Electron-core Interaction Research Articles

Ionization and recombination times of the long trajectory in high-order harmonic generation

Measuring the ionization and recombination times in high-order harmonic generation driven by strong laser fields is of fundamental importance in attosecond science and vital for assessing the temporal accuracy of trajectory-resolved high-harmonic spectroscopy. We investigate the effect of the electron-core interaction on the ionization and recombination times of the long trajectory in high-order harmonic generation. Using a classical model and the analytical $R$-matrix theory for helium, it is found that the attractive interaction leads to a 30-as shift of the ionization times for the long trajectory. By numerically solving the time-dependent Schr\"odinger equation for a helium atom model, we demonstrate that this small time shift can be probed by using orthogonally polarized two-color fields with high probe frequencies.

Probing ultrafast C-Br bond fission in the UV photochemistry of bromoform with core-to-valence transient absorption spectroscopy.

UV pump–extreme UV (XUV) probe femtosecond transient absorption spectroscopy is used to study the 268 nm induced photodissociation dynamics of bromoform (CHBr3). Core-to-valence transitions at the Br(3d) absorption edge (∼70 eV) provide an atomic scale perspective of the reaction, sensitive to changes in the local valence electronic structure, with ultrafast time resolution. The XUV spectra track how the singly occupied molecular orbitals of transient electronic states develop throughout the C–Br bond fission, eventually forming radical Br and CHBr2 products. Complementary ab initio calculations of XUV spectral fingerprints are performed for transient atomic arrangements obtained from sampling excited-state molecular dynamics simulations. C–Br fission along an approximately symmetrical reaction pathway leads to a continuous change of electronic orbital characters and atomic arrangements. Two timescales dominate changes in the transient absorption spectra, reflecting the different characteristic motions of the light C and H atoms and the heavy Br atoms. Within the first 40 fs, distortion from symmetry to form a quasiplanar CHBr2 by the displacement of the (light) CH moiety causes significant changes to the valence electronic structure. Displacement of the (heavy) Br atoms is delayed and requires up to ∼300 fs to form separate Br + CHBr2 products. We demonstrate that transitions between the valence-excited (initial) and valence + core-excited (final) state electronic configurations produced by XUV absorption are sensitive to the localization of valence orbitals during bond fission. The change in valence electron-core hole interaction provides a physical explanation for spectral shifts during the process of bond cleavage.

Holographic interferences in photoelectron spectra: different approaches

We perform a theoretical study of the holographic structures in photoelectron spectra for ionization of hydrogen atoms induced by short laser pulses. To elucidate the nature of the holographic structures present in the momentum distributions of photoelectrons, we use several quantum approximations, such as the strong field and Coulomb–Volkov approximations up to second order, as well as semiclassical Monte Carlo simulations. In a single-cycle pulse, we eliminate the intracycle interference from the spectra isolating the holographic structure formed in the photoionization process. We probe the different approaches and analyze the role of electron–core interaction numerically by solving the time dependent Schrodinger equation. We show that the two-step semiclassical model of Shvetsov-Shilovski et al. [Phys. Rev. A 94, 013415 (2016)] fully considers the effect of the Coulomb potential on the electron dynamics and semiclassical phase reproducing the holographic structure in full quantum calculations. Contrarily, perturbative quantum (strong field and Coulomb–Volkov) and semiclassical (quantum trajectory Monte Carlo) methods account only partially for some of the characteristics of the holographic interference pattern.

Looking inside the tunnelling barrier: I. Strong field ionisation from orbitals with high angular momentum in circularly polarised fields

Here and in the two companion papers we use time-dependent analytical R-Matrix (ARM) theory to consider the impact of electron-core interaction on (i) sensitivity of strong field ionisation to the sense of electron rotation in the initial state and (ii) electron spin polarisation. ARM is a rigorous approach to strong field ionisation that takes advantage of the semiclassical nature of electron dynamics in strong laser fields and naturally incorporates complex-valued classical trajectories in the time-propagation. While the appearance of complex time is associated with optical tunnelling, complex coordinates reflect non-adiabaticity of the electron response to the strong laser field. We focus on non-adiabatic electron-core interaction in the sub-barrier region and show how it affects ionisation from orbitals with high angular momentum ℓ = 2, 3 in multiply charged atomic ions with strong electron-core interaction. In this paper we discuss sub-cycle ionisation yields, while in the companion papers we focus on the effects of the long-range core potential on the ‘initial conditions’ (from the ARM perspective, companion paper II) for the photo electron as it emerges from the classically forbidden region and on the spin polarisation of the ejected electron (companion paper III).

