Wave packet dynamics and control in excited states of molecular nitrogen.

Wave packet interferometry with vacuum ultraviolet light has been used to probe a complex region of the electronic spectrum of molecular nitrogen, N2. Wave packets of Rydberg and valence states were excited by using double pulses of vacuum ultraviolet (VUV), free-electron-laser (FEL) light. These wave packets were composed of contributions from multiple electronic states with a moderate principal quantum number (n ∼ 4-9) and a range of vibrational and rotational quantum numbers. The phase relationship of the two FEL pulses varied in time, but as demonstrated previously, a shot-by-shot analysis allows the spectra to be sorted according to the phase between the two pulses. The wave packets were probed by angle-resolved photoionization using an infrared pulse with a variable delay after the pair of excitation pulses. The photoelectron branching fractions and angular distributions display oscillations that depend on both the time delays and the relative phases of the VUV pulses. The combination of frequency, time delay, and phase selection provides significant control over the ionization process and ultimately improves the ability to analyze and assign complex molecular spectra.

Anisotropy Parameters for Two-Color Photoionization Phases in Randomly Oriented Molecules: Theory and Experiment in Methane and Deuteromethane.

We present combined theoretical and experimental work investigating the angle-resolved phases of the photoionization process driven by a two-color field consisting of an attosecond pulse train and an infrared pulse in an ensemble of randomly oriented molecules. We derive a general form for the two-color photoelectron (and time-delay) angular distribution valid also in the case of chiral molecules and when relative polarizations of the photons contributing to the attosecond photoelectron interferometer differ. We show a comparison between the experimental data and theoretical predictions in an ensemble of methane and deuteromethane molecules, discussing the effect of nuclear dynamics on the photoionization phases. Finally, we demonstrate that the oscillating component and the phase of the two-color signal can be fitted by using complex asymmetry parameters, in perfect analogy to the atomic case.

Femtosecond Polarization Shaping of Free-Electron Laser Pulses.

We demonstrate the generation of extreme-ultraviolet (XUV) free-electron laser (FEL) pulses with time-dependent polarization. To achieve polarization modulation on a femtosecond timescale, we combine two mutually delayed counterrotating circularly polarized subpulses from two cross-polarized undulators. The polarization profile of the pulses is probed by angle-resolved photoemission and above-threshold ionization of helium; the results agree with solutions of the time-dependent Schrödinger equation. The stability limit of the scheme is mainly set by electron-beam energy fluctuations, however, at a level that will not compromise experiments in the XUV. Our results demonstrate the potential to improve the resolution and element selectivity of methods based on polarization shaping and may lead to the development of new coherent control schemes for probing and manipulating core electrons in matter.

Influence of nuclear dynamics on molecular attosecond photoelectron interferometry.

In extreme ultraviolet spectroscopy, the photoionization process occurring in a molecule due to the absorption of a single photon can trigger an ultrafast nuclear motion in the cation. Taking advantage of attosecond photoelectron interferometry, where the absorption of the extreme ultraviolet photon is accompanied by the exchange of an additional infrared quantum of light, one can investigate the influence of nuclear dynamics by monitoring the characteristics of the photoelectron spectra generated by the two-color field. Here, we show that attosecond photoelectron interferometry is sensitive to the nuclear response by measuring the two-color photoionization spectra in a mixture of methane (CH4) and deuteromethane (CD4). The effect of the different nuclear evolution in the two isotopologues manifests itself in the modification of the amplitude and contrast of the oscillations of the photoelectron peaks. Our work indicates that nuclear dynamics can affect the coherence properties of the electronic wave packet emitted by photoionization on a time scale as short as a few femtoseconds.

Alternative Pathway to Double-Core-Hole States.

Excited double-core-hole states of isolated water molecules resulting from the sequential absorption of two x-ray photons have been investigated. These states are formed through an alternative pathway, where the initial step of core ionization is accompanied by the shake-up of a valence electron, leading to the same final states as in the core-ionization followed by core-excitation pathway. The capability of the x-ray free-electron laser to deliver very intense, very short, and tunable light pulses is fully exploited to identify the two different pathways.

Time-resolved photoelectron imaging of complex resonances in molecular nitrogen.

