Methoden der Dichtefunktionaltheorie (DFT) sind beliebte quantenmechanische (QM) Verfahren. Einige Größen, wie z.B. Dispersionsenergien oder Reaktionsbarrieren, werden mit Standardfunktionalen jedoch schlecht beschrieben. Solche Probleme sind für kleine Systeme mit Elektronenkorrelationsmethoden lösbar. In dieser Arbeit wird ein Hybridansatz vorgestellt, der Vorzüge von DFT und Elektronenkorrelationsmethoden vereint. Dazu erfolgen DFT-Rechnungen für das Gesamtsystem und ein darin eingebettetes Modell des aktiven Zentrums. Dieses wird außerdem mit Moller–Plesset Störungstheorie zweiter Ordnung (MP2) zur Korrektur entsprechender DFT-Werte beschrieben. Die Zuverlässigkeit so erzielter Ergebnisse wird durch Extrapolation auf den Grenzfall einer vollständigen Orbitalbasis und eines unverkleinerten Modells erhöht. MP2-Korrekturen werden für eine Reihe unterschiedlich großer Modelle ermittelt. Daran wird ein C6-Paarpotential angepasst, das auch für das (periodische) Gesamtsystem die Ableitung von Werten in MP2-Qualität erlaubt. Zur Anwendung der Hybridmethode in der Katalyseforschung werden Protonensprünge im Zeolith Chabasit und Protonierungsreaktionen von Isobuten im Zeolith Ferrierit untersucht. Die MP2/DFT-Ergebnisse bestätigen, dass Aktivierungsbarrieren mit einfachen Dichtefunktionalen unterschätzt werden. Geschwindigkeitskonstanten sind nach Korrektur um ein bis zwei Größenordnungen kleiner. DFT-Adsorptions- und -Chemisorptionsenergien für Kohlenwasserstoffe in Zeolithen sind nicht verlässlich. Unterschiedlich große MP2-Korrekturen für die untersuchten Produkte liegen in einem Bereich von –29 bis –70 kJ/mol. Gegenüber dem wasserstoffgebundenen tert-Butylcarbeniumion profitieren Oberflächenalkoxide energetisch am meisten von der Erfassung der Dispersion. Die berechnete MP2-Adsorptionswärme des Isobutens im Zeolith Ferrierit (–74+–10 kJ/mol) entspricht experimentellen Anhaltspunkten und zeigt die Zuverlässigkeit des in dieser Arbeit vorgestellten Hybridansatzes. / Density functional theory (DFT) belongs to the most popular computational approaches in quantum mechanics (QM). For certain terms, e.g., dispersion energies or reaction barriers, widely used functionals do not yield reliable results. For small systems these problems can be overcome by using electron correlation methods. In this work a hybrid approach is presented combining advantages of both DFT and electron correlation methods. DFT calculations are performed for the full system and an embedded model representing the active site. The embedded model is also described by second-order Moller–Plesset perturbation theory (MP2) to obtain corrections to corresponding DFT values. The reliability of the results obtained with this hybrid method is further improved by extrapolation to the limiting case of a complete orbital basis set and an unreduced model system. MP2 corrections are obtained for a series of models of increasing size to fit a C6 pair potential. The fitted potential is applied to the full (periodic) system yielding results of MP2 quality. The hybrid method is applied in the field of catalysis research to investigate proton jump reactions in the zeolite chabazite and protonation reactions of isobutene in the zeolite ferrierite. The MP2/DFT results obtained confirm that with purely gradient corrected density functionals reaction barriers are clearly underestimated. Rate constants are corrected by one to two orders of magnitude. DFT reaction energies for adsorption and chemisorption of hydrocarbons in zeolites are not reliable. MP2 corrections obtained range between –29 and –70 kJ/mol and are not the same for different products. Compared to the hydrogen-bonded tert-butyl carbenium ion the surface alkoxides benefit most from treating dispersion explicitly. The calculated MP2 heat of adsorption of isobutene in ferrierite (–74+–10 kJ/mol) corresponds to experimental clues and underlines the reliability of the hybrid MP2/DFT approach presented in this work.