Looking inside the tunnelling barrier III: spin polarisation in strong field ionisation from orbitals with high angular momentum

Strong field ionisation is known as optical tunnelling of an electron through the barrier created by the laser field and core potential. Time-dependent analytical R-matrix takes advantage of the semiclassical nature of electron dynamics in strong laser fields and naturally incorporates complex-valued trajectories in time propagation. The language of trajectories enables straightforward ‘kinematic’ interpretation of several new phenomena such as ‘inversion’ of the conventional propensity rules in photo-ionisation (Barth and Smirnova 2011 Phys. Rev. A 84 063415) and generation of spin-polarised electrons (Barth and Smirnova 2013 Phys. Rev. A 88 013401) during ionisation in strong laser fields. Both phenomena are due to the kinematics of the electron motion under the barrier and were predicted for short-range potentials, i.e. neglecting the electron–core interaction. However, the electron–core interaction can and does affect the kinematics of tunnelling defining the ionisation propensity rules (companion paper I) and spin-polarisation. The latter is the focus of this paper. We consider orbitals with arbitrary angular momentum and extend our results to positively charged ions.

Electronic structure and x-ray spectroscopy of Cu2MnAl1–xGax

We explore the electronic and related properties of Cu2MnAl1–xGax with a first-principles, relativistic multiscattering Green function approach. We discuss our results in relation to existing experimental data and show that the electron-core hole interaction is essential for the description of the optical spectra especially in describing the X-ray absorption and magnetic circular dichroism spectra at the L2,3 edges of Cu and Mn.

Hole dynamics and spin currents after ionization in strong circularly polarized laser fields

We apply the time-dependent analytical R-matrix theory to develop a movie of hole motion in a Kr atom upon ionization by strong circularly polarized field. We find rich hole dynamics, ranging from rotation to swinging motion. The motion of the hole depends on the final energy and the spin of the photoelectron and can be controlled by the laser frequency and intensity. Crucially, hole rotation is a purely non-adiabatic effect, completely missing in the framework of quasistatic (adiabatic) tunneling theories. We explore the possibility to use hole rotation as a clock for measuring ionization time. Analyzing the relationship between the relative phases in different ionization channels we show that in the case of short-range electron-core interaction the hole is always initially aligned along the instantaneous direction of the laser field, signifying zero delays in ionization. Finally, we show that strong-field ionization in circular fields creates spin currents (i.e. different flow of spin-up and spin-down density in space) in the ions. This phenomenon is intimately related to the production of spin-polarized electrons in strong laser fields Barth and Smirnova (2013 Phys. Rev. A 88 013401). We demonstrate that rich spin dynamics of electrons and holes produced during strong field ionization can occur in typical experimental conditions and does not require relativistic intensities or strong magnetic fields.

Ab‐initiosimulations of materials using VASP: Density‐functional theory and beyond

During the past decade, computer simulations based on a quantum-mechanical description of the interactions between electrons and between electrons and atomic nuclei have developed an increasingly important impact on solid-state physics and chemistry and on materials science-promoting not only a deeper understanding, but also the possibility to contribute significantly to materials design for future technologies. This development is based on two important columns: (i) The improved description of electronic many-body effects within density-functional theory (DFT) and the upcoming post-DFT methods. (ii) The implementation of the new functionals and many-body techniques within highly efficient, stable, and versatile computer codes, which allow to exploit the potential of modern computer architectures. In this review, I discuss the implementation of various DFT functionals [local-density approximation (LDA), generalized gradient approximation (GGA), meta-GGA, hybrid functional mixing DFT, and exact (Hartree-Fock) exchange] and post-DFT approaches [DFT + U for strong electronic correlations in narrow bands, many-body perturbation theory (GW) for quasiparticle spectra, dynamical correlation effects via the adiabatic-connection fluctuation-dissipation theorem (AC-FDT)] in the Vienna ab initio simulation package VASP. VASP is a plane-wave all-electron code using the projector-augmented wave method to describe the electron-core interaction. The code uses fast iterative techniques for the diagonalization of the DFT Hamiltonian and allows to perform total-energy calculations and structural optimizations for systems with thousands of atoms and ab initio molecular dynamics simulations for ensembles with a few hundred atoms extending over several tens of ps. Applications in many different areas (structure and phase stability, mechanical and dynamical properties, liquids, glasses and quasicrystals, magnetism and magnetic nanostructures, semiconductors and insulators, surfaces, interfaces and thin films, chemical reactions, and catalysis) are reviewed.

