Most ab initio simulation packages based on Density Functional Theory (DFT) use the Superposition of Atomic Densities (SAD) as a starting point of the self-consistent fi eld (SCF) iteration. However, this trial charge density without modeling atomic iterations nonlinearly may lead to a relatively slow or even failed convergence. This thesis proposes a machine learning-based scheme to improve the initial guess. We train a 3-Dimensional Convolutional Neural Network (3D CNN) to map the SAD initial guess to the corresponding converged charge density with simple structures. We show that the 3D CNN-processed charge density reduces the number of required SCF iterations at different unit cell complexity levels.

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A rich variety of phases can exist in quantum systems. For example, the fractional quantum Hall states have persistent topological characteristics that derive from strong interaction. This thesis uses the exact diagonalization method to investigate quantum lattice models with strong interaction. Our research topics revolve around quantum phase transitions between novel phases. The goal is to find the best schemes for realizing these novel phases in experiments. We studied the fractional Chern insulator and its transition to uni-directional stripes of particles. In addition, we studied topological Mott insulators with spontaneous time-reversal symmetry breaking induced by interaction. We also studied emergent kinetics in one-dimensional lattices with spin-orbital coupling. The exact diagonalization method and its implementation for studying these systems can easily be applied to study other strongly correlated systems. / PHD / Topological quantum states are a new type of quantum state that have properties that cannot be described by local order parameters. These types of states were first discovered in the 1980s with the integer quantum Hall effect and the fractional quantum Hall effect. In the 2000s, the predicted and experimentally discovered topological insulators triggered studies of new topological quantum states. Studies of strongly correlated systems have been a parallel research topic in condensed matter physics. When combining topological systems with strong correlation, the resulting systems can have novel properties that emerge, such as fractional charge. This thesis summarizes our work that uses the exact diagonalization method to study topological states with strong interaction.

The thesis entitled “Addressing subtle physicochemical features exhibited by molecular crystals via Experimental and Theoretical Charge Density Analysis” consists of five chapters. An introductory note provides a brief description of experimental and theoretical charge density methodology, followed by its utilization in obtaining certain physical and chemical properties in molecular crystals. Chapter 1 addresses not so easily accessed molecular property arising due to electron conjugation, highlighting antiaromaticity in tetracyclones. A systematic study of six tetracyclone derivatives with electron withdrawing and electron donating substituents has been carried out using experimental and theoretical charge density analysis. A three pronged approach based on quantum theory of atoms in molecules (QTAIM), nucleus independent chemical shifts (NICS), and source function (SF) has been employed to establish the degree of antiaromaticity of the central five-membered ring in all the derivatives. Electrostatic potentials mapped on the is density surface reveal the finer effects of different electron withdrawing and electron donating substituents on the carbonyl group. Chapter 2 presents a temperature induced reversible first order single crystal to single crystal phase transition (Room temperature Orthorhombic, P22121 to low temperature Monoclinic, P21) in a  hybrid peptide, Boc-γ4(R)Val-Val-OH. The thermal behavior accompanying the phase transition of the dipeptide crystal was characterized by differential scanning calorimetry, visual changes in birefringence of the sample during heating and cooling cycles on a hot-stage microscope with polarized light. Variable-temperature unit cell check measurements from 300 to 100 K showed discontinuity in the volume and