Multiconfiguration Time-Dependent Hartree-Fock Treatment of Electronic and Nuclear Dynamics in Diatomic Molecules

The multiconfiguration time-dependent Hartree-Fock (MCTDHF) method is formulated for treating the coupled electronic and nuclear dynamics of diatomic molecules without the Born- Oppenheimer approximation. The method treats the full dimensionality of the electronic motion, uses no model interactions, and is in principle capable of an exact nonrelativistic description of diatomics in electromagnetic fields. An expansion of the wave function in terms of configurations of orbitals whose dependence on internuclear distance is only that provided by the underlying prolate spheroidal coordinate system is demonstrated to provide the key simplifications of the working equations that allow their practical solution. Photoionization cross sections are also computed from the MCTDHF wave function in calculations using short pulses.Comment: Submitted to Phys Rev

FERM3D: A finite element R-matrix electron molecule scattering code

FERM3D is a three-dimensional finite element program, for the elastic scattering of a low energy electron from a general polyatomic molecule, which is converted to a potential scattering problem. The code is based on tricubic polynomials in spherical coordinates. The electron-molecule interaction is treated as a sum of three terms: electrostatic, exchange. and polarisation. The electrostatic term can be extracted directly from ab initio codes ({\sc{GAUSSIAN 98}} in the work described here), while the exchange term is approximated using a local density functional. A local polarisation potential based on density functional theory [C. Lee, W. Yang and R. G. Parr, {Phys. Rev. B} {37}, (1988) 785] describes the long range attraction to the molecular target induced by the scattering electron. Photoionisation calculations are also possible and illustrated in the present work. The generality and simplicity of the approach is important in extending electron-scattering calculations to more complex targets than it is possible with other methods.Comment: 30 pages, 4 figures, preprint, Computer Physics Communications (in press

Two-photon ionization of Helium studied with the multiconfigurational time-dependent Hartree-Fock method

The multiconfigurational time-dependent Hartree-Fock method (MCTDHF) is applied for simulations of the two-photon ionization of Helium. We present results for the single- and double ionization from the groundstate for photon energies in the non-sequential regime, and compare them to direct solutions of the Schr\"odinger equation using the time-dependent (full) Configuration Interaction method (TDCI). We find that the single-ionization is accurately reproduced by MCTDHF, whereas the double ionization results correctly capture the main trends of TDCI

Ionization of pyridine: interplay of orbital relaxation and electron correlation

The valence shell ionization spectrum of pyridine was studied using the third-order algebraic-diagrammatic construction approximation scheme for the one-particle Green’s function and the outer-valence Green’s function method. The results were used to interpret angle resolved photoelectron spectra recorded with synchrotron radiation in the photon energy range of 17–120 eV. The lowest four states of the pyridine radical cation, namely, 2A2 (1a 2 −1 1a2−1 ), 2A1(7a 1 −1 7a1−1), 2B1(2b 1 −1 2b1−1), and 2B2(5b 2 −1 5b2−1), were studied in detail using various high-level electronic structure calculation methods. The vertical ionization energies were established using the equation-of-motion coupled-cluster approach with single, double, and triple excitations (EOM-IP-CCSDT) and the complete basis set extrapolation technique. Further interpretation of the electronic structure results was accomplished using Dyson orbitals, electron density difference plots, and a second-order perturbation theory treatment for the relaxation energy. Strong orbital relaxation and electron correlation effects were shown to accompany ionization of the 7a1 orbital, which formally represents the nonbonding σ-type nitrogen lone-pair (nσ) orbital. The theoretical work establishes the important roles of the π-system (π-π* excitations) in the screening of the nσ-hole and of the relaxation of the molecular orbitals in the formation of the 7a1(nσ)−1 state. Equilibrium geometric parameters were computed using the MP2 (second-order Møller-Plesset perturbation theory) and CCSD methods, and the harmonic vibrational frequencies were obtained at the MP2 level of theory for the lowest three cation states. The results were used to estimate the adiabatic 0-0 ionization energies, which were then compared to the available experimental and theoretical data. Photoelectron anisotropy parameters and photoionization partial cross sections, derived from the experimental spectra, were compared to predictions obtained with the continuum multiple scattering approach