Density functional calculations of the electronic structure and optical properties of aluminosilicate polymorphs (Al2SiO5)

The density functional theory (DFT) based orthogonalized linear combination of atomic orbitals (OLCAO) method is used to study the electronic structure and spectroscopic properties of three alumino silicate polymorphs (Al 2 SiO 5 ), andalusite, sillimanite, and kyanite. These polymorphs are precursors to mullite, which is an excellent refractory material. The electronic structure results include the band structure, total and partial density of states, bond order, and Mullikan effective charge (Q*), whereas the spectroscopic properties include X-ray absorption near-edge-structure (XANES), and the complex optical dielectric functions (e 1 + ie 2 ) for each polymorph. For the XANES calculations, we use a supercell approach and account for the electron-core hole interaction. Our calculations show that the polymorphs are insulators with direct band gaps of 5.05, 5.21, and 5.80 eV for andalusite, sillimanite, and kyanite, respectively. The calculated refractive indices (n) for each material are in agreement with experimental values from the literature. Results on the XANES spectral calculations ( K -edge and L -edge) for all crystallographically nonequivalent ions in the polymorphs are presented. It is shown that to achieve excellent agreement with the experimentally measured spectrum, a weighted sum of the spectra from crystallographically inequivalent sites must be used. The analysis of the XANES spectra based on differences in the local bonding environments are provided.

Calculated Electronic Behavior and Spectrum of Mg+@C60 Using a Simple Jellium-shell Model

We present a method for calculating the energy levels and wave functions of any atom or ion with a single valence electron encapsulated in a Fullerene cage using a jelluim-shell model. The valence electron-core interaction is represented by a one-body pseudo-potential obtained through density functional theory with strikingly accurate parameters for Mg+ and which reduces to a purely Coulombic interaction in the case of H. We find that most energy states are affected little by encapsulation. However, when either the electron in the non-encapsulated species has a high probability of being near the jellium cage, or when the cage induces a maximum electron probability density within it, the energy levels shift considerably. Mg+ shows behavior similar to that of H, but since its wave functions are broader, the changes in its energy levels from encapsulation are slightly more pronounced. Agreement with other computational work as well as experiment is excellent and the method presented here is generalizable to any encapsulated species where a one-body electronic pseudo-potential for the free atom (or ion) is available. Results are also presented for off-center hydrogen, where a ground state energy minimum of -14.01 eV is found at a nuclear displacement of around 0.1 Å.

Rydberg states about dipolar cores: The quantum dynamics of the long-range anisotropic interaction.

High Rydberg states about a dipolar molecular core can exhibit special features due to the exceptionally long range of the electrical anisotropy of the core. Unlike all other, more localized, couplings of the Rydberg electron to the ion, here the interaction is not shielded by the centrifugal barrier. The influence of the core even on states of the electron with higher angular momentum l and the significant matrix elements between states that differ considerably in the principal quantum number n make this problem worthy of separate considerations. Using specialized computational techniques (both analytical and numerical) for the exact evaluation of the relevant matrix elements, the role of both inter- and intra-Rydberg series coupling is discussed. The importance of the latter (i.e., the coupling of the Rydberg electron to the rotation of the core) is emphasized. Special attention is given to the role of an external dc electrical field that is different in the present problem in that it does not significantly dilute the strength of the electron-core interaction. A positively charged core can have a dipole moment (defined with respect to its center of mass) larger than that of neutral polar molecules, particularly if the charge is localized. Hence the interseries and intraseries dynamics discussed in this paper can give rise to experimentally measurable special effects. \textcopyright{} 1996 The American Physical Society.

Potential curves for the ground and excited states of the Na2 molecule up to the (3s+5p) dissociation limit: Results of two different effective potential calculations

Theoretical calculations for the ground state and for 83 excited states of the Na2 molecule are presented in the framework of two independent approaches. The electron–core interaction is represented either by a pseudopotential or by a model potential, and a core polarization potential is introduced in both cases. The basis set contains either Gaussian orbitals or two-center generalized Slater orbitals. The two methods appear to give similar results, one being more accurate for the ground and first excited states, the other being better adapted to the intermediate Rydberg states. A very good agreement is obtained with the experimental spectroscopic constants determined for 26 states, the mean deviation being ΔRe=0.05a0, Δωe=0.86 cm−1, and ΔDe=57 cm−1.