In dieser Doktorarbeit untersuchen wir den Einfluss von Elektron-Phonon-Wechselwirkungen (EPW) auf die Bandlueckenrenormierung in kristallinen Festkoerpern bei endlichen Temperaturen. Das Hauptziel besteht darin, den Einfluss der Kernbewegung und der thermischen Ausdehnung des Gitters auf die Bandstruktur in einer Vielzahl von Materialien zu quantifizieren. Zu diesem Zweck wird der Temperatureinfluss auf das EPW in harmonischen Naeherungen unter Verwendung der stochastischen Abtastmethode und vollstaendig anharmonisch durch Durchführung von ab initio Molekulardynamiksimulationen (aiMD). Die Bandluecke bei endlichen Temperaturen wird aus der thermodynamisch gemittelten Spektralfunktion extrahiert, die unter Verwendung der Bandentfaltungstechnik berechnet wird. Waehrend die Verwendung von aiMD bereits fuer Berechnungen von EPW verwendet wurde, wurde die Kombination von aiMD und Bandentfaltung zur Behandlung der Bandluecken renormalisierung erst kuerzlich verwendet. In dieser Doktorarbeit haben wir eine verbesserte Bandentfaltungstechnik verwendet, um die Berechnung effektiv zu verwalten. Diese verbesserte Methode enthaelt mehrere methodische Neuerungen, die dazu dienen, den Rechenaufwand zu verringern und das statistische Rauschen in den Endergebnissen zu minimieren. Die aktualisierte Methode wurde gruendlich bewertet, dokumentiert und mit einer benutzerfreundlichen Oberflaeche gestaltet. Wir praesentieren eine umfassende Untersuchung der numerischen Aspekte der thermodynamischen Mittelung, der Schaetzung von Fehlerbalken und der Bewertung der Konvergenz in Bezug auf die Groesse der Simulationssuperzelle. Unser etabliertes Protokoll ermoeglicht die Berechnung der Bandlückenrenormierung bei endlichen Temperaturen, was in guter Uebereinstimmung mit frueheren theoretischen Studien und experimentellen Daten steht. / In this thesis, we investigate the influence of electron-phonon interactions (EPI) on the band gap renormalization in crystalline solids at finite temperatures. The main goal is to identify the impact of the nuclear motion and the lattice thermal expansion on the band structure in a wide range of materials. For this purpose, the temperature influence on the EPI is calculated in the harmonic approximations by utilizing the stochastic sampling methodology and fully anharmonically, by performing ab initio molecular dynamics simulations (aiMD). The band gap at finite temperatures is extracted from the thermodynamically averaged spectral function, which is calculated using band-unfolding technique. While utilization of aiMD was already used for calculations of EPI the combination of aiMD and band-unfolding to treat the band gap renormalization was used only recently. In this thesis, we employed an improved band unfolding technique in order to effectively manage the calculations. This improved method incorporates several methodological innovations that serve to mitigate computational cost and minimize statistical noise in the final results. The updated method was thoroughly benchmarked, documented, and designed with a user-friendly interface. We present a comprehensive examination of the numerical aspects of thermodynamic averaging, the estimation of error bars, and the evaluation of convergence with respect to the size of the simulation supercell. Our established protocol enables the calculation of band gap renormalization at finite temperatures, which is in good agreement with prior theoretical studies and experimental data.

Substitutional dopants in III-V semi-conductors, such as Si atoms in GaAs, are of great interest for the applications in transistors, Schottky diodes, and doping super-lattices which have been widely employed to control the electrical properties of semi-conductors. Although Si doped GaAs systems have been intensively investigated theoretically and experimentally in the last several decades, some properties are still debated. In order to give a further explanation of Si doped GaAs systems, we systematically studied DX center in bulk GaAs and in GaAs(110), as well as the relative stabilities of different charged systems for Si atom replacing Ga atom at the substitutional site near GaAs(110) surface from first principles ground state method. We show that DX centre is a metastable state in bulk GaAs and completely unstable in the top few layers of GaAs(110). When Si atom replaces Ga atom at the surface, Charge states have an important influence on the stability of the system, and the additional charge is mainly concentrated on the Si atom for charged system. In addition, we studied the STM images of clean GaAs(110) and charged Si:GaAs(110) by employing Tersoff-Hamann approximation. The calculated STM images are in good agreement with experimental results. We show that at the positive bias voltage the positively charged Si atom presents a bright feature while the negatively charged Si atom shows a dark feature. In a semi-conductor, all bands are either completely full or completely empty. It is well known that DFT underestimates the band gaps of semi-conductors, a simple rigid shift can be used to correct the band energies of semi-conductors. Unlike semi-conductor, the fermi energies of metals lie in some bands. Furthermore, it turned out that some noble metals such as Cu and Ag depend on the considered band and k point , therefore, the so-called scissors operator can not be used for the metallic systems. The most successful approach within theoretical method for these metals is the many body perturbation theory. On the other hand, an interesting study for metals is quasi-particle excitations, which play an important role in a rich variety of physical and chemical phenomena such as energy transfer in photochemical reaction, desorption and oxidation of molecules at surfaces, spin transport within bulk metals, across interfaces, and at surfaces. One of the crucial properties of quasi-particle excitation is their lifetimes which determine the duration of these excitations. We carried out the calculations of quasi-particle band-structures and lifetimes for noble metals Cu and Ag within the GW approximation. For Cu, both the calculated positions of the d bands and the width of the d bands is within 0.1 eV compared to the experimental results. For Ag, partial core correction should be included in the pseudo-potential to get reliable positions of the d bands. The calculated lifetime agree with the experiment in the energy region away from the Fermi level, but deviates from the experimental results near the Fermi level where short range interactions which GW approach fails to describe play an important role. For a better description of the lifetime near the Fermi level, higher terms beyond the GW approximation in the many body perturbation theory need to be considered. In addition, the image potential state lifetimes in Cu(100) have been calculated using GW approximation based on the localized Gaussian basis set, and the calculated n=1, 2 imagepotential state lifetimes are in good agreement with experimental results.