cell parameters near the transition temperature, supporting the first-order behavior. The reversible nature of the phase transition is traced to be due to an interplay between enthalpy and entropy. Chapter 3 brings out an unusual stabilizing interaction involving a cooperative -hole and ¬hole character in a short NCS···NCS bond. This chapter describes structural features of four isothiocyanate derivatives, FmocXCH2NCS; X=Leu, Ile, Val and Ala. Among these it is observed that only FmocLeuCH2NCS which crystallizes in a tetragonal space group, P41, (a=b=12.4405(5) Å; c= 13.4141(8) Å) transforms isomorphously to a low temperature form, P41, (a=b=17.4665(1) Å; c= 13.1291(1) Å). The characteristics of the phase transition have been monitored by Differential Scanning Calorimetry, variable temperature IR and temperature dependent unit cell measurements. The short NCS···NCS intermolecular interaction (3.296(1) Å) is analyzed based on detailed experimental charge density analysis which reveals the nature of this stabilizing interaction. Chapter 4 explains a comparative study of syn and anti conformations of carboxylic acids in peptides from both structural aspect and charge density features. Single crystal structures of four peptides having syn conformations [BocLeuγ4(R)Valγ4(R)ValOH, BocLeuγ4(R)ValLeuγ4(R)ValOH, Boc3(S)Leu3(S)LeuOH] and one with anti conformation, BocLeuγ4(R)ValValOH have been analyzed. Experimental charge density analysis has been carried out exclusively on BocLeuγ4(R)ValValOH having anti form, because of its rare occurrence in literature. However, low temperature datasets on the four peptides with syn conformations were collected and theoretical charge density analysis has been carried out on two of these compounds. Electrostatic potentials mapped on is density surface bring out a significant difference at the oxygen atoms of the carboxyl group in the two conformations. However, lone pair orientation of different types of Oxygen atoms in the two forms (urethane, amide, acid) doesn’t exclusively indicate the differences in the corresponding charge density features. Chapter 5 addresses the issue of how sensitive are the charge density features associated with amino acid residues when the backbone conformational angles are varied. Three model systems, 1, L-alanyl–L-alanyl–L-alanine dehydrate; 2, anhydrous L-alanyl–L-alanyl–L¬alanine and 3, cyclo-(D,L-Pro)2(L-Ala)4 monohydrate have been chosen for this evaluation. Compound 1 has ant parallel alignment of tripe tide strands, and compound 2 has parallel alignment. All the alanine residues in compound 1 and 2 are in the -sheet region of the Ramachandran plot, whereas, the four Alanine residues in the cyclic hex peptide 3 span different regions of the Ramachandran plot. Theoretical multipole modelling has been carried out in order to explore the plausibility of transferring multipole parameters across different regions of Ramachandran Plot. Appendix I contains a brief description of charge shift bonding in Ph-CH2-Se-Se-CH2-Ph, as determined based on both experimental and theoretical charge density analysis. Appendix II contains a reprint of a published article on “Conformation-Changing Aggregation in Hydroxyacetone: A Combined Low-Temperature FTIR, Jet, and Crystallographic Study”.

Thesis (PhD)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: In this thesis the structural dynamics, upon photo-excitation, of the charge-densitywave (CDW) material 4Hb-TaSe2 is investigated on the time-scale of atomic motion and simultaneously on the spatial-scale of atomic dimensions. CDW materials have been of interest since their discovery in the 1970’s because of their remarkable non-linear and anisotropic electrical properties, gigantic dielectric constants, unusual elastic properties and rich dynamical behaviour. Some of these exotic properties were extensively investigated in thermal equilibrium soon after their discovery but only recently have ultrafast techniques like femtosecond spectroscopy become available to study their out-of-equilibrium behaviour on the time-scale of atomic motion. By studying their behaviour on this time-scale a more in-depth understanding of their macroscopic properties can be gained. However, to do investigations on