<p> This thesis presents the results of an attempt to study the chemical bond in terms of the three-dimensional electronic charge distribution and the force which this charge distribution exerts on the nuclei. The homonuclear diatomic molecules Li2, B2, C2, N2, O2, and F2 are discussed in terms of covalent binding while the heteronuclear diatomic molecules LiF and LiH are discussed in terms of ionic binding.</p> / Thesis / Doctor of Philosophy (PhD)

No description available.

This thesis studies two important carbon structures, graphene and carbon nanotubes, with the purpose of understanding how their three-dimensional electron density distribution affects the way fast ions interact with them. <br /><br /> A brief introduction to research in pure carbon structures is made. We then use different models to calculate the equilibrium electron density distribution in graphene and carbon nanotubes. <br /><br /> In the second part of the thesis we investigate fast ions moving parallel to a graphene sheet and experiencing forces due to the dynamic polarization of carbon valence electrons. Using the three-dimensional electron density distribution of graphene, we calculate the force directly opposing the ion's motion (stopping force), as well as the force which bends the ion's trajectory towards the sheet (image force). It is our purpose to compare these results with those based on a two-dimensional hydrodynamic model of graphene, which approximates the electron distribution of graphene by a charged fluid confined to the two-dimensional plane of the sheet. <br /><br /> The results obtained for interactions of ions with a single graphene sheet should be useful for a further analysis of ion channeling through carbon nanostructures.

Several measurement campaigns took place at the ALOMAR observatory at Andøya, Northern Norway during July-November 2001 to validate ionospheric electron density and dry temperature profiles in the troposphere and lower stratosphere derived from radio occultation measurements of the low earth orbiter satellite CHAMP. For temperature sounding, three balloons are released around GPS satellite occultation events that occurred inbetween a distance of 200 km around Andøya. At altitudes of 7–20 km the CHAMP profile shows a positive mean deviation increasing with height by about 1.5-2 Kelvin/ 10 km overlayed with variations of ±1 K when compared to the radiosonde. Taking into account the previous and following radiosonde ascents the mean deviation seems to be of systematic nature due to the occultation principle or the retrieval algorithm and the variations are related to geographical variations of temperature and to the horizontal averaging by the radio occultation technique. During the period from mid July to mid August, four occultations for ionospheric soundings occurred. The values of the F2 layer calculated from the CHAMP derived electron density profiles are compared to the readings of the Alomar and Tromsø ionosondes for these times. Comparison shows that using the radio occultation technique electron densities of the maximum value layer are calculated inbetween the same order of magnitude as the ionosondes measurements, however, they overestimate it in the cases discussed here. / Zur Validierung von Elekronendichte- und Temperaturprofilen, abgeleitet aus Radiookkultationsmessungen von CHAMP wurden im Juli-November 2001 mehrere Messkampagnen am ALOMAR Institut auf Andøya, Nordnorwegen durchgeführt. Zur Temperatursondierung wurden drei aufeinanderfolgende Radiosonden um den Zeitpunkt von Okkultationsereignissen im Umkreis von weniger als 200 km gestartet. Das hier diskutierte Temperaturprofil von CHAMP zeigt im Höhenbereich 7-20 km eine mit der Höhe zunehmende positive Abweichung von ca. 1,5-2 K/10 km mit Variationen um ±1 K verglichen mit dem Temperaturprofil der zum Okkultationszeitpunkt fliegenden Radiosonde. Der Vergleich mit den vorhergehenden und nachfolgenden Sondierungen lässt darauf schließen, dass die mittlere Abweichung durch systematische Fehler des Okkultationsverfahrens oder den Retrieval-Algorithmus bedingt sind, die Variationen jedoch durch die örtliche Abweichung und die horizontale Mittelung des Messverfahrens. Während des Zeitraumes von Mitte Juli bis Mitte August ereigneten sich vier Okkultationen zur Sondierung der Ionosphäre. Von den abgeleiteten Elektronendichteprofilen werden jeweils die Werte der F2-Schicht mit den zur gleichen Zeit gemessenen Elektronendichten der Ionosonden auf Andøya und bei Tromsø verglichen. Der Vergleich zeigt, dass mit Hilfe der Radiookkultaktionstechnik die Elektronendichtewerte der F2-Schicht in der gleichen Größenordnung berechnet, in diesen konkreten Fällen jedoch überschätzt werden.

