-slit interferences in a polyatomic molecule, which we have observed in the experimental carbon 1s photoelectron spectra of acetylene (or ethyne). The spectra have been measured over the photon energy range of 310-930 eV and show prominent oscillations in the intensity ratios σ g (υ)/σ u (υ) for the vibrational quantum numbers υ = 0, 1 and for the ratios σ s (υ = 1)/σ s (υ = 0) for the symmetry s = g, u.The experimental findings are in very good agreement with ab initio density 9

Esta es la versión de autor del artículo publicado en: This is an author produced version of a paper published in: We present a detailed account of existing theoretical methods specially designed to provide vibrationally resolved photoionization cross sections of simple molecules within the Born-Oppenheimer approximation, with emphasis on newly developed methods based on density functional theory. The performance of these methods is shown for the case of N 2 and CO photoionization. Particular attention is paid to the region of high photon energies, where the electron wavelength is comparable to the bond length and, therefore, two-center interferences and diffraction are expected to occur. As shown in a recent work [Canton et al., Proc. Natl. Acad. Sci., 2011, 108, 73027306], the main experimental difficulty, which is to extract the relatively small diffraction features from the rapidly decreasing cross section, can be easily overcome by determining ratios of vibrationally resolved photoelectron spectra and existing theoretical calculations. From these ratios, one can thus get direct information about the molecular geometry. In this work, results obtained in a wide range of photon energies and for many different molecular orbitals of N 2 and CO are discussed and compared with the available experimental measurements. From this comparison, limitations and further possible improvements of the existing theoretical methods are discussed. The new results presented in the manuscript confirm that the conclusions reported in the above reference are of general validity.

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.

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