<div>Photoconductive Semiconductor Switches (PCSS) are metal-semiconductor-metal devices used to switch an electrical signal through photoconduction. Rapidly switched PCSS under high bias voltages have shown remarkable potential for high power electronic and electromagnetic wave generation, but are dependent on precise optoelectronic material parameters such as defect ionization energy and optical absorption. These properties can be measured but are difficult to attribute definitively to specific defects and materials without the aid of high-accuracy, predictive modeling and simulation. This work combines well-established methods for first principles electronic structure calculations such as Density Functional Theory (DFT) with novel modern approaches such as Local Moment Counter Charge (LMCC) boundary conditions to adequately describe charge states and Maximally Localized Wannier Functions (MLWF) to render the summation of optical excitation paths as computationally tractable. This approach is demonstrated to overcome previous barriers to obtaining reliable qualitative or quantitative results, such as DFT band gap narrowing and the prohibitive computational cost of coupled electron-phonon processes. This work contributes electronic structure calculations of 4H-SiC doped with first-row transition metals (V through Ni) that are consistent with prior published work where applicable and add new possibilities for prospective semi-insulating metal-semiconductor systems where investigating new dopant possibilities. The results indicate a spectrum of highly localized, mid-gap, spin-dependent defect energy levels which suggest a wider range of potential amphoteric dopants suitable for producing semi-insulating material. Additionally, this work contributes MLWF-based calculations of phonon-resolved optical properties in 3C and 4H-SiC, indirect gap semiconductors, which accurately produce the expected onset of optical absorption informed by experiment. These results were further expanded upon with small V-doped cells of 4H-SiC, which while not fully converged in terms of cell size still provided a qualitative point of comparison to the ground state results for determining the true optical excitation energy required for substantial photoconductivity. The subsequent speculative analysis suggests the importance of anisotropic absorption and alternative metal defects for optimizing high current optoelectronic devices such as PCSS.</div>

Chemische Reaktionen in der Natur sowie Prozesse in synthetischen Materialien werden oft erst durch die Wechselwirkung von Licht mit Materie ausgelöst. Üblicherweise werden diese komplexen Prozesse mit Hilfe von Näherungen beschrieben. Im ersten Teil der Arbeit wird die Gültigkeit der Born-Oppenheimer Näherung in einem vibronischen Modellsystem (Trans-Polyacetylene) unter Photoelektronenspektroskopie im Gleichgewicht sowie zeitaufgelöster Photoelektronenspektroskopie im Nichtgleichgewicht überprüft. Die vibronische Spektralfunktion zeigt aufgrund des faktorisierten Anfangs- und Endzustandes in der Born-Oppenheimer Näherung zusätzliche Peaks, die in der exakten Spektralfunktion nicht auftreten. Im Nichtgleichgewicht zeigen wir für eine Franck-Condon Anregung und eine Anregung mit Pump-Probe Puls, wie die Bewegung des vibronischen Wellenpaktes im zeitabhängigen Photoelektronenspektrum verfolgt werden kann. Im zweiten Teil der Arbeit werden sowohl die Materie als auch das Licht quantisiert behandelt. Für eine volle quantenmechanische Beschreibung des Elektron-Licht Systems, verwenden wir die kürzlich entwickelte quantenelektrodynamische Dichtefunktionaltheorie (QEDFT) für gekoppelte Elektron-Photon Systeme. Wir zeigen erste numerische QEDFT-Berechnungen voll quantisierter Atome und Moleküle in optischen Kavitäten, die an das quantisierte elektromagnetische Feld gekoppelt sind. Mit Hilfe von Fixpunktiterationen berechnen wir das exakte Kohn-Sham Potential im diskreten Ortsraum, wobei unser Hauptaugenmerk auf dem Austausch-Korrelations-Potential liegt. Wir zeigen die erste Näherung des Austausch-Korrelations-Potentials mit Hilfe eines optimierten effektiven Potential Ansatzes angewandt auf einen Jaynes-Cummings-Dimer. Die dieser Arbeit zugrunde liegenden Erkenntnisse und Näherungen ermöglichen es neuartige Phänomene an der Schnittstelle zwischen den Materialwissenschaften und der Quantenoptik zu beschreiben. / Many natural and synthetic processes are triggered by the interaction of light and matter. All these complex processes are routinely explained by employing various approximations. In the first part of this work, we assess the validity of the Born-Oppenheimer approximation in the case of equilibrium and time-resolved nonequilibrium photoelectron spectra for a vibronic model system of