In modelling the energetics of molecules and solids, the need for practical electron density functionals that seamlessly include the van der Waals interaction is growing. Such functionals are still in their infancy, and there is yet much experimentation to be performed in the formulation and numerical testing of the requisite approximations. A ground-state density functional approach that uses the exact relations of the adiabatic connection formula and the fluctuation-dissipation theorem to obtain the xc energy from the density-density response function seems promising, though a direct local density approximation for the interacting susceptibility will fail to yield the vdW interaction. Significant nonlocality can be built into the interacting susceptibility by screening a 'bare' susceptibility, for which a carefully chosen constraint-obeying local approximation is sufficient to yield a non-trivial van der Waals energy [6]. The constraints of charge conservation, and no response to a constant potential, are guaranteed by expressing the bare susceptibility in terms of the double gradients of a nonlocal bare polarisability. for which it should be easier to make an approximation based on physical principles than it would be for the susceptibility. The 'no-flow' condition is also deemed important. In this work, a simple delta-function approximation for the nonlocal polarisability is fully constrained by a new version of a recently-discovered force theorem (sum rule), requiring the additional input of the independent-electron Kohn-Sham potential. This constrained polarisability cannot be used as input for the seamless vdW scheme, which requires a non-delta-function bare polarisability, and is instead applied to systems containing spherical fragments in a perturbative/asymptotic fashion for calculation of the widely-separated van der Waals interaction. The main thrust of this work is an investigation of the efficacy of the force theorem to constrain simple approximations for response quantities. Many recent perturbative vdW density functionals are based on response functions that are electron-hydrodynamical approximations to the response of the uniform electron gas. These schemes require their response functions to be 'cut off' at low density and high density-gradient, where the approximation overestimates the true response. The imposition of the cut-off is crucial to the success of such schemes. Here, we replace the cut-off with an exact theorem (the force theorem) which naturally 'ties down' the response, based on the potential- and density-functions of the system. This is the first time that the force theorem has been directly applied as a constraint upon a model response function (its original use, by Vignale and Kohn (7), was as an exact identity in time-dependent DFT). Also new in this work is the orbital-by-orbital Kohn-Sham version of the force theorem, and its proof (differing significantly from Vignale's original derivation (8) of the interacting theorem) by directly appealing to the Kohn-Sham orbitals makes its first appearance here. For quantum dots, our constrained response-approximation exactly recovers the net linear dipole response, due mainly to the force theorem's ideal applicability to harmonically confined systems. For angularly-averaged atoms, reasonable static dipole polarisabilities are obtained for the independent-electron Kohn-Sham (bare) case. The results are poor for the fully-interacting case, attributable to the local nature of the approximation. This lends weight to the assertion that it is better to approximate a bare quantity, then screen it, than it is to directly approximate a fully-interacting quantity. Dynamic net polarisabilities constrained by the force theorem are guaranteed to have the correct high-frequency asymptotic convergence to the free electron response. It is seen that the calculated dynamic polarisabilities for atoms are too small at intermediate frequencies, since the calculated vdW C6 coefficients (Hamaker constants) of atomic dimers are up to an order of magnitude too small, even without the use of a low-density cutoff. It is seen that our constrained local model response is non-analytic along the imaginary-frequency axis, and this is very detrimental to the C6 calculations, even though the integrated net polarisability is analytic. Improvement of the polarisability ansatz is indicated, perhaps to a non-deltafunction uniform-gas-based approximation. The use of pseudopotentials may improve the force theorem results, by softening the extreme nature of the bare Coulomb potential.

No description available.

This thesis studies two important carbon structures, graphene and carbon nanotubes, with the purpose of understanding how their three-dimensional electron density distribution affects the way fast ions interact with them. <br /><br /> A brief introduction to research in pure carbon structures is made. We then use different models to calculate the equilibrium electron density distribution in graphene and carbon nanotubes. <br /><br /> In the second part of the thesis we investigate fast ions moving parallel to a graphene sheet and experiencing forces due to the dynamic polarization of carbon valence electrons. Using the three-dimensional electron density distribution of graphene, we calculate the force directly opposing the ion's motion (stopping force), as well as the force which bends the ion's trajectory towards the sheet (image force). It is our purpose to compare these results with those based on a two-dimensional hydrodynamic model of graphene, which approximates the electron distribution of graphene by a charged fluid confined to the two-dimensional plane of the sheet. <br /><br /> The results obtained for interactions of ions with a single graphene sheet should be useful for a further analysis of ion channeling through carbon nanostructures.

Not available / text

The single-particle momentum is studied as a tool for the visualization of the electronic regions in atoms and molecules. The limiting values of this function correctly obey two fundamental theorems: Kato's cusp condition and the Hoffmann-Ostenhof and Hoffmann-Ostenhof exponential decay. The local momentum also depicts the electron shell structure in atoms as given by its local maxima and inflection points. The integration of the electron density in a shell gives electron populations that are in agreement with the ones expected from the periodic table of the elements. The shell structure obtained is in agreement with higher level of theory computations. The average of the local kinetic energy associated with the local momentum is the Weizsäcker kinetic energy. It is shown that this quantity provides an estimate of steric interactions in molecules. The single-particle momentum is a practical tool for the exploration of new stabilizing interactions for all kinds of molecular systems. It provides a three-dimensional representation of the molecular structure and depicts the polarizability regions, a feature not available with other continuous analyses. A general definition of the radius of an atom in terms of its ionization energy is found. A relationship between these two fundamental properties is derived from the radial distribution function and the local momentum for the valence electrons. Strong correlations with well-known atomic radii suggest that this is a universally valid definition of the atomic radius. The stability of peptides in the alpha-helix conformation upon replacement of the central amino acid is studied. These systems were optimized with a continuous solvent model and a recently developed DFT functional with empirical terms accounting for dispersion interactions. Both, the dispersion terms and the solvent model are directly related to the polarizability of the involved atoms. A new formula for an ab initio computation of the polarizability is introduced and tested for the amino acids.

Thesis (Ph.D. (Physics & Electronics)) - Rhodes University, 2008.