the atomic time-scale and simultaneously directly observe the evolution of the atomic arrangements is another challenge. One approach is through the previously mentioned technique of femtosecond pump-probe spectroscopy but converting the usual ultrashort optical probing source to an ultrashort electron or x-ray source that can diffract off the sample and reveal structural detail on the atomic level. Here, the femto-to-picosecond out-of-equilibrium behaviour upon photo-excitation in 4Hb-TaSe2 is investigated using an ultrashort electron probe source. Two variations of using an electron probe source are used: conventional scanning Femtosecond Electron Diffraction (FED) and a new approach namely Femtosecond Streaked Electron Diffraction (FSED). The more established FED technique, based on femtosecond pumpprobe spectroscopy, is used as the major investigating tool while the FSED technique, based on ultrafast streak camera technology, is an attempt at broadening the scope of available techniques to study structural dynamics in crystalline material on the subpicosecond time-scale. With these two techniques, the structural dynamics during the phase transition from the commensurate- to incommensurate-CDW phase in 4Hb-TaSe2 is observed through diffraction patterns with a temporal resolution of under 500 fs. The study reveals strong coupling between the electronic and lattice systems of the material and several time-constants of under and above a picosecond are extracted from the data. Using these time-constants, the structural evolution during the phase transition is better understood and with the newly gained knowledge, a model of all the processes involved after photo-excitation is proposed. / AFRIKAANSE OPSOMMING: In hierdie tesis word die strukturele dinamika van die lading-digtheid-golf (LDG) materiaal 4Hb-TaSe2 ondersoek op die tydskaal van atomiese bewegings en gelyktydig op die ruimtelikeskaal van atomiese dimensies. LDG materie is al van belang sedert hul ontdekking in die 1970’s as gevolg van hul merkwaardige nie-lineêre en anisotrope elektriese eienskappe, reuse diëlektriese konstantes, ongewone elastiese eienskappe en ryk dinamiese gedrag. Sommige van hierdie eksotiese eienskappe is omvattend ondersoek in termiese ewewig kort na hul ontdekking, maar eers onlangs is dit moontlik deur middle van ultravinnige tegnieke soos femtosekonde spektroskopie om hulle uit-ewewigs gedrag te bestudeer op die tydskaal van atomiese beweging. Deur die gedrag op hierdie tydskaal te bestudeer kan ’n meer insiggewende begrip van hul makroskopiese eienskappe verkry word. Om ondersoeke in te stel op die atomiese tydskaal en gelyktydig direk die evolusie van die atoom posisie te waarneem is egter ’n moeilike taak. Een benadering is deur middle van femtosekonde “pump-probe” spektroskopie maar dan die gewone optiese “probe” puls om te skakel na ’n electron of x-straal puls wat van die materiaal kan diffrak en dus strukturele inligting op die atomiese vlak kan onthul. Hier word die femto-tot-pico sekonde uit-ewewig gedrag in 4Hb-TaSe2 ondersoek met behulp van elektron pulse. Twee variasies van die gebruik van ’n elektron bron word gebruik: konvensionele “Femtosecond Electron Diffraction” (FED) en ’n nuwe benadering, naamlik, “Femtosecond Streaked Electron Diffraction” (FSED). Die meer gevestigde FED tegniek, wat gebaseer is op femtosekonde “pump-probe” spektroskopie, word gebruik as die hoof ondersoek metode terwyl die FSED tegniek, wat gebaseer is op die ultra vinnige “streak camera” tegnologie, ’n poging is om beskikbare tegnieke uit te brei wat gebruik kan word om strukturele dinamika in materie te bestudeer op die sub-picosekonde tydskaal. Met behulp van hierdie twee tegnieke, word die strukturele dinamika tydens die fase oorgang van die ooreenkomstige tot nie-ooreenkomstige LDG fase in 4Hb-TaSe2 deur diffraksie patrone met ’n tydresolusie van minder as 500 fs waargeneem. Die studie toon ’n sterk korrelasie tussen die elektroniese sisteem en kristalrooster. Verskeie tydkonstantes van onder en bo ’n picosekonde kon ook uit die data onttrek word en gebruik word om die strukturele veranderinge beter te verstaan. Hierdie nuwe kennis het ons in staat gestel om ’n model van al die betrokke prosesse voor te stel.

