Wave packet theory for non-resonant x-ray emission and non-resonant Auger electron emission in molecules.

We present a time-dependent theory for non-resonant x-ray emission spectrum (XES) and normal Auger spectrum (NAS) calculation, based on a fully quantum description of nuclear dynamics using the vibrational wave packet concept. We compare two formulations of the time-dependent theory, either employing a two-time propagation scheme or using spectral integration over the electron energy continuum. We find that the latter formulation is more efficient for numerical simulations, providing a reasonable accuracy when the integration step is shorter than the lifetime broadening of the core-ionized state. We demonstrate our approach using the example of non-resonant x-ray emission from a water molecule, considering the lowest core-ionized K-1 and first core-ionized shake-up K-1V-1V1 intermediate states. These channels exemplify the developed theory on bound-bound, bound-continuum, continuum-bound, and continuum-continuum transitions. Our results suggest that the time-dependent approach is efficient for simulating XES involving dissociative states, whereas the time-independent approach, based on Franck-Condon factors, is more efficient for bound-bound transitions expressed as discrete frequency dependence in the energy domain. The methods and discussion have general applicability, including both NAS and more complex systems, such as liquid water.

Role of the Cohen-Fano interference in recoil-induced rotation.

We study the rotational dynamics induced by the recoil effect in diatomic molecules using time-resolved two-color x-ray pump-probe spectroscopy. A short pump x-ray pulse ionizes a valence electron inducing the molecular rotational wave packet, whereas the second time-delayed x-ray pulse probes the dynamics. An accurate theoretical description is used for analytical discussions and numerical simulations. Our main attention is paid to the following two interference effects that influence the recoil-induced dynamics: (i) Cohen-Fano (CF) two-center interference between partial ionization channels in diatomics and (ii) interference between the recoil-excited rotational levels manifesting as the rotational revival structures in the time-dependent absorption of the probe pulse. The time-dependent x-ray absorption is computed for the heteronuclear CO and homonuclear N2 molecules as showcases. It is found that the effect of CF interference is comparable with the contribution from independent partial ionization channels, especially for the low photoelectron kinetic energy case. The amplitude of the recoil-induced revival structures for the individual ionization decreases monotonously with a decrease in the photoelectron energy, whereas the amplitude of the CF contribution remains sufficient even at the photoelectron kinetic energy below 1 eV. The profile and intensity of the CF interference depend on the phase difference between the individual ionization channels related to the parity of the molecular orbital emitting the photoelectron. This phenomenon provides a sensitive tool for the symmetry analysis of molecular orbitals.

Time-resolved study of recoil-induced rotation by X-ray pump - X-ray probe spectroscopy.

Modern stationary X-ray spectroscopy is unable to resolve rotational structure. In the present paper, we propose to use time-resolved two color X-ray pump-probe spectroscopy with picosecond resolution for real-time monitoring of the rotational dynamics induced by the recoil effect. The proposed technique consists of two steps. The first short pump X-ray pulse ionizes the valence electron, which transfers angular momentum to the molecule. The second time-delayed short probe X-ray pulse resonantly excites a 1s electron to the created valence hole. Due to the recoil-induced angular momentum the molecule rotates and changes the orientation of transition dipole moment of core-excitation with respect to the transition dipole moment of the valence ionization, which results in a temporal modulation of the probe X-ray absorption as a function of the delay time between the pulses. We developed an accurate theory of the X-ray pump-probe spectroscopy of the recoil-induced rotation and study how the energy of the photoelectron and thermal dephasing affect the structure of the time-dependent X-ray absorption using the CO molecule as a case-study. We also discuss the feasibility of experimental observation of our theoretical findings, opening new perspectives in studies of molecular rotational dynamics.

Nuclear dynamics in resonant inelastic X-ray scattering and X-ray absorption of methanol.

We report on a combined theoretical and experimental study of core-excitation spectra of gas and liquid phase methanol as obtained with the use of X-ray absorption spectroscopy (XAS) and resonant inelastic X-ray scattering (RIXS). The electronic transitions are studied with computational methods that include strict and extended second-order algebraic diagrammatic construction [ADC(2) and ADC(2)-x], restricted active space second-order perturbation theory, and time-dependent density functional theory-providing a complete assignment of the near oxygen K-edge XAS. We show that multimode nuclear dynamics is of crucial importance for explaining the available experimental XAS and RIXS spectra. The multimode nuclear motion was considered in a recently developed "mixed representation" where dissociative states and highly excited vibrational modes are accurately treated with a time-dependent wave packet technique, while the remaining active vibrational modes are described using Franck-Condon amplitudes. Particular attention is paid to the polarization dependence of RIXS and the effects of the isotopic substitution on the RIXS profile in the case of dissociative core-excited states. Our approach predicts the splitting of the 2a″ RIXS peak to be due to an interplay between molecular and pseudo-atomic features arising in the course of transitions between dissociative core- and valence-excited states. The dynamical nature of the splitting of the 2a″ peak in RIXS of liquid methanol near pre-edge core excitation is shown. The theoretical results are in good agreement with our liquid phase measurements and gas phase experimental data available from the literature.

