Electron Thermal Runaway in Atmospheric Electrified Gases: a microscopic approach

Thesis elaborated from 2018 to 2023 at the Instituto de Astrofísica de Andalucía under the supervision of Alejandro Luque (Granada, Spain) and Nikolai Lehtinen (Bergen, Norway). This thesis presents a new database of atmospheric electron-molecule collision cross sections which was published separately under the DOI : With this new database and a new super-electron management algorithm which significantly enhances high-energy electron statistics at previously unresolved ratios, the thesis explores general facets of the electron thermal runaway process relevant to atmospheric discharges under various conditions of the temperature and gas composition as can be encountered in the wake and formation of discharge channels

Numerical Studies on Surplus Electrons in Polar Media

Accurate numerical solutions of the polarized cavity and semicontinuum models for excess electrons in polar media are derived. Part I presents the results of a numerical investigation of similar models for the surplus electron in crystalline solids. Here, the existence of a few analytical and numerical solutions affords an excellent check on the accuracy and efficiency of the presently-used finite-difference technique. In addition, the extent of amelioration produced in approximate variational treatments is disclosed. Some relevant theory is developed. In Part II the numerical technique is used in a thorough-going study of polarized cavity and semicontinuum models, within both the adiabatic and scf formulations, for the excess single-electron species. The considerable improvements effected on existing one-parameter variational approaches is demonstrated and several results are called into question. In particular the scf treatment of the polarized cavity model for the hydrated electron is shown to be inadequate. This refutes a recent, variationally-based claim to the contrary. In the realm of semicontinuum theories it is shown that the presently used parameterizations do, on accurate solution, no longer give concurrence with experimental data. While this could be renewed for any given observation by a more appropriate selection of variables, deviations will generally remain in the other predictions. It is shown to be unlikely that transitions to higher excited states contribute much to the observed band width, which the present treatments based on a single 1s-2p transition badly underestimate. Localized dielectron species form the subject of Part III. The numerical solution technique is carried through on similar levels of approximation in an attempt to resolve recent contradictory statements as to the dissociative stability of the ammoniated dielectron made by the alternative formulations of the semicontinuum model. The disparity remains. The introduction of a second solvation shell is effected in an attempt to reduce the computational differences of the models used, but to no avail. The adiabatic treatment prefers two singly-solvated species while an scf scheme favours a trapped dielectron. Absorption at doubly-charged sites is shown to be of doubtful importance in the observed spectrum. Clearly some major alterations in the present models are necessary. The contradiction has now been removed. More recent calculations have revealed that, within the semicontinuum model, the adiabatic approximation also favours stable dielectrons

Commemorative Issue in Honor of Professor Karlheinz Schwarz on the Occasion of His 80th Birthday

A collection of 18 scientific papers written in honor of Professor Karlheinz Schwarz's 80th birthday. The main topics include spectroscopy, excited states, DFT developments, results analysis, solid states, and surfaces

Accurate Prediction of Core Properties for Chiral Molecules using Pseudo Potentials