We have used the FERMI free-electron laser to perform time-resolved photoelectron imaging experiments on a complex group of resonances near 15.38 eV in the absorption spectrum of molecular nitrogen, N2, under jet-cooled conditions. The new data complement and extend the earlier work of Fushitani et al. [Opt. Express 27, 19702-19711 (2019)], who recorded time-resolved photoelectron spectra for this same group of resonances. Time-dependent oscillations are observed in both the photoelectron yields and the photoelectron angular distributions, providing insight into the interactions among the resonant intermediate states. In addition, for most states, we observe an exponential decay of the photoelectron yield that depends on the ionic final state. This observation can be rationalized by the different lifetimes for the intermediate states contributing to a particular ionization channel. Although there are nine resonances within the group, we show that by detecting individual photoelectron final states and their angular dependence, we can identify and differentiate quantum pathways within this complex system.

Attosecond pulse shaping using a seeded free-electron laser.

Attosecond pulses are central to the investigation of valence- and core-electron dynamics on their natural timescales1-3. The reproducible generation and characterization of attosecond waveforms has been demonstrated so far only through the process of high-order harmonic generation4-7. Several methods for shaping attosecond waveforms have been proposed, including the use of metallic filters8,9, multilayer mirrors10 and manipulation of the driving field11. However, none of these approaches allows the flexible manipulation of the temporal characteristics of the attosecond waveforms, and they suffer from the low conversion efficiency of the high-order harmonic generation process. Free-electron lasers, by contrast, deliver femtosecond, extreme-ultraviolet and X-ray pulses with energies ranging from tens of microjoules to a few millijoules12,13. Recent experiments have shown that they can generate subfemtosecond spikes, but with temporal characteristics that change shot-to-shot14-16. Here we report reproducible generation of high-energy (microjoule level) attosecond waveforms using a seeded free-electron laser17. We demonstrate amplitude and phase manipulation of the harmonic components of an attosecond pulse train in combination with an approach for its temporal reconstruction. The results presented here open the way to performing attosecond time-resolved experiments with free-electron lasers.

Tracking attosecond electronic coherences using phase-manipulated extreme ultraviolet pulses.

The recent development of ultrafast extreme ultraviolet (XUV) coherent light sources bears great potential for a better understanding of the structure and dynamics of matter. Promising routes are advanced coherent control and nonlinear spectroscopy schemes in the XUV energy range, yielding unprecedented spatial and temporal resolution. However, their implementation has been hampered by the experimental challenge of generating XUV pulse sequences with precisely controlled timing and phase properties. In particular, direct control and manipulation of the phase of individual pulses within an XUV pulse sequence opens exciting possibilities for coherent control and multidimensional spectroscopy, but has not been accomplished. Here, we overcome these constraints in a highly time-stabilized and phase-modulated XUV-pump, XUV-probe experiment, which directly probes the evolution and dephasing of an inner subshell electronic coherence. This approach, avoiding any XUV optics for direct pulse manipulation, opens up extensive applications of advanced nonlinear optics and spectroscopy at XUV wavelengths.

Complete Characterization of Phase and Amplitude of Bichromatic Extreme Ultraviolet Light.

Intense, mutually coherent beams of multiharmonic extreme ultraviolet light can now be created using seeded free-electron lasers, and the phase difference between harmonics can be tuned with attosecond accuracy. However, the absolute value of the phase is generally not determined. We present a method for determining precisely the absolute phase relationship of a fundamental wavelength and its second harmonic, as well as the amplitude ratio. Only a few easily calculated theoretical parameters are required in addition to the experimental data.

Thermoelectric Properties of p-Type Cu2O, CuO, and NiO from Hybrid Density Functional Theory.

The electronic transport coefficients of three Earth-abundant metal oxides Cu2O, CuO, and NiO were investigated using hybrid density functional theory (DFT). Hybrid DFT methods combined with local Gaussian-type basis sets enabled band structure studies on both non-magnetic and magnetic p-type metal oxides without empirical corrections. The CRYSTAL code was used for obtaining the wavefunction, and the transport properties were calculated with two different methodologies to benchmark their accuracy: a numerical approach as implemented in the BoltzTraP code and an analytical approach recently implemented in CRYSTAL17. Both computational methods produce identical results in good agreement with experimental measurements of the Seebeck coefficient. The predicted electrical conductivities are overestimated, owing likely to the used approximation of a constant electronic relaxation time in the calculations, as explicit electron scattering is neglected and relaxation time is considered only as a free parameter. The obtained results enable us to critically review and complement the available theoretical and experimental literature on the studied p-type thermoelectric metal oxide materials.

On the exfoliation and anisotropic thermal expansion of black phosphorus.