Thesis (PhD)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: Low-dimensional materials are known to undergo phase transitions to differently or- dered states, when cooled to lower temperatures. These phases often show a periodic modulation of the charge density (called a charge density wave – CDW) coupled with a periodic perturbation of the crystal lattice (called a periodic lattice distortion – PLD). Although many experiments have been performed and much has been learnt about CDW phases in low-dimensional materials, the reasons for their existence are still not fully understood yet. Many processes, involving either strong electron–electron or electron–lattice coupling, have been observed which all might play a role in explaining the formation of different phases under different conditions. With the availability of femtosecond lasers it has become possible to study materials under highly nonequilibrium conditions. By suddenly introducing a known amount of energy into the system, the equilibrium state is disturbed and the subsequent relax- ation processes are then observed on timescales of structural and electronic responses. These experiments can deliver valuable information about the complex interactions between the different constituents of condensed matter, which would be inaccessible under equilibrium conditions. We use time resolved electron diffraction to investigate the behaviour of a CDW system perturbed by a short laser pulse. From the observed changes in the diffraction patterns we can directly deduce changes in the lattice structure of our sample. A femtosecond electron diffraction setup was developed at the Laser Research In- stitute in Stellenbosch, South Africa. Short laser pulses produce photo electrons which are accelerated to an energy of 30 keV. Despite space charge broadening effects, elec- tron pulses shorter than 500 fs at sample position can be achieved. Technical details of this system and its characterisation as well as sample preparation techniques and analysis methods are described in detail in this work. Measurements on two members of the quasi-two-dimensional transition metal di- chalcogenides, namely 4Hb-TaSe2 and 1T-TaS2, are shown and discussed. Both show fast (subpicosecond) changes due to the suppression of the PLD and a rapid heating of the lattice. When the induced temperature rise heats the sample above a phase tran- sition temperature, a complete transformation into the new phase was observed. For 4Hb-TaSe2 we found that the recovery to the original state is significantly slower if the PLD was completely suppressed compared to only disturbing it. On 1T-TaS2 we could not only study the suppression of the original phase but also the formation of the higher energetic CDW phase. Long (100 ps) time constants were found for the tran- sition between the two phases. These suggest the presence of an energy barrier which has to be overcome in order to change the CDW phase. Pinning of the CDW by de- fects in the crystal structure result in such an energy barrier and consequently lead to a phase of domain growth which is considerably slower than pure electron or lattice dynamics. / AFRIKAANSE OPSOMMING: Dit is bekend dat lae-dimensionele materie fase oorgange ondergaan na anders ge- ori¨enteerde toestande wanneer afgekoel word tot laer temperature. Hierdie fases toon dikwels ’n periodiese modulasie van die elektron digtheid (genoem ’n “charge density wave” – CDW), tesame met ’n periodiese effek op die kristalrooster (genoem ’n “peri- odic lattice distortion” – PLD). Alhoewel baie eksperimente al uitgevoer is en al baie geleer is oor hierdie CDW fase, is die redes vir hul bestaan nog steeds nie ten volle verstaan nie. Baie prosesse, wat of sterk elektron–elektron of elektron–fonon interaksie toon, is al waargeneem en kan ’n rol speel in die verduideliking van die vorming van die verskillende fases onder verskillende omstandighede. Met die beskikbaarheid van femtosekonde lasers is dit nou moontlik om materie onder hoogs nie-ewewig voorwaardes te bestudeer. Deur skielik ’n bekende hoeveel- heid energie in die stelsel in te voer, word die ewewigstaat versteur en word die daar- opvolgende ontspanning prosesse waargeneem op die tydskaal van atomies struktu- rele en elektroniese bewiging. Hierdie eksperimente kan waardevolle inligting lewer oor die komplekse interaksies tussen die verskillende atomiese komponente van ge- kondenseerde materie, wat ontoeganklik sou wees onder ewewig voorwaardes. Ons gebruik elektrondiffraksie met tyd resolusie van onder ’n pikosekonde om die gedrag van ’n CDW stelsel te ondersoek nadat dit versteur is deur ’n kort laser puls. Van die waargenome veranderinge in die diffraksie patrone kan ons direk aflei watse veranderinge die