This thesis is concerned with the development and application of <i>quantum Monte Carlo </i>(QMC) methods for calculating the energies of atoms, molecules and solids from first principles. Several modifications to the variational and diffusion Monte Carlo (VMC and DMC) methods are investigated. It is shown that biases due to the use of finite time steps largely cancel when the ionisation energy of neon is calculated. A new form of trial wave function, which is more flexible and computationally efficient than existing forms, is proposed for use in QMC simulations. Results obtained with the new trial wave function are analysed and discussed. The results of an investigation into some aspects of a class of QMC methods in which the computer time is proportional to the square of the number of particles simulated are given. It is found that the least biased method of truncating localised orbitals is to cut them off abruptly. The results of applying QMC methods to two different electronic systems are presented: (i) An accurate calculation of the density at which a three-dimensional uniform gas of electrons will crystallise at zero temperature is described. The DMC energy of the crystalline phase is evaluated at different densities, and the point at which the energy curve crosses that of the fluid phase is located. (Accurate energy data for the fluid phase are already available). The transition density is found to be <i>r_s</i> = 106 ± 1 a.u. (ii) DMC calculations of the <i>optical gaps </i>of various nanometre-sized diamond molecules are reported. It is found that molecules which are smaller than about 1 nm have larger optical gaps than bulk diamond. These <i>quantum-confinement </i>effects are not found to be present in molecules with diameters in excess of 1 nm. The electron affinity of C₂₉H₃₆ is found to be negative.

This thesis is concerned with the classical and semi-classical behaviour of solitons in three dimensions. In Chapter 2 we consider the zero mode quantization of the minimal energy Skyrmions for nucleon numbers between four and nine and also the conjectured solution with nucleon number of seventeen. The method relies on determining the contractibility of the loops in the configuration space corresponding to the discrete symmetry of the minimal energy solution. We find that for nucleon numbers four, six and eight the ground states obtained agree with the observed quantum numbers of the ground states of Helium, Lithium and Beryllium. But for nucleon numbers five, seven, nine and seventeen the spins obtained conflict with the observed isodoublet nuclear states. In Chapter 3 we discuss the gradient flow curves for two well-separated Skyrmions. The form of the equations are quite simple and lead to an unambiguous interpretation of how the solution curves behave. There exists a large number of symmetries which enable us to find the solutions in closed form in the case of massless pions. An algorithm is described that estimates the positions and relative orientation of two-separated Skyrmions, given the numerically generated Skyrme field. Chapters 4 and 5 are concerned with monopoles in SU(3) gauge theory. In Chapter 4 we consider charge two monopoles in the minimally broken case. A certain class of solutions looks like SU(2) monopoles embedded in SU(3) with a transition region or "cloud" surrounding the monopoles. We solve for the long-range fields in this region, confirming the existence of the cloud. The moduli space metric found by Dancer, is expressed in an explicit form. Chapter 5 discusses the case of maximal symmetry breaking for SU(3) monopoles for magnetic charge (2,1). Some properties of this space are discussed, we also find the axially symmetric geodesic submanifold of the moduli space and study the case of monopole scattering there. We analyse the limit where minimal symmetry breaking occurs, comparing to the results in Chapter 4.

Aspects of a theoretical and computational basis for the simulation of fast electron scattering in a solid due to elastic, electron-phonon and atomic ionisation events are developed. The primary motivation for this work arises from the need for detailed simulations of fast electron scattering to assist in the quantitative interpretation of experimental data acquired using high-spatial-resolution analytical techniques in the scanning transmission electron microscope. The scattering behaviour of Å-scale electron probes in simple atomic structures is examined with specific reference to the origin of core energy-loss signals and the spatial resolution of annular dark-field images generated by such probes. A multiscale theory of the dynamical elastic and inelastic scattering of fast electrons is then developed. This theory is applicable to many forms of inelastic scattering, and is developed in the form of a multi-dimensional extension of the well-known multislice theory of dynamical elastic scattering of fast electrons. Methods for obtaining the key quantities required for the application of this theory to the inelastic scattering of fast electrons due to atomic ionisation are presented. One of these methods is extended to enable the inclusion of relativistic effects in the ionisation process. A preliminary test of the multislice theory is made by comparing calculated and experimental characteristic-loss electron diffraction patterns acquired from silicon. The treatment of incoherent electron waves using Monte Carlo integration, which in certain circumstances can reduce computation time dramatically, is also demonstrated. Finally, the predictions of the theory are compared with those of approximate methods for calculating the origin of the core energy-loss signal in the scanning transmission electron microscope.