Trans-Polyacetylene. We show that spurious peaks appear for the vibronic spectral function in the Born-Oppenheimer approximation, which are not present in the exact spectral function of the system. This effect can be traced back to the factorized nature of the Born-Oppenheimer initial and final photoemission states. In the nonequilibrium case, we illustrate for an initial Franck-Condon excitation and an explicit pump-pulse excitation how the vibronic wave packet motion can be traced in the time-resolved photoelectron spectra as function of the pump-probe delay. In the second part of this work, we aim at treating both, matter and light, on an equal quantized footing. We apply the recently developed quantum electrodynamical density-functional theory, (QEDFT), which allows to describe electron-photon systems fully quantum mechanically. We present the first numerical calculations in the framework of QEDFT. We focus on the electron-photon exchange-correlation contribution by calculating exact Kohn-Sham potentials in real space using fixed-point inversions and present the performance of the first approximate exchange-correlation potential based on an optimized effective potential approach for a Jaynes-Cummings-Hubbard dimer. This work opens new research lines at the interface between materials science and quantum optics.

Advances in the knowledge of chemical structure of coal and development of high performance computational techniques led to more than hundred and thirty four proposed molecular level representations (models) of coal between 1942 and 2010. These models were virtually on the carboniferous coals from the northern hemisphere. There are only two molecular models based on the inertinite- and vitrinite-rich coals from the southern hemisphere. The current investigation is based on the chars derived from the Permian-aged coals in two major South African coalfields, Witbank #4 seam and Waterberg Upper Ecca. The two coals were upgraded to 85 and 93% inertinite- and vitrinite-rich concentrates, on visible mineral matter free basis. The coals were slow heated in inert atmosphere at 20 ℃ min-1 to 450, 700 and 1000 ℃ and held at that temperature for an hour. After the HCl-HF treatment technique at ambient temperatures, the characteristics of the coals and chars were examined with proximate, ultimate, helium density, porosity, surface area, petrographic, solid-state 13C NMR, XRD and HRTEM analytical techniques. The results largely showed that substantial transitions occurred at 700-1000 ℃, where the chars became physically different but chemically similar. Consequently, the chars at the highest temperature (1000 ℃) drew attention to the detailed study of the atomistic properties that may give rise to different reactivity behaviours with CO2 gas. The H/C atomic ratios for the inertinite- and vitrinite-rich chars were respectively 0.31 and 0.49 at 450 ℃ and 0.10 and 0.12 at 1000 ℃. The true density was respectively 1.48 and 1.38 g.cm-3 at 450 ℃ and 1.87 and 1.81 g.cm-3 at 1000 ℃. The char form results from the petrographic analysis technique indicated that the 700-1000 ℃ inertinite-rich chars have lower proportions of thick-walled isotropic coke derived from pure vitrinites (5-8%) compared with the vitrinite-rich chars (91-95%). This property leads to the creation of pores and increases of volume and surface area as the softening walls expand. It was found that the average crystallite diameter, La, and the mean length of the aromatic carbon fringes from the XRD and HRTEM techniques, respectively, were in good agreement and made a definite distinction between the 1000 ℃ inertinite- and vitrinite-rich chars. The crystallite diameter on peak (10) approximations, La(10), of 37.6Å for the 1000 ℃ inertinite-rich chars fell within the HRTEM’s range of minimummaximum length boundary of 11x11 aromatic fringes (27-45Å). The La (10) of 30.7Å for the vitrinite-rich chars fell nearly on the minimum-maximum length range of 7x7 aromatic fringes (17-28Å.) The HRTEM results showed that the 1000 ℃ inertinite-rich chars comprised a higher distribution of larger aromatic fringes (11x11 parallelogram catenations) compared with a higher distribution of smaller aromatic fringes (7x7 parallelogram catenations). The mechanism for the similarity between the 700-1000 ℃ inertinite- and vitrinite-rich chars was the greater transition occurring in the vitrinite-rich coal to match the more resistant inertinite-rich coal. This emphasised that the transitions in the properties of vitrinite-rich coals were more thermally accelerated than those of the inertinite-rich coals. The similarity between the inertinite- and vitrinite-rich chars was shown by the total maceral reflectance, proximate, ultimate, skeletal density and aromaticity results. Evidence for this