Multiconfiguration methods for the numerical simulation of photoionization processes of many-electron atoms

Numerical simulations present an indispensable way to the understanding of physical processes. In quantum mechanics, where the theoretical description is given in terms of the time-dependent Schrödinger equation (TDSE), the road is, however, difficult for any but the simplest systems. This is particularly true if one considers photoionization processes of atoms and mole\-cules, which at the same time require an accurate description of bound and continuum states, and therefore an extensive region of space to be sampled during the calculation. As a consequence, direct simulations of photoionization processes are currently only feasible for systems composed of up to three particles. Despite this fundamental restriction, many physical effects can be essentially described by single- and two-electron models, among them high-order harmonic generation and non-sequential double-ionization of atoms and mole\-cules. A plethora of numerical investigations have been performed on atomic and molecular hydrogen and helium in the last two decades, and these have had a strong impact on the current understanding of photoionization. On the other hand, there are processes which are characterized by the interplay of a larger number of electrons, such as tunnel ionization, the Auger effect, and, to give a more recent example, the temporal delay between the photo-emission of electrons from different shells of neon and krypton. The many-electron character of these effects complicates the accurate, time-resolved simulation, and hence, no universally applicable method exists. The present work develops two theoretical methods which are promising candidates for closing this gap, the multiconfigurational time-dependent Hartree-Fock (MCTDHF) method and the time-dependent restricted active space configuration interaction (TD-RASCI) method. Both represent the wavefunction in a linear subspace of the many-body Hilbert space and follow particular strategies to avoid the exponential problem. This makes it possible to treat a much larger number of electrons than with the direct techniques mentioned previously. The MCTDHF method is already well established in the scientific community, but has been applied only rarely to photoionization processes so far. On the other hand, the TD-RASCI method is an original contribution, and is applied for the first time to solutions of the time-dependent Schrödinger equation. Further, through the invention of appropriate, grid-like single-particle basis sets, we adjust these general approaches to efficiently treat photoionization processes in many-electron atoms and molecules. After their thorough introduction, the MCTDHF and the TD-RASCI method are applied to several topics of photoionization physics. Among them is, first, the problem of calculating cross sections of atoms, for which we particularly consider helium, beryllium and neon. In most parts, this is accomplished for the first time in the framework of the developed methods. Next, we consider the two-photon double-ionization of helium, which has attracted considerable interest in recent years, and perform simulations with the MCTDHF method. We further apply the TD-RASCI method to study two-color pump-probe process in beryllium, the simulation of which requires an explicitly time-dependent treatment. We find that both methods are highly appropriate for accurately describing correlated single-ionization processes. Moreover, the TD-RASCI method is able to model relevant doubly-excited states, which are of central importance for a variety of physical processes.Trotz dieser fundamentalen Einschränkung lassen sich viele physikalische Effekte bereits durch Ein- und Zweiteilchenmodelle beschreiben, darunter zum Beispiel die Erzeugung höherer Harmonischer oder die nicht-sequentielle Doppelionisation. In diesem Sinne wurde in den letzten zwei Jahrzehnten eine Vielzahl numerischer Untersuchungen an atomarem und molekularem Wasserstoff sowie Helium unternommen, welche einen starken Einfluss auf das momentane Verständnis von Photoionisations-Prozessen nahmen. Andererseits gibt es jedoch physikalische Effekte, die durch das Zusammenwirken einer größeren Anzahl von Elektronen gekennzeichnet sind, etwa die Tunnel-Ionisation, der Auger-Effekt oder die kürzlich entdeckte zeitliche Verzögerung in der Emission von Elektronen aus verschiedenen atomaren Schalen von Neon und Krypton. Der immanente Vielteilchencharakter macht die zeitaufgelöste Simulation dieser Prozesse zu einer schwierigen Aufgabe, für die es bisher keine universell einsetzbare und gleichzeitig akkurate Methode gibt. In dieser Arbeit werden zwei theoretische Methoden zur Simulation von Photoionisations-Prozessen von Vielteilchenatomen und -molekülen vor\-gestellt, die vielversprechende Kandidaten zur Schließung dieser vorhandenen Lücke darstellen, nämlich die zeitabhängige Multikonfigurations-Hartree-Fock (MCTDHF) Methode sowie die zeitabhängige restricted-active-space Konfigurations-Wechselwirkungsmethode (TD-RASCI). Beide stellen die quantenmechanische Wellenfunktion in einem linearen Unterraum des Vielteilchen-Hilbertraumes dar und folgen dabei speziellen Ansätzen um das Problem des exponentiellen Wachstums zu vermeiden. Dadurch kann eine weitaus größere Teilchenzahl als mit der zuvor erwähnten direkten Technik simuliert werden. Weiterhin werden diese zunächst sehr allgemeinen Methoden durch den Gebrauch geeigneter Basissätze auf die effiziente Beschreibung von Photoionisations-Prozessen optimiert. Nach ihrer Einführung werden die MCTDHF und TD-RASCI Methode auf aktuelle Themen der Photoionisations-Physik angewandt. Zunächst wenden wir uns der Berechnung von Ionisations-Streuquerschnitten der Atome Helium, Beryllium und Neon zu, welche weitgehend zum ersten Male mithilfe der eingeführten Methoden untersucht wird. Des Weiteren studieren wir die Zwei-Photonen-Ionisation von Helium, der in jüngerer Zeit großes theoretisches Interesse zukam, mithilfe von Simulationen mit der MCTDHF Methode. Als grundlegendes Beispiel eines explizit zeitabhängigen Prozesses wird darüberhinaus die Pump-Probe Ionisation von Beryllium betrachtet. Unsere Untersuchungen zeigen, dass sowohl die MCTDHF Methode als auch die TD-RASCI Methode die Einelektronen-Photoionisation akkurat zu beschreiben vermag. Mithilfe der TD-RASCI Methode ist es zudem möglich, selektierte doppelt-angeregte Zustände in die Rechnung zu integrieren, welche eine zentrale Rolle bei einer Vielzahl physikalischer Prozesse spielen