Ultrafast dissociation features in RIXS spectra of the water molecule.

In this combined theoretical and experimental study we report on an analysis of the resonant inelastic X-ray scattering (RIXS) spectra of gas phase water via the lowest dissociative core-excited state |1s-1O4a11. We focus on the spectral feature near the dissociation limit of the electronic ground state. We show that the narrow atomic-like peak consists of the overlapping contribution from the RIXS channels back to the ground state and to the first valence excited state |1b-114a11 of the molecule. The spectral feature has signatures of ultrafast dissociation (UFD) in the core-excited state, as we show by means of ab initio calculations and time-dependent nuclear wave packet simulations. We show that the electronically elastic RIXS channel gives substantial contribution to the atomic-like resonance due to the strong bond length dependence of the magnitude and orientation of the transition dipole moment. By studying the RIXS for an excitation energy scan over the core-excited state resonance, we can understand and single out the molecular and atomic-like contributions in the decay to the lowest valence-excited state. Our study is complemented by a theoretical discussion of RIXS in the case of isotopically substituted water (HDO and D2O) where the nuclear dynamics is significantly affected by the heavier fragments' mass.

Gradual collapse of nuclear wave functions regulated by frequency tuned X-ray scattering.

As is well established, the symmetry breaking by isotope substitution in the water molecule results in localisation of the vibrations along one of the two bonds in the ground state. In this study we find that this localisation may be broken in excited electronic states. Contrary to the ground state, the stretching vibrations of HDO are delocalised in the bound core-excited state in spite of the mass difference between hydrogen and deuterium. The reason for this effect can be traced to the narrow "canyon-like" shape of the potential of the state along the symmetric stretching mode, which dominates over the localisation mass-difference effect. In contrast, the localisation of nuclear motion to one of the HDO bonds is preserved in the dissociative core-excited state . The dynamics of the delocalisation of nuclear motion in these core-excited states is studied using resonant inelastic X-ray scattering of the vibrationally excited HDO molecule. The results shed light on the process of a wave function collapse. After core-excitation into the state of HDO the initial wave packet collapses gradually, rather than instantaneously, to a single vibrational eigenstate.

The central fragment of Reelin, generated by proteolytic processing in vivo, is critical to its function during cortical plate development.

Reelin is a large extracellular protein that controls cortical development. It binds to lipoprotein receptors very-low-density lipoprotein receptor and apolipoprotein-E receptor type 2, thereby inducing phosphorylation of the adapter Dab1. In vivo, Reelin is cleaved into three fragments, but their respective function is unknown. Here we show the following: (1) the central fragment is necessary and sufficient for receptor binding in vitro and for Dab1 phosphorylation in neuronal cultures; (2) Reelin does not bind the protocadherin cadherin-related neuronal receptor (CNR1) as reported previously; (3) Reelin and its central fragment are equally able to rescue the reeler phenotype in a slice culture assay; and (4) anti-receptor antibodies can induce Dab1 phosphorylation but do not correct the reeler phenotype in slices. These observations show that the function of Reelin is critically dependent on the central fragment generated by processing but primarily independent of interactions with CNR1 and on the N-terminal region. They also indicate that events acting in parallel to Dab1 phosphorylation might be required for full activity.

Characterization of the various forms of the Reelin protein in the cerebrospinal fluid of normal subjects and in neurological diseases.

Reelin is a large extracellular glycoprotein that is defective in reeler mutant mice and plays a well-established role during brain development in human as well as rodents. In the adult brain, Reelin is expressed in a subset of GABAergic interneurons. Its role in disease states is not clearly defined, although it is implicated in autism and psychoses such as schizophrenia. In this report, we show that Reelin immunoreactive proteins can be detected in the human cerebrospinal fluid (CSF) with monoclonal antibodies directed against the N- and C-terminal regions of the protein. In CSF, Reelin is present as different products due to processing at two main sites; preservation at -20 degrees C increases processing further. CSF Reelin originates from the brain tissue and not from plasma. The protein was detected in comparable concentrations in children and adults, and the signal varied largely from subject to subject with no obvious correlation with age or neurological disease state.

The reelin signaling pathway: some recent developments.

The Reelin signaling pathway plays a key role in the architectonic development of the central nervous system. Extracellular Reelin binds to receptors of the lipoprotein receptor family and induces tyrosine phosphorylation of the adaptor Dab1. In this paper, we discuss three recent developments. First, we show that the central part of Reelin is involved in receptor binding and signal activation as reflected in Dab1 phosphorylation. Second, we examine the genomic organization, alternative splicing and promoter use of the Dab1 gene, which hint at a particularly complex regulation. Third, we present preliminary studies by in situ hybridization that demonstrate regulated expression of Reelin receptors and Dab1 by radial precursors in the ventricular zone.