Pseudo potentials (PPs) constitute perhaps the most common way to treat relativity, often in a formally non-relativistic framework, and reduce the electronic structure to the chemically relevant part. The drawback is that orbitals obtained in this picture (called pseudo orbitals (POs)) show a reduced nodal structure and altered amplitude in the vicinity of the nucleus, when compared to the corresponding molecular orbitals (MOs). Thus expectation values of operators localized in the spatial core region that are calculated with POs, deviate significantly from the same expectation values calculated with all-electron (AE) MOs. This study describes the reconstruction of AE MOs from POs, with a focus on POs generated by energy consistent pseudo Hamiltonians. The method reintroduces the nodal structure into the POs, thus providing an inexpensive and easily implementable method that allows to use nonrelativistic, efficiently calculated POs for good estimates of expectation values of core-like properties. The discussion of the method proceeds in two parts: Firstly, the reconstruction scheme is developed for atomic cases. Secondly, the scheme is discussed in the context of MO reconstruction and successfully applied to numerous numerical examples. Starting from the equations of the state-averaged multi-configuration self- consistent field method, used for the generation of energy consistent pseudo potentials, the electronic spectrum of the many-electron Hamiltonian is linked to the spectrum of the effective one-electron Fock operator by means of various models systems. This relation and the Topp–Hopfield–Kramers theorem, are used to show the shape-consistency of energy-consistent POs for atomic systems. Shape-consistency describes POs that follow distinct AOs exactly outside a core-radius r_core . In the cases presented here, shape-consistency holds to a high degree and it follows that in atomic systems every PO has one distinct partner in the set of AOs. The overlap integral between these two orbitals is close to one, as it is determined mainly by the spatial orbital parts outside r_core . Expanding, e.g., a 5s PO in occupied AOs, the 5s AOs will have the highest contribution. The POs itself contains contributions from high-energy unoccupied AOs as well (e.g. 15s), which damp the nodal structure of the POs near the nucleus. Consequently, neglecting contributions from unoccupied orbitals in a projection of the POs reintroduces the nodal structure. This approach is not directly suitable for the reconstruction of MOs, as they often need to be expanded in a full set of AOs at each atomic center, including all unoccupied orbitals, to properly account for the electron density distribution in the molecule. However, it is shown that the occupied MOs are well described by occupied and low-energy unoccupied AOs only and a mapping of the POs onto a basis containing only these orbitals reconstructs the nodal structure of the MO. The approach uses only standard integrals available in most quantum chemistry programs. The computational cost of these integrals scales with N^2 , where N is the number of basis functions. The most time consuming step is a Gram-Schmidt orthogonalization, which scales in this implementation with MN^2 , M being the number of reconstructed orbitals. The reconstruction method is subsequently tested: Valence orbitals of atomic, closed-shell systems were reconstructed numerically exactly. The influence of numerical parameters is investigated using the molecule BaF . It is shown that the method is basis set dependent: One has to ensure that the PO basis can be expanded exactly in the basis of AOs. Violating this rule of thumb may degrade the quality of reconstructed orbitals. Additionally, the representation of MOs by a linear combination of occupied and unoccupied AOs is investigated. For the exemplary systems, the shells included in the fitting procedure of the PP were sufficient. Reconstruction of the alkaline earth monofluorides showed that periodic trends can be reconstructed as well. Scaling of hyperfine structure parameters with increasing atomic number is discussed. For hydrogenic atoms, the scaling should be linear, whereas small deviations from the linear behavior were observed for molecules. The scaling laws computed from reconstructed and reference orbitals were almost identical. In this context, the failure of commonly used relativistic enhancement factors beyond atomic number 100 is discussed. Applicability of the method is also tested on parity violating properties for which the main contribution is generated by the valence orbitals near the nucleus. Symmetry-independence of the method is shown by successful reconstruction of orbitals of the tetrahedral PbCl_4 and chiral NWHClF. The reliable reconstruction of chemical trends is shown with the help of the NWHClF derivatives NWHBrF and NWHFI. The study of chiral compounds as, e.g., NWHClF and its group 17 derivatives, which have been proposed as paradigm for the detection of parity-violation in chiral molecules, remains of great importance. Especially the direct determination of absolute configuration of chiral centers is still non-trivial. The author contributed to this field with a self-written molecular dynamics (MD) program to simulate Coulomb explosions and thus to provide an insight especially into the early explosion stages directly after an instantaneous multi-ionization of the molecule CHBrClF, comparable to experiments using the Cold Target Recoil Ion Momentum Spectroscopy (COLTRIMS) technique. An algorithm for the determination of the investigated molecule’s absolute configuration from time-of-flight data and detection locations of molecular fragments is included in the program. The program was used to generate experiment-equivalent data which allowed for the first time the investigation of non-racemic mixtures by the analysis routines of the experiment. The MD program includes harmonic and anharmonic bond potentials. A charge-exchange model can model partial charges in early phases of the Coulomb explosion. Furthermore, Born–Oppenheimer MD simulations and statistical models are used to explain the relative abundance of products belonging to competing reaction channels, as obtained by photoion coincidence measurements. Additionally, qualitative statements about reaction branching ratios are made by comparing the partition functions of involved degrees of freedom. Analytic equations for partition functions of simple models are used to provide a simple formula allowing fast estimates of reaction branching ratios

Applications of electronic structure theory to problems in strong-field chemistry, inorganic chemistry, and nanomaterial systems