Attosecond dynamics of collective electron effects in nanostructures and molecules

In this work several time-resolved experimental studies on collective electron phenomena are presented. The first set of measurements aims to reveal the dynamics of surface plasmon polaritons (SPP), which emerge as coherent excitation of quasi-free conduction band electrons at a metal-dielectric-interface. The experiments employ a pump-probe scheme, where a few-cycle near-infrared (NIR) laser pulse, considered as pump beam, excites SPPs at a nanostructure grating. After propagation towards a nanoscale apex, where adiabatic focusing and localization is observed, the SPP electric field is probed by a second few-cycle laser field with variable delay, which constitutes a direct replica of the pump beam. The cross-correlation of SPP and near-infrared probe beam at the apex facilitates multi-photon ionization (MPI) from the metal sample and allows to obtain the convoluted temporal dynamics of both electric fields from the delay-dependent photoionization yield. To achieve temporal resolution on the attosecond (1 as = 10^{−18} s) scale, consecutive studies are performed to demonstrate the applicability of the attosecond streaking technique to nanoscale electric near-fields. These proof-of-principle measurements are conducted on tapered gold (Au) nanowires, which are illuminated by a few-cycle near-infrared laser pulse. The superposition of incident and scattered laser field gives rise to a characteristic near-field at the streaking target surface. A synchronized, extreme-ultraviolet (XUV) laser pulse of attosecond temporal duration generates photoelectrons from the target, whose final kinetic energy is modulated whilst propagating through the electric near-field. Acquisition of delaydependent photoelectron energy spectra unambiguously shows the signature of the nanoscale near field, which appears phase shifted relative to the incident laser field. Experimental findings are supported by theoretical simulations, which consider the specific target geometry. Based on trajectory calculations, generic prerequisites on the experimental setup and target geometry are formulated to facilitate sampling of nanoscale electric fields with attosecond temporal resolution. In the third set of experiments, the fundamental influence of collective electron effects on photoionization delays is investigated using the attosecond streaking technique on gaseous ethyl iodide molecules. Here, the photon energy of the extreme-ultraviolet radiation is chosen to overlap with the giant dipole resonance of the 4d shell in atomic iodine. The resulting photoionization delays are referenced by a simultaneous streaking measurement on atomic neon. The experiments, performed at different XUV photon energies, reveal a drastic increase of photoionization delays with decreasing XUV photon energy. To explain the observed temporal delays, simulations at different levels of theory are performed, including ab initio, quantum scattering and semi-classical calculations. Besides collective electron effects, the influence from molecular orbitals on the obtained photoionization delays is discussed.In der vorliegenden Arbeit werden mehrere zeitaufgelöste, experimentelle Studien über die Dynamik kollektiver Elektronenphänomene vorgestellt. Im ersten Teil der Messungen wird