kristalstruktuur van ons monster ondergaan. ’n Femtosekonde elektronendiffraksie opstelling is ontwikkel by die Lasernavors- ingsinstituut in Stellenbosch, Suid-Afrika. Kort laser pulse produseer foto-elektrone wat dan na ’n energie van 30 keV versnel word. Ten spyte van Coulomb afstoting ef- fekte, kan elektron pulse korter as 500 fs by die monster posisie bereik word. Tegniese besonderhede van hierdie opstelling, tegnieke van die voorbereiding van monsters asook analise metodes word volledig in hierdie tesis beskryf. Metings op twee voorbeelde van kwasi-tweedimensionele semi-metale, naamlik 4Hb-TaSe2 en 1T-TaS2, word gewys en bespreek. Beide wys ’n vinnige (subpikosekon- de) verandering as gevolg van die versteuring van die PLD en ’n vinnige verhitting van die kristalrooster. Wanneer die ge¨ınduseerde temperatuur bo die fase oorgang tempe- ratuur styg, is ’n volledige transformasie na die nuwe fase waargeneem. Vir 4Hb-TaSe2 het ons gevind dat die herstelling na die oorspronklike toestand aansienlik stadiger is as die PLD heeltemal viernietig is in vergelyking met as die PLD net versteur is. Met 1T-TaS2 kon ons nie net alleenlik die vernietiging van die oorspronklike fase sien nie, maar ook die vorming van ’n ho¨er energie CDW fase. Lang (100 ps) tydkonstante is gevind vir die oorgang tussen die twee fases. Hierdie dui op die teenwoordigheid van ’n energie-versperring wat eers oorkom moet word om die CDW fase voledig te ver- ander. Vaspenning van die CDW deur defekte in die kristalstruktuur veroorsaak so’n energie versperring en gevolglik lei dit tot ’n fase van groeiende CDW gebiede wat heelwat stadiger as pure elektron of kritalrooster dinamika is.

Thesis (MSc)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: Ultrafast electron diffraction is a powerful method to study atomic movement in crystals on sub-picosecond timescales. This thesis consists of three parts. In part one the ultrafast electron diffraction machine is described, followed by improvements that were made and techniques that were developed in order to bring the system to state of the art level and enable the acquisition of suffcient data to obtain information on the structural dynamics in crystals. The second part contains a description of the sample which was studied in our fi rst time-resolved measurements, the transition-metal dichalcogenide 4Hb-TaSe2. This particular crystal is an example of a strongly coupled electronic system which develops a charge density wave (CDW) accompanied by a periodic lattice distortion (PLD). An overview of the formation of electron diffraction patterns and what can be learned from them are also given, followed by the results of the ultrafast electron diffraction experiments done with 4Hb-TaSe2. Part three describes an alternative source to study dynamics in crystalline samples, namely laser plasma-based ultrafast X-ray diffraction. The ultrafast electron diffraction group functions as a unit, but my tasks ranged from sample preparation and characterisation of the electron beam to the setting up and execution of experiments. I was involved in analysing the data and contributed small parts to the data analysis software. / AFRIKAANSE OPSOMMING: Ultravinnige elektron diffraksie is a metode om die beweging van atome in kristalle op sub-pikosekonde tydskale te bestudeer. Hierdie tesis bestaan uit drie dele. In deel een van die tesis word die ultravinnige elektron diffraksie masjien beskryf, gevolg deur verbeteringe wat aangebring is en tegnieke wat ontwikkel is om die sisteem tot op 'n wêreldklas vlak te bring waar die insameling van genoegsame data om inligting oor die strukturele dinamika in kristalle te bekom, moontlik is. Die tweede deel bevat 'n beskrywing van die monster wat in ons eerste tydopgeloste eksperimente gebruik is, naamlik die oorgangsmetaaldichalkogenied 4Hb-TaSe2. Hierdie kristal is 'n voorbeeld van 'n sterk gekoppelde elektroniese sisteem wat 'n ladingsdigtheid-golf en 'n gepaardgaande periodiese versteuring van die kristalrooster ontwikkel. 'n Oorsig van die formasie van elektron diffraksiepatrone en wat ons daaruit kan leer word ook gegee. Daarna word die resultate van die ultravinnige elektron diffraksie eksperimente wat op 4Hb-TaSe2uitgevoer is beskryf en bespreek. In deel drie word 'n alternatiewe metode om die dinamika in kristalmonsters te bestudeer, naamlik laser plasma-gebaseerde ultravinnige X-straal diffraksie, beskryf. Die ultravinnige elektron diffraksie groep funksioneer as 'n eenheid, maar my verantwoordelikhede het gestrek van die voorbereiding van monsters en die karakterisering van die elektron bundel tot die opstel en uitvoer van eksperimente. Ek was ook betrokke by die analisering van data en het dele van die data analise sagteware geskryf.