Black phosphorus is a bulk solid allotrope of elemental phosphorus and can be seen as an infinite stack of phosphorene sheets. It is interesting from a technological point of view as well as from an electronic structure perspective due to the importance of electron correlation effects. In a recent paper [M. Schütz, L. Maschio, A. J. Karttunen and D. Usvyat, J. Phys. Chem. Lett., 2017, 8, 1290-1294] a highly accurate exfoliation energy has been computed. Building upon these results we carefully benchmark various dispersion-corrected density functional approximations. The choice of the range-separating function that suppresses London dispersion at short interatomic distances apparently has a substantial influence on the results. Having chosen the suitable functional, we have computed the thermal expansion coefficients of black phosphorous via a quasi-harmonic approximation. The computed coefficients manifest a strong anisotropy between the two in-plane directions. Our calculations, however, do not support the existence of negative thermal expansion in black phosphorus, as reported in some theoretical studies.

Coherent control schemes for the photoionization of neon and helium in the Extreme Ultraviolet spectral region.

The seeded Free-Electron Laser (FEL) FERMI is the first source of short-wavelength light possessing the full coherence of optical lasers, together with the extreme power available from FELs. FERMI provides longitudinally coherent radiation in the Extreme Ultraviolet and soft x-ray spectral regions, and therefore opens up wide new fields of investigation in physics. We first propose experiments exploiting this property to provide coherent control of the photoionization of neon and helium, carry out numerical calculations to find optimum experimental parameters, and then describe how these experiments may be realized. The approach uses bichromatic illumination of a target and measurement of the products of the interaction, analogous to previous Brumer-Shapiro-type experiments in the optical spectral range. We describe operational schemes for the FERMI FEL, and simulate the conditions necessary to produce light at the fundamental and second or third harmonic frequencies, and to control the phase with respect to the fundamental. We conclude that a quantitative description of the phenomena is extremely challenging for present state-of-the-art theoretical and computational methods, and further development is necessary. Furthermore, the intensity available may already be excessive for the experiments proposed on helium. Perspectives for further development are discussed.

Ab initio electronic transport and thermoelectric properties of solids from full and range-separated hybrid functionals.

Within the semiclassical Boltzmann transport theory in the constant relaxation-time approximation, we perform an ab initio study of the transport properties of selected systems, including crystalline solids and nanostructures. A local (Gaussian) basis set is adopted and exploited to analytically evaluate band velocities as well as to access full and range-separated hybrid functionals (such as B3LYP, PBE0, or HSE06) at a moderate computational cost. As a consequence of the analytical derivative, our approach is computationally efficient and does not suffer from problems related to band crossings. We investigate and compare the performance of a variety of hybrid functionals in evaluating Boltzmann conductivity. Demonstrative examples include silicon and aluminum bulk crystals as well as two thermoelectric materials (CoSb3, Bi2Te3). We observe that hybrid functionals other than providing more realistic bandgaps-as expected-lead to larger bandwidths and hence allow for a better estimate of transport properties, also in metallic systems. As a nanostructure prototype, we also investigate conductivity in boron-nitride (BN) substituted graphene, in which nanoribbons (nanoroads) alternate with BN ones.

One-Dimensional Phosphorus Nanostructures: from Nanorings to Nanohelices.

Phosphorus nanorings and nanohelices-speculated to exist over 20 years ago-have been systematically derived from one parent structure and studied with quantum chemical methods. The (P8 P2 )n nanorings have been recently synthetized inside carbon nanotube templates, and our comprehensive analysis of possible structural arrangements strongly supports the possibility to experimentally determine the closely related (P8 P2 )n nanohelices. The nanohelices possess very low stiffness, suggesting interesting mechanical properties with nano-spring-like behavior.

The A-center defect in diamond: quantum mechanical characterization through the infrared spectrum.

The A-center in diamond, which consists of two nitrogen atoms substituting two neighboring carbon atoms, has been investigated at the quantum mechanical level using an all-electron Gaussian type basis set, hybrid functionals and the periodic supercell approach. In order to simulate different defect concentrations, four supercells have been considered containing 32, 64, 128 and 216 atoms, respectively. The ground state is a closed shell system where the two neighboring nitrogen atoms are separated, as a consequence of the strong repulsive interaction between the lone pairs, by 2.22 Å. The calculated band gap of a perfect diamond is 5.75 eV, which is in very good agreement with the experimental value of 5.80 eV (at 0 °K); the vertical electronic transition energy from the defective band to the conduction band is 4.75 and 4.46 eV for the cells containing 128 and 216 atoms, respectively. The presence of the A-center does not affect the Raman spectrum of diamond. Several intense peaks appear on the contrary in the IR spectrum, which permit (or should permit) the identification of this defect. The four peaks proposed by Sutherland et al. (Nature, 1954, 174, 901-904) and widely accepted as fingerprints of the A-center (at 480, 1093, 1203, 1282 cm-1), and the most important features of the spectrum published by Davies 22 years later (J. Phys. C: Solid State Phys., 1976, 9, 537-542) are very well reproduced by our simulated spectrum with the largest supercell. The modes in which the nitrogen atoms are more involved are identified by the frequency shift due to the 14N → 15N isotopic substitution; the two modes corresponding to the experimental ones at 480 and 1282 cm-1 show the largest isotopic shift. The graphical animation of the modes (available at ) not only confirms this attribution, but permits also the investigation of the nature of the full set of modes.