versucht, die Dynamik von Oberflächenplasmonen (SPP) offenzulegen, die als kohärente Anregung an Grenzflächen zwischen Metallen und Dielektrika in Erscheinung treten. Die Experimente nutzen ein Pump-Probe Schema, wobei der Pumppuls einen wenige Zyklen umfassenden Laserpuls im nah-infraroten Spektralbereich darstellt, der die SPPs an einem nanostrukturierten Gitter erzeugt. Ausgehend vom Gitter breiten sich die SPPs in Richtung einer Nanospitze aus, an der das elektrische Feld der Plasmonen adiabatisch fokussiert und eingegrenzt wird. Mit einem zweiten, zeitlich verzögerten Laserpuls, der im Folgenden als Probepuls bezeichnet ist und eine direkte Kopie des Pumppulses darstellt, wird das elektrische Feld der SPPs untersucht. Die Überlagerung des elektrischen SPP-Feldes mit dem Probepuls führt zur Multi-Photonen Ionisation (MPI) der metallischen Probe. Aus der Ionisationsrate, die von der zeitlichen Verzögerung zwischen Pump- und Probepuls abhängt, ergibt sich die Dynamik von SPP und Probepuls als Faltung beider elektrischer Felder. Um eine zeitliche Auflösung auf der Attosekunden-Zeitskala (1 as = 10^{-18} s) zu ermöglichen, wurden weiterführende Untersuchungen durchgeführt, die die Anwendbarkeit des Attosekunden Streakings bei nanoskaligen elektrischen Feldern demonstrieren. Die Pilotexperimente wurden an konisch verjüngten Gold (Au) Nanodrähten durchgeführt. Dabei wurden die Proben von einem wenige Zyklen umfassenden Laserstrahl im nah-infraroten Spektralbereich beleuchtet, wodurch aus der Überlagerung von einfallendem und gestreutem Laserstrahl ein charakteristisches Nahfeld entsteht. Ein synchronisierter Attosekundenlaserstrahl im extremen ultravioletten (XUV) Spektralbereich führt zur Emission von Photoelektronen vom Nanodraht. Nach Propagation durch das elektrische Nahfeld wurde die kinetische Energie der Photoelektronen gemessen, die grundsätzlich von der zeitlichen Verzögerung zwischen XUV und NIR Laserstrahl abhängt. Im aufgenommen Spektrogramm der Photoelektronen zeigt sich die eindeutige Signatur des Nahfeldes, das im Vergleich zum einfallenden NIR Laserstrahl phasenverschoben erscheint. Die experimentellen Ergebnisse werden durch theoretische Simulationen, die die spezifische Probengeometrie berücksichtigen, unterstützt. Basierend auf Trajektorien Rechnungen, werden allgemeingültige Bedingungen an den experimentellen Aufbau sowie die Probengeometrie formuliert, unter denen die Untersuchung von nanoskaligen elektrischen Feldern möglich ist. Der dritte Teilbereich der Experimente untersucht den fundamentalen Einfluss kollektiver Elektroneneffekte auf die zeitliche Verzögerung der Photoionisation von gasförmigen Ethyliodidmolekülen unter Anwendung der Attosekunden Streaking-Methode. Die Photonenenergie des XUV Pulses wurde dabei so gewählt, dass die Ionisation im Bereich der Riesenresonanz der 4d-Elektronenschale des Iods erfolgt. Die Experimente, die bei verschiedenen XUV Photonenenergien durchgeführt wurden, offenbaren einen deutlichen Anstieg der Verzögerung der Photoionisation in Richtung niedrigerer XUV Energien. Um die zeitliche Verzögerung zu erklären, werden unterschiedliche theoretische Ansätze verfolgt, wobei semi-klassische, ab initio und Quanten-Streurechnungen durchgeführt werden. Neben den kollektiven Elektroneneffekten werden auch mögliche Einflüsse der Molekülorbitale diskutiert