was the carbon content by mass for the inertinite- and vitrinite-rich chars of respectively 90.5 and 85.3% at 450 ℃ and 95.9 and 94.1% at 1000 ℃. The aromaticity from the XRD technique was respectively 87 and 77% at 450 ℃ and 98 and 96% at 1000 ℃. A similar pattern was found in the hydrogen and oxygen contents, the atomic O/C ratios and the aromaticity from the NMR technique. The subsequent construction of large-scale molecular structures for the 1000 ℃ inertinite-rich chars comprised 106 molecules constructed from a total of 42929 atoms, while the vitrinite-rich char model was made up of 185 molecules consisting of a total of 44315 atoms. The difference between the number of molecules was due to the inertinite-rich char model comprising a higher distribution of larger molecules compared with the vitrinite-rich char model, in agreement with the XRD and HRTEM results. These char structures were used to examine the behaviour on the basis of gasification reactivity with CO2. The density functional theory (DFT) was used to evaluate the interactions between CO2 and the atomistic representations of coal char derived from the inertinite- and vitrinite rich South African coals. The construction of char models used the modal aromatic fringes (fringes of highest frequencies in size distributions) from the HRTEM, for the inertinite- and vitrinite-rich chars, respectively (11x11 and 7x7 parallelogram-shaped aromatic carbon rings). The structures were DFT geometrically optimized and used to measure reactivity with the Fukui function, f+(r) and to depict a representative reactive carbon edge for the simulations of coal gasification reaction mechanism with CO2 gas. The f+(r) reactivity indices of the reactive edge follows the sequence: zigzag C remote from the tip C (Czi = 0.266) > first armchair C (Cr1 = 0.087) > tip C (Ct = 0.075) > second armchair C (Cr2 = 0.029) > zigzag C proximate to the tip C (Cz = 0.027). The DFT simulated mean activation energy, ΔEb, for the gasification reaction mechanism (formation of second CO gas molecule) was 233 kJ mol-1. The reaction for the formation of second CO molecule is defines gasification in essence. The experimental activation energy determined with the TGA and random pore model to account essentially for the pore variation in addition to the gasification chemical reaction were found to be very similar: 191 ± 25 kJ mol-1 and 210 ± 8 kJ mol-1; and in good agreement with the atomistic results. The investigation gave promise towards the utility of molecular representations of coal char within the context of fundamental coal gasification reaction mechanism with CO2. / PhD (Chemical Engineering), North-West University, Potchefstroom Campus, 2015

Advances in the knowledge of chemical structure of coal and development of high performance computational techniques led to more than hundred and thirty four proposed molecular level representations (models) of coal between 1942 and 2010. These models were virtually on the carboniferous coals from the northern hemisphere. There are only two molecular models based on the inertinite- and vitrinite-rich coals from the southern hemisphere. The current investigation is based on the chars derived from the Permian-aged coals in two major South African coalfields, Witbank #4 seam and Waterberg Upper Ecca. The two coals were upgraded to 85 and 93% inertinite- and vitrinite-rich concentrates, on visible mineral matter free basis. The coals were slow heated in inert atmosphere at 20 ℃ min-1 to 450, 700 and 1000 ℃ and held at that temperature for an hour. After the HCl-HF treatment technique at ambient temperatures, the characteristics of the coals and chars were examined with proximate, ultimate, helium density, porosity, surface area, petrographic, solid-state 13C NMR, XRD and HRTEM analytical techniques. The results largely showed that substantial transitions occurred at 700-1000 ℃, where the chars became physically different but chemically similar. Consequently, the chars at the highest temperature (1000 ℃) drew attention to the detailed study of the atomistic properties that may give rise to different reactivity behaviours with CO2 gas. The H/C atomic ratios for the inertinite- and vitrinite-rich chars were respectively 0.31 and 0.49 at 450 ℃ and 0.10 and 0.12 at 1000 ℃. The true density was respectively 1.48 and 1.38 g.cm-3 at 450 ℃ and 1.87 and 1.81 g.cm-3 at 1000 ℃. The char form results from the petrographic analysis technique indicated that the 700-1000 ℃ inertinite-rich chars have lower proportions of thick-walled isotropic coke derived from pure vitrinites (5-8%) compared with the vitrinite-rich chars (91-95%). This property leads to the creation of pores and increases of volume and surface area as the softening walls expand. It was found that the