Interference stabilization of autoionizing states in molecular N2 studied by time- and angular-resolved photoelectron spectroscopy.

An autoionizing resonance in molecular N2 is excited by an ultrashort XUV pulse and probed by a subsequent weak IR pulse, which ionizes the contributing Rydberg states. Time- and angular-resolved photoelectron spectra recorded with a velocity map imaging spectrometer reveal two electronic contributions with different angular distributions. One of them has an exponential decay rate of 20 ± 5 fs, while the other one is shorter than 10 fs. This observation is interpreted as a manifestation of interference stabilization involving the two overlapping discrete Rydberg states. A formalism of interference stabilization for molecular ionization is developed and applied to describe the autoionizing resonance. The results of calculations suggest, that the effect of the interference stabilization is facilitated by rotationally-induced couplings of electronic states with different symmetry.

Direct Imaging of Transient Fano Resonances in N_{2} Using Time-, Energy-, and Angular-Resolved Photoelectron Spectroscopy.

Autoionizing Rydberg states of molecular N_{2} are studied using time-, energy-, and angular-resolved photoelectron spectroscopy. A femtosecond extreme ultraviolet pulse with a photon energy of 17.5 eV excites the resonance and a subsequent IR pulse ionizes the molecule before the autoionization takes place. The angular-resolved photoelectron spectra depend on pump-probe time delay and allow for the distinguishing of two electronic states contributing to the resonance. The lifetime of one of the contributions is determined to be 14±1 fs, while the lifetime of the other appears to be significantly shorter than the time resolution of the experiment. These observations suggest that the Rydberg states in this energy region are influenced by the effect of interference stabilization and merge into a complex resonance.

Toward an Accurate Estimate of the Exfoliation Energy of Black Phosphorus: A Periodic Quantum Chemical Approach.

The black phosphorus (black-P) crystal is formed of covalently bound layers of phosphorene stacked together by weak van der Waals interactions. An experimental measurement of the exfoliation energy of black-P is not available presently, making theoretical studies the most important source of information for the optimization of phosphorene production. Here, we provide an accurate estimate of the exfoliation energy of black-P on the basis of multilevel quantum chemical calculations, which include the periodic local Møller-Plesset perturbation theory of second order, augmented by higher-order corrections, which are evaluated with finite clusters mimicking the crystal. Very similar results are also obtained by density functional theory with the D3-version of Grimme's empirical dispersion correction. Our estimate of the exfoliation energy for black-P of -151 meV/atom is substantially larger than that of graphite, suggesting the need for different strategies to generate isolated layers for these two systems.

Range-separated double-hybrid density-functional theory applied to periodic systems.

Quantum chemistry methods exploiting density-functional approximations for short-range electron-electron interactions and second-order Møller-Plesset (MP2) perturbation theory for long-range electron-electron interactions have been implemented for periodic systems using Gaussian-type basis functions and the local correlation framework. The performance of these range-separated double hybrids has been benchmarked on a significant set of systems including rare-gas, molecular, ionic, and covalent crystals. The use of spin-component-scaled MP2 for the long-range part has been tested as well. The results show that the value of µ = 0.5 bohr(-1) for the range-separation parameter usually used for molecular systems is also a reasonable choice for solids. Overall, these range-separated double hybrids provide a good accuracy for binding energies using basis sets of moderate sizes such as cc-pVDZ and aug-cc-pVDZ.

The effect of electron correlation on the adsorption of hydrogen fluoride and water on magnesium fluoride surfaces.

We have performed periodic density functional and periodic local MP2 calculations for the adsorption of hydrogen fluoride and water on the four low index surfaces (001), (100), (101) and (110) of magnesium fluoride. While the adsorption of HF is described well using B3LYP, MP2 is required for a good description of the adsorption of H2O. Post-optimization dispersion corrections of B3LYP are found to consistently overestimate the adsorption energy. The coordination of surface cations, the presence of hydroxyls on the surface, as well as the coverage appear to play an equally important role in the adsorption.