Spin-orbit and interference asymmetries in elastic scattering of electrons from heavy one-electron atoms

Two asymmetries in the differential cross section for elastic scattering of electrons from one-electron atoms are discussed. Numerical results for the standard left-right asymmetry (electrons polarised, atoms unpolarised) and the interference asymmetry (electrons unpolarised, atoms polarised) are presented for caesium and thallium targets. For electron-thallium scattering, it is found that the former left-right asymmetry is predominantly due to spin-nonconserving processes in the electron-core interaction, even for very low scattering energies. This result explains the relatively small importance of the fine-structure effect (based on exchange between the continuum and the target electrons) for this particular collision system.

State-selective one-electron capture by multiply charged ions, investigated with a modified multichannel Landau-Zener model

The predictions of a multichannel Landau-Zener model, which includes Taulbjerg's fnl factor, for single-electron capture by multicharged ions, have been compared with different kinds of experimental results (electron, X, UV and energy gain spectroscopies). A reasonable agreement has been found for the populations of individual nl sublevels of capture when the electron-core interaction prevails over the l Stark mixing and when the rotational coupling can be ignored. This model has been tested with large core ions such as Ar8+ (2p6), Ar8+(2p53s 3P) and with ground state (C4+, N5+, O6+, Ne8+) and metastable 1s2s 3S (C4+, N5+) helium-like ions on various targets, below 0.5 au collision velocity.

High-resolution two-photon spectroscopy of the NO 23pσ 2Σ u+ Rydberg state

The high-resolution two-photon absorption spectrum of the X̃ 2A 1(000)→3pσ 2Σ u +(000) system in NO 2 shows rotational fine structure characteristic of a bent-to-linear transition. This structure is well fit by a simple Hamiltonian incorporating an upper state rotational constant B XXX = 0.419 ± 0.001 cm −1 and a spin-rotation coupling constant ψ = 0.150 ± 0.005 cm −1. These parameters evidence a somewhat contracted Rydberg core NO bond length of 1.126 ± 0.002 Å with moderate Rydberg electron-core interaction.

Ionicity-dependent structural properties of zinc-blende semiconductors

Structural properties of Si, AlP and MgS, obtained within the density-functional pseudopotential method, are analyzed as a function of crystal ionicity. For all considered crystals both kinetic and exchange-correlation energies are affected mostly by the pressure-induced density increase, whereas electron-core interaction and the Hartree energy are influenced mainly by the pressure-induced density metallisation. The role of the metallisation effect increases with ionicity, which leads to a qualitatively different pressure dependence of the electron gas energy for Si and MgS.

Model potential calculation of the electron affinity of lithium

Abstract A configuration interaction calculation, using model potential methods, is employed to evaluate the energy of the lowest 1S state of Li−. The model potential describing the valence electron-core interaction is chosen so as to reproduce the observed spectra of the neutral lithium atom with high precision. The calculated result of 0.591 eV is compared with other theoretical estimates and experimental data.

Erratum: Some New Applications of the FE Theory to the Spectra of Linear Unsaturated Compounds

A linear FE model with electron—electron and electron—core interaction appeared to be fairly accurate in reproducing the experimental data for (i) lowest excited singlet—triplet separation in polyenes, (ii) twisting frequencies of ethylene, and (iii) location of the absorption maxima in cumulenes. For calculations of (i) and (ii), electron—electron interaction has been assumed to play the dominant role. With the same assumption made, cis—trans isomerization of polyenes was found to be easier with long chains than with short. It also is easier about a central double bond in the chain than about an outer double bond. In the case of a single double bond, an important part of the energy path in isomerization is that for the triplet state; however, the role of triplet states in isomerization should diminish rapidly with an increase in the number of double bonds in the chain. With ethylene as the example, the effect of pi‐electron correlations in the FE model was briefly investigated, and the correlation for th...

Some New Applications of the FE Theory to the Spectra of Linear Unsaturated Compounds

A linear FE model with electron—electron and electron—core interaction appeared to be fairly accurate in reproducing the experimental data for (i) lowest excited singlet—triplet separation in polyenes, (ii) twisting frequencies of ethylene, and (iii) location of the absorption maxima in cumulenes. For calculations of (i) and (ii), electron—electron interaction has been assumed to play the dominant role. With the same assumption made, cis—trans isomerization of polyenes was found to be easier with long chains than with short. It also is easier about a central double bond in the chain than about an outer double bond. In the case of a single double bond, an important part of the energy path in isomerization is that for the triplet state; however, the role of triplet states in isomerization should diminish rapidly with an increase in the number of double bonds in the chain. With ethylene as the example, the effect of pi-electron correlations in the FE model was briefly investigated, and the correlation for the perturbation calculus of an order higher than the first was found to be in the FE model much less important than in the LCAO theory. No empirical parameters other than the fundamental atomic constants and the length of the FE path of a given molecule were used in the calculations.