average crystallite diameter, La, and the mean length of the aromatic carbon fringes from the XRD and HRTEM techniques, respectively, were in good agreement and made a definite distinction between the 1000 ℃ inertinite- and vitrinite-rich chars. The crystallite diameter on peak (10) approximations, La(10), of 37.6Å for the 1000 ℃ inertinite-rich chars fell within the HRTEM’s range of minimummaximum length boundary of 11x11 aromatic fringes (27-45Å). The La (10) of 30.7Å for the vitrinite-rich chars fell nearly on the minimum-maximum length range of 7x7 aromatic fringes (17-28Å.) The HRTEM results showed that the 1000 ℃ inertinite-rich chars comprised a higher distribution of larger aromatic fringes (11x11 parallelogram catenations) compared with a higher distribution of smaller aromatic fringes (7x7 parallelogram catenations). The mechanism for the similarity between the 700-1000 ℃ inertinite- and vitrinite-rich chars was the greater transition occurring in the vitrinite-rich coal to match the more resistant inertinite-rich coal. This emphasised that the transitions in the properties of vitrinite-rich coals were more thermally accelerated than those of the inertinite-rich coals. The similarity between the inertinite- and vitrinite-rich chars was shown by the total maceral reflectance, proximate, ultimate, skeletal density and aromaticity results. Evidence for this was the carbon content by mass for the inertinite- and vitrinite-rich chars of respectively 90.5 and 85.3% at 450 ℃ and 95.9 and 94.1% at 1000 ℃. The aromaticity from the XRD technique was respectively 87 and 77% at 450 ℃ and 98 and 96% at 1000 ℃. A similar pattern was found in the hydrogen and oxygen contents, the atomic O/C ratios and the aromaticity from the NMR technique. The subsequent construction of large-scale molecular structures for the 1000 ℃ inertinite-rich chars comprised 106 molecules constructed from a total of 42929 atoms, while the vitrinite-rich char model was made up of 185 molecules consisting of a total of 44315 atoms. The difference between the number of molecules was due to the inertinite-rich char model comprising a higher distribution of larger molecules compared with the vitrinite-rich char model, in agreement with the XRD and HRTEM results. These char structures were used to examine the behaviour on the basis of gasification reactivity with CO2. The density functional theory (DFT) was used to evaluate the interactions between CO2 and the atomistic representations of coal char derived from the inertinite- and vitrinite rich South African coals. The construction of char models used the modal aromatic fringes (fringes of highest frequencies in size distributions) from the HRTEM, for the inertinite- and vitrinite-rich chars, respectively (11x11 and 7x7 parallelogram-shaped aromatic carbon rings). The structures were DFT geometrically optimized and used to measure reactivity with the Fukui function, f+(r) and to depict a representative reactive carbon edge for the simulations of coal gasification reaction mechanism with CO2 gas. The f+(r) reactivity indices of the reactive edge follows the sequence: zigzag C remote from the tip C (Czi = 0.266) > first armchair C (Cr1 = 0.087) > tip C (Ct = 0.075) > second armchair C (Cr2 = 0.029) > zigzag C proximate to the tip C (Cz = 0.027). The DFT simulated mean activation energy, ΔEb, for the gasification reaction mechanism (formation of second CO gas molecule) was 233 kJ mol-1. The reaction for the formation of second CO molecule is defines gasification in essence. The experimental activation energy determined with the TGA and random pore model to account essentially for the pore variation in addition to the gasification chemical reaction were found to be very similar: 191 ± 25 kJ mol-1 and 210 ± 8 kJ mol-1; and in good agreement with the atomistic results. The investigation gave promise towards the utility of molecular representations of coal char within the context of fundamental coal gasification reaction mechanism with CO2. / PhD (Chemical Engineering), North-West University, Potchefstroom Campus, 2015