This dissertation covers research performed on applications of electronic structure theory to various fields of chemistry and is divided into eight chapters. Chapters 2 through 4 describe a series of related works which explore applications of excited state electronic structure methods to problems in strong field chemistry. Chapters 5, 6, and 7 discuss the application of electronic structure theory methods to solving problems in inorganic chemistry. Finally, Chapter 8 looks at an application of electronic structure theory to nanomaterials. Chapter 2 covers the modeling of electron dynamics of butadiene interacting with a short, intense laser pulse in the absence of ionization This chapter lays down the ground work for the following two chapters by examining the effects of basis set size and number of excited states included in the TD-CI simulation on the amount of population transferred from the ground state into the excited states by the interaction with an short, intense, non-resonant laser pulse. This chapter focuses mostly on TD-CI simulations using excited state energies and transition dipole matrices found by wavefunction based methods: TD-HF, TD-CIS, and TD-CIS(D). Chapter 3 expands on the work established in Chapter 2 by examining the excited state populations of butadiene using excitation energies and transition dipoles calculated by time-dependent density functional theory. Several DFT functionals are tested including GGA, meta-GGA, hybrid and long-range corrected functionals. The degree to which excited state energies and transition dipoles contribute to the final populations of the excited states is also examined. Chapter 4 wraps up the series by including ionization using a heuristic ionization model. This chapter examines the strong-field ionization of a series of linear polyenes of increasing length: ethylene, butadiene, hexatriene, and octatetraene. Also tested is the ionization dependence on parameters of the ionization model, basis set size, and number of states included in the simulation. Chapters 5-7 discuss collaborative works with members of the inorganic division of chemistry at Wayne State University. Chapter 5 describes a study on a chiral pentadenate ligand synthesized by the Kodanko group and the geometrical preference for a single isomer out of five possible isomers. Electronic structure theory indicates that the favored geometry is due to the chiral ligand, which prefers to be in a single conformation in metal complexes due to steric interactions. Chapter 6 covers a paddlewheel dinculear Cu(II) complex synthesized by the Winter group. This complex has the shortest Cu--Cu separation reported to date and electronic structure theory is used to explore the cause of this small separation. A simple model is proposed where the metal separation is governed by twisting of the ligand due to interligand π orbital interactions. Chapter 7 describes work done in collaboration with the Verani group, exploring the redox properties of some five-coordinate Fe(III) complexes. Chapter 8 sets out to develop an inexpensive model that can be used to optimize guest systems inside single walled nanotubes. The model takes advantage of the highly polarizable nature of nanotubes. The model is calibrated using a simple hydrogen bonded system and comparisons are made to test the reliability of the model

Colloquium: Nonlinear collective interactions in quantum plasmas with degenerate electron fluids

The current understanding of some important nonlinear collective processes in quantum plasmas with degenerate electrons is presented. After reviewing the basic properties of quantum plasmas, we present model equations (e.g. the quantum hydrodynamic and effective nonlinear Schr\"odinger-Poisson equations) that describe collective nonlinear phenomena at nanoscales. The effects of the electron degeneracy arise due to Heisenberg's uncertainty principle and Pauli's exclusion principle for overlapping electron wavefunctions that result in tunneling of electrons and the electron degeneracy pressure. Since electrons are Fermions (spin-1/2), there also appears an electron spin current and a spin force acting on electrons due to the Bohr magnetization. The quantum effects produce new aspects of electrostatic (ES) and electromagnetic (EM) waves in a quantum plasma that are summarized in here. Furthermore, we discuss nonlinear features of ES ion waves and electron plasma oscillations (ESOs), as well as the trapping of intense EM waves in quantum electron density cavities. Specifically, simulation studies of the coupled nonlinear Schr\"odinger (NLS) and Poisson equations reveal the formation and dynamics of localized ES structures at nanoscales in a quantum plasma. We also discuss the effect of an external magnetic field on the plasma wave spectra and develop quantum magnetohydrodynamic (Q-MHD) equations. The results are useful for understanding numerous collective phenomena in quantum plasmas, such as those in compact astrophysical objects, in plasma-assisted nanotechnology, and in the next-generation of intense laser-solid density plasma interaction experiments.Comment: 25 pages, 14 figures. To be published in Reviews of Modern Physic

Aspects of charge exchange in ion-atom collisions

The straight line semi-classical Impact Parameter method has been modified for use with classical trajectories. Ion-atom collisions have been modelled using wavefunctions expanded in terms of atomic basis states which were centred on either the target or projectile ions. Total and differential charge exchange cross-sections are presented for (^4)He(^++) and (^4)He(^+) collisions within the centre of mass energy range 0.21 kev < E(_em) < 2.5 keV. Results using curved and straight line paths are compared with data from other authors. Significant trajectory effects were found at the lower energies in the range. The curved trajectory results were lower than those from the straight line model and also lower than previous calculations carried out. At higher energies in the range there was good agreement between straight line and curved trajectory models and previous work. Differential cross-sections were found to be sensitive to the trajectories employed, and comparisons have been made with previous work. Total, state specific and differential cross- sections for charge exchange are presented for Be(^++) and H collisions using a five state basis, within the centre of mass energy range 0.111 keV < E(_em) < 0.4444 keV. There was reasonable agreement between the straight line results and previous work. There were significant trajectory effects for all the final charge transfer states. Results are presented for low-energy collisions between positively charged muons and atomic hydrogen. An eight state basis has been used. Direct excitation cross sections for n = 2 atomic states and charge transfer cross sections to Is and n = 2 have been calculated. The effect on the cross sections of using different internuclear potentials has been examined. Trajectory effects were small for charge transfer to Is but were more pronounced in the direct excitation and charge exchange cross- sections to n = 2. These results have been compared to those obtained for curved trajectory H(^+) and H collisions at the same relative velocity, to assess the validity of velocity scaling. It was found that velocity scaling was reliable for charge transfer to Is and for total electron capture cross-sections. However, it was progressively inaccurate for direct excitation and for electron capture into excited states for µ(^+) impact energies of less than 300 eV. These results are discussed and suggestions for further work are made