Photoabsorption In Carbon Monoxide: Stieltjes-tchebycheff Calculations In The Separated-channel Static-exchange Approximation

Theoretical investigations of total and partial-channel photoabsorption cross sections in carbon monoxide are reported employing the Stieltjes-Tchebycheff (S-T) technique and separated-channel static-exchange calculations. Pseudospectra of discrete transition frequencies and oscillator strengths appropriate for individual excitations of each of the six occupied molecular orbitals are constructed using Hartree-Fock core functions and normalizable Gaussian orbitals to describe the photoexcited and ejected electrons. Use of relatively large basis sets of compact and diffuse functions insures the presence of appropriate discrete Rydberg states in the calculations and provides sufficiently dense pseudospectra for the determination of convergent photoionization cross sections from the S-T technique. The calculated discrete vertical electronic excitation spectra are in very good agreement with measured band positions and intensities, and the partial-channel photoionization cross sections are in correspondingly good accord with recent electron-electron (e,2e) coincidence, synchrotron-radiation, and line-source branching-ratio measurements. Predicted resonance features in the X, B, O2s -1, and carbon K-shell channels are in particularly good agreement with the positions and intensities in the measured cross sections. A modest discrepancy between experiment and theory in the A-channel cross section is tentatively attributed to channel-coupling mechanisms associated with opening of the 1π shell. The total vertical electronic S-T photoionization cross section for parent-ion production is in excellent agreement with recent electron-ion coincidence measurements. Comparisons are made between ionization processes in carbon monoxide and in the previously studied nitrogen molecule, and similarities and differences in the respective cross sections are clarified in terms of conventional molecular-orbital theory. © 1978 American Institute of Physics.6972992300

Photoionization Suppression by Continuum Coherence: Experiment and Theory

We present experimental and theoretical results of a detailed study of laser-induced continuum structures (LICS) in the photoionization continuum of helium out of the metastable state 2s $^1S_0$. The continuum dressing with a 1064 nm laser, couples the same region of the continuum to the {4s $^1S_0$} state. The experimental data, presented for a range of intensities, show pronounced ionization suppression (by as much as 70% with respect to the far-from-resonance value) as well as enhancement, in a Beutler-Fano resonance profile. This ionization suppression is a clear indication of population trapping mediated by coupling to a contiuum. We present experimental results demonstrating the effect of pulse delay upon the LICS, and for the behavior of LICS for both weak and strong probe pulses. Simulations based upon numerical solution of the Schr\"{o}dinger equation model the experimental results. The atomic parameters (Rabi frequencies and Stark shifts) are calculated using a simple model-potential method for the computation of the needed wavefunctions. The simulations of the LICS profiles are in excellent agreement with experiment. We also present an analytic formulation of pulsed LICS. We show that in the case of a probe pulse shorter than the dressing one the LICS profile is the convolution of the power spectra of the probe pulse with the usual Fano profile of stationary LICS. We discuss some consequences of deviation from steady-state theory.Comment: 29 pages, 17 figures, accepted to PR