In this thesis, a series of computational studies based on density functional theory (DFT) and density functional tight-binding (DFTB) is presented to deeply understand experimental results on the synthesis of endohedral fullerenes and graphene/iron hybrids at atomic level. In the first part, a simple and efficient model is proposed to evaluate the strain experienced by clusters encapsulated in endohedral metallofullerenes (EMFs). Calculations for the sole cluster, either in the neutral or the charged state, cannot be used for this goal. However, when the effect of the carbon cage is mimicked by small organic π-systems (such as pentalene and sumanene), the cluster has sufficient freedom to adopt the optimal configuration, and therefore the energetic characteristics of the EMF-induced distortion of the cluster can be evaluated. Both nitride and sulfide clusters were found to be rather flexible. Hence, they can be encapsulated in carbon cages of different size and shape. For carbide M2C2 cluster the situation is more complex. The optimized cluster can adopt either butterfly or linear shapes, and these configurations have substantially different metal-metal distance. Whereas for Sc2C2 both structures are isoenergetic, linear form of the Y2C2 cluster is substantially less stable than the butterfly-shaped configuration. These results show that phenomenon of the “nanoscale fullerene compression” once proposed by Zhang et al. (J. AM. CHEM. SOC. (2012),134(20)) should be “nanoscale fullerene stretching”. Finally, the results also reveal that both Ti2S and Ti2C2 cluster are strained in corresponding EMF molecules, but the origin of the strain is opposite: C78-D3h(5) cage imposes too long Ti···Ti distance for the sulfide cluster and too short distance for the carbide cluster. In the second part of the thesis, possible fullerene geometries and electronic structures have been explored theoretically for the species detected in mass spectra of the Sc-EMF extract synthesized using CH4 as a reactive gas. Two most promising candidates, namely Sc4C@C80-Ih(7) and Sc4C3@C80-Ih(7), have been identified and further studied at the DFT level. For Sc4C@C80, the tetrahedral Sc4 cluster with the central μ4-C atom was found to be 10 kJ/mol more stable than the square cluster. For Sc4C3@C80, the calculation showed that the most stable is the Sc4C3 cluster in which the triangular C3 moiety is η3- and η2-coordinated to Sc atoms. Whereas Sc4C@C80 has rather small HOMO-LUMO gap and low ionization potential, the HOMO-LUMO gap of Sc4C3@C80 is substantially higher and exceeds that of Sc4C2@C80. In the third part, computational studies of structures and reactivity are described for a new type of EMFs with a heptagon that has been produced in the arc-discharge synthesis. DFT computations predict that LaSc2N@Cs(hept)-C80 is more stable than LaSc2N@D5h-C80, so the former should be synthesized in much higher yield than observed. This disagreement may be ascribed to the kinetic factors rather than thermodynamic stability. Because of prospective applications of this EMFs by introducing functional groups, the influence of the heptagon on the chemical properties have been further evaluated. Thermodynamically and kinetically preferred reaction sites are studied computationally for Prato and Bingel-Hirsch cycloaddition reactions. In both types of reactions the heptagon is not affected, and chemical reactivity is determined by the adjacent pentalene units. Thermodynamically controlled Prato addition is predicted to proceed regioselectively across the pentagon/pentagon edges, whereas the most reactive sites in kinetically-controlled Bingel-Hirsch reaction are the carbon atoms next to the pentagon/pentagon edge. Fourth, although various EMFs have been successfully synthesized and characterized, the formation mechanism is still not known in details, and hence control of the synthesis products is rather poor. Therefore, EMF self-assembly process in Sc/carbon vapor in the presence and absence of cooling gas (helium) and reactive gas (NH3 and CH4) is systematically investigated using quantum chemical molecular dynamics (QM/MD) simulations based on the DFTB potentials. The cooling gas effect is that the presence of He atoms accelerates formation of pentagons and hexagons and reduces the size of formed carbon cages in comparison to the analogous He-free simulations. As a result, the Sc/C/He system yields a large number of successful trajectories (i.e. leading to the Sc-EMFs) with more realistic cage-size distribution than the Sc/C system. Encapsulation of Sc atoms within the carbon cage was found to proceed via two parallel mechanisms. The main mechanism involves nucleation of the several hexagons and pentagons with Sc atoms already at the early stages of the carbon vapor condensation. In such proto-cages, both Sc–C σ-bonds and coordination bonds between Sc atoms and the π-system of the carbon network are present. Sc atoms are thus rather labile and can move along the carbon network, but the overall bonding is sufficiently strong to prevent dissociation even at high temperatures. Further growth of the carbon cage results in encapsulation of one or two Sc atoms within the forming fullerene. Another encapsulation mechanism is observed in rare cases. In this process, the closed cage is formed with Sc being a part of the carbon network, i.e. being bonded by three or four Sc–C σ-bonds. However, such intermediates are found to be unstable, and transform