No description available.

In this thesis, the theoretical electronic structures of diamond-like amorphous carbons (DLC) are studied using the total energy code "Fast Structure" based on local orbitals, Harris functional and local density approximation (LDA) molecular dynamics simulations. The carbon atom can exhibit different bonding configurations including <I>sp<SUP>3</SUP>, sp<SUP>2</SUP></I> and <I>sp<SUP>1</SUP></I> hybridizations. Firstly, the structural trend of the amorphous carbon (a-C) shows an increasing <I>sp<SUP>3</SUP></I> fraction with the increase of mass densities. The existence of both <I>sp<SUP>3</SUP></I> and <I>sp<SUP>2</SUP></I> sites in a-C accentuates the band-tailing process with σ and π bonding. The smaller band gap found in the DLC is mainly due to the distortions of π-bonded clusters. The large distortions of π dihedral angles cause the entire π band to be localized. The localization of π states causes the mobility gap to exceed the optical gap, which accounts for the low carrier mobility and the flat photoluminescence excitation spectrum. The stabilities of various nitrogen doping configurations in a-C are also studied. At low N contents, N dopants exhibit σ bonding and are in favour of forming non-doping trivalent coordination N<SUP>0</SUP><SUB>3 </SUB>sites. At high N contents, the non-doping π-bonded sites are preferred. These results account for the low doping efficiency in a-C. Surface properties of the a-C structures show the formation of the <I>sp<SUP>2</SUP>-</I>rich surface layers compared to the predominant <I>sp<SUP>3</SUP></I> regions. These structures are further applied to the study of defect formation energies for vacancies and interstitials in the near surface region. The considerably low defect formation energy found in a-C supports the possibility of deposition mechanism described by the subplantation model.

The first part of the work is an attempt to develop improved exchange-correlation. This is initially approached by separating the exchange-correlation functional into an exchange functional and a correlation functional. The simplest chemical systems, atoms, are used to help develop new functionals. This leads to a proposal for an exchange functional, OPTX, and a correlation functional, OPTC. A total exchange-correlation functional, HCTH, is then developed by choosing a functional form with several parameters. These parameters are chosen to minimise the error in a least squares fit to energy, potential, and geometry of 93 chemical species. To further understand the nature of exchange, molecules are examined. In molecules the separation of exchange and correlation is not as simple as in atoms. By studying the geometries and the energetic contributions to dissociation energies of the molecules, it is seen that local exchange functionals do not approximate Hartree-Fock exchange. It is concluded that local exchange functionals also include non-dynamical correlation. In the next part the performance of a wide range of exchange-correlation functionals, ranging from LDA (containing just the density, <IMG WIDTH=7 HEIGHT=14 ALIGN=MIDDLE SRC="/maths/rho.gif">) to GGA (containing <IMG WIDTH=7 HEIGHT=14 ALIGN=MIDDLE SRC="/maths/rho.gif"> and <img src=/inline/symbol_209.gif><IMG WIDTH=7 HEIGHT=14 ALIGN=MIDDLE SRC="/maths/rho.gif">) to meta GGA (containing <IMG WIDTH=7 HEIGHT=14 ALIGN=MIDDLE SRC="/maths/rho.gif">, <img src=/inline/symbol_209.gif><IMG WIDTH=7 HEIGHT=14 ALIGN=MIDDLE SRC="/maths/rho.gif">, <img src=/inline/symbol_209.gif><SUP>2</SUP><IMG WIDTH=7 HEIGHT=14 ALIGN=MIDDLE SRC="/maths/rho.gif"> and the kinetic energy density, <IMG WIDTH=7 HEIGHT=7 ALIGN=BOTTOM SRC="/maths/tau.gif">) and hybrid functionals (containing a fraction of exact exchange), are assessed. By looking at two sets of molecules it is concluded that more recently developed functionals are an improvement over the older functionals.