Transition metal oxides (TMO) have proven to exhibit novel properties such as high temperature superconductivity, magnetic ordering, charge and spin density waves, metal to insulator transitions and colossal magnetoresistance. Among these are a spin-orbit coupling (SOC) induced Mott insulator Sr2IrO4. The electric transport properties of this material remain finite even at cryogenic temperatures enabling its complex electronic structure to be investigated by a scanning tunneling microscope. At T = 77 K, we observed two features which represent the Mott gap with a value of 2D ~ 615 meV. Additionally an inelastic loss feature was observed inside this gap due to a single magnon excitation at an energy of ~ 125 meV. These features are consistent with similar measurements with other probes. In addition to these features, at T = 4.2 K lower energy features appear which are believed to be due to additional magnetic ordering. Another material that exhibits a unique physical behavior is the sliding charge density wave (CDW) material TaS3. It is a quasi-one dimensional material that forms long narrow ribbon shaped crystals. It exhibits anomalies including non-ohmic conductivity, a decrease in the Young’s modulus, a decrease in the shear modulus and voltage induced changes in the crystal’s overall length. In addition, we have observed the torsional piezo-like response, voltage induced torsional strain (VITS), in TaS3 which was first discovered by Pokrovskii et. al. in 2007. Our measurements were conducted with a helical resonator. The VITS response has a huge effective piezoelectric coefficient of ~ 104 cm/V. In addition we have concluded that the VITS is a very slow response with time constants of ~ 1 s near the CDW depinning threshold, that these time constants are dependent on the CDW current, and we suggest that the VITS is due to residual twists being initially present in the crystal.

Electrospinning is a method of using high voltage electric fields to transform polymer solutions into nano-scale fibres. The field has seen significant work on processing different polymers and their resulting fibres but less work has focused the electrospinning process itself. The aim of this thesis is to present experimental observations of charge behaviour in the electrospinning process in the context of the underlying physics typically used to describe electrospinning. This thesis presents a review of existing methods of measuring aspects of the electrospinning process, and reviews published mathematical models of the process as representative examples of the current understanding of the underlying physics that drive the electrospinning phenomena. A novel measurement technique is introduced - high frequency data capture of the electric current flow simultaneously at the high voltage and collector electrode. This is used in three ways: to examine bulk charge density, to measure fibre flight time, and to quantify charge lost from the fibre in flight. Charge density is studied by comparing current and mass flow at the Taylor cone under a wide range of conditions. For 8% PVOH in water a constant bulk charge density was found of 7.7 C/kg. Flight time is studied by determining the time from the application of high voltage to the charged fibre first arriving at the collector electrode. It was found that for 8% PVOH the flight time depended strongly on applied voltage while electrode distance had a negligible effect. Charge loss was studied by comparing the magnitude of the simultaneous current flows in the quasi-steady state to determine if the charge flowing into the Taylor cone arrives with the fibre at the collector. For 8% PVOH, 8% PVOH with ionic salt, 9% PVOH in water and 18% PVB in ethanol, it was found that charge is always lost.