into the endohedral fullerenes within few picoseconds of annealing. In perfect agreement with experimental studies, extension of the simulation to Fe and Ti showed that Fe-EMFs are not formed at all, whereas Ti is prone to form Ti-EMFs with small cage sizes, including Ti@C28-Td and Ti@C30-C2v(3). The role of “reactive gas” in the EMF synthesis is revealed in dedicated simulations of the fullerene formation in the presence of several molecules of CH4 or NH3. When concentration of reactive gas is high, carbon vapor tends to form graphene flakes or other carbon species terminated by hydrogen atoms, whereas the yield of empty fullerenes is very low. Conversely, with additional metal atoms (Sc) and the same number of NH3 molecules, the yield of fullerenes constantly increase from 5 to 65% which is ascribed to the catalytic activity of metal atoms in the nucleation of carbon cages already at early stage. Moreover, due to the presence of hydrogen atoms from the reactive gas, the carbon cage formation requires much longer time, which provides sufficient reaction time to encapsulate 3 or 4 Sc atoms within one cage. It explains preferential formation of clusterfullerenes in experiments with reactive gas. At the same time, monometallofullerenes and dimetallofullerenes are the main products in absence of reactive gas. We also provide possible growth mechanisms of carbide and cyano-clusterfullerenes in details to elucidate how the intracluster goes into the cage. A possible growth mechanism of nitride clusterfullerenes has been proposed based on DFT results. In the last part, a free-standing crystalline single-atom thick layer of Fe has been studied theoretically. By investigating the energy difference, ΔE, between a suspended Fe monolayer and a nanoparticle using the equivalent number of Fe atoms, one can estimate that the largest stable membrane should be ca. 12 atoms wide or 3 × 3 nm2 which is in excellent agreement with the experimental observation. Otherwise, the possibility of C, O, N atoms embedded into the Fe membrane can been fully excluded by DFTB and DFT simulations, which agrees with electron energy loss spectroscopy (EELS) measurement. A significantly enhanced magnetic moment for single atom thick Fe membranes (3.08 μB) is predicted by DFT as compared to the bulk BCC Fe (2.1 μB), which originates from the 2D nature of the Fe membrane since the dz2 orbital is out-of-plane while the dxy orbital is in-plane.

The development of interatomic potentials for magnetic transition metals, and particularly for iron, is difficult, yet it is also necessary for large-scale atomistic simulations of industrially important iron and steel alloys. The magnetism of iron is especially important as it is responsible for many of the element's unique physical properties -- its bcc ground state structure, its high-temperature phase transitions, and the mobility of its self-interstitial atom (SIA) defects. Yet an accurate description of itinerant magnetism within a real-space formalism is particularly challenging and existing interatomic potentials based on the Embedded Atom Method are suited only for studies of near-equilibrium ferritic iron, due to their restricted functional forms. For this work, the magnetic analytic Bond-Order Potential (BOP) method has been implemented in full to test the convergence properties in both collinear and non-collinear magnetic iron. The known problems with negative densities of states (DOS) are addressed by assessing various possible definitions for the bandwidth and by including the damping factors adapted from the Kernel Polynomial Method. A 9-moment approximation is found to be sufficient to reproduce the major structural energy differences observed in Density Functional Theory (DFT) and Tight Binding (TB) reference calculations, as well as the volume dependence of the atomic magnetic moments. The Bain path connecting bcc and fcc structures and the formation energy of mono- and divacancies are also described well at this level of approximation. Other quantities such as the high-spin/low-spin transition in fcc iron, the bcc elastic constants and the SIA formation energies converge more slowly towards the TB reference data. The theory of non-collinear magnetism within analytic BOP is extended as required for a practical implementation. The spin-rotational behaviour of the energy is shown to converge more slowly than the collinear bulk energy differences, and there are specific problems at low angles of rotation where the magnitude of the magnetic moment depends sensitively on the detailed structure of the local DOS. Issues of charge transfer in relation to magnetic defects are discussed, as well as inadequacies in the underlying d-electron TB model.

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