No description available.

No description available.

The electronic configurations of molecular states of iodine are studied through the Optical-Optical Double Resonance excitation of the ion pair states in low vibrational levels. The two photon OODR excitation of <i>ungerade</i> IP states from the <i>gerade</i> ground state is rationalised and the strength of <i>u</i>/<i>g</i> coupling at the intermediate step interpreted in terms of a hyperfine interaction first described by Broyer <i>et al</i>. The potential function of the cl<SUB>g</SUB>(<i>ab</i>) <i>gerade</i> coupling partner in the hyperfine Hamiltonian is derived, along with the lowest levels of a new IP state in the second cluster, <i>H</i>1<SUB>u</SUB>(2) state. An OODR excitation scheme for populating the 0<SUP>-<SUB>u</SUB></SUP>(2) IP state is proposed and the dominant component of the c1<SUB>g</SUB>(<i>ab</i>) state configuration is found for <i>R</i> ≈ 5.5AA. The radiative lifetimes of nine IP states in low vibrational levels are determined and combined with the relative fluorescent intensities of the IP→Valence charge transfer transitions to derive the Einstein <i>A</i>-coefficients for all the strong transitions from these IP states. A theoretical model is developed in terms of a separated atom description for the electronic configurations of these states and is used to predict the relative dipole strengths of the IP→Valence transitions. The Einstein <i>A</i>-coefficients are then interpreted to give the electronic configurations of the IP states around <i>R</i>^IP_e and the relative strengths of the transition dipoles for <i>p</i>igma͍<i>p</i><SUB>igma and <i>p</i> </SUB>_π͍<i>p</i><SUB>π</SUB> electron transfer between ionic centres. A significant difference from the free ion configurations is found with the lowest energy IP states of a given symmetry adopting as low a <i>p</i><SUB>igma</SUB> occupancy at the cationic centre as the inter-electron repulsion and spin-orbit energies will allow. This stabilisation is driven by the field gradient due to the anionic charge.

The resonance enhanced multiphoton ionization (REMPI) spectra of I<SUB>2</SUB> and IBr have been recorded at room temperature in a static cell and in a supersonic-jet (circa. 20K). The results of both sets of data provide an interesting contrast between two similar, yet distinct species. The room temperature REMPI spectrum of I<SUB>2</SUB> has been recorded in the region 48000-75300cm<SUP>-1</SUP> using both linearly and circularly polarized light. Rydberg states (ns) up to n = 11, based on the [3/2]<SUB>g</SUB> ionic core, and up to n = 8 based on the [1/2]<SUB>g</SUB> ionic core, have been observed together with three 5d states based on each core. Of these, twelve states have been observed for the first time and six other states have been reassigned. Assignments have been made by comparing the observed molecular quantum defects with those of atomic iodine, by using band contour analysis and by measurement of polarization ratios. Polarization ratios which are widely different from those expected have been observed for some systems. Preliminary jet-cooled REMPI spectra revealed that some Rydberg states are homogeneously perturbed by high vibrational levels of one or more ion-pair states from the first ion-pair cluster. The REMPI spectrum of IBr has been recorded in the region 62500-55500cm<SUP>-1</SUP>. In contrast to the I<SUB>2</SUB> (and BR<SUB>2</SUB>) REMPI spectra, where Rydberg transitions dominate, strong transition to ion-pair states dominate the spectrum of the interhalogen IBr (and ICI). Pronounced resonance structure caused by coupling between the b's Rydberg state, observed for the first time, and the ion-pair states has been observed.