Eigenvalue fluctuations for lattice Anderson Hamiltonians

We consider the random Schrödinger operator on a large box in the lattice with a large prefactor in front of the Laplacian part of the operator, which is proportional to the square of the diameter of the box. The random potential is assumed to be independent and bounded; its expectation function and variance function is given in terms of continuous bounded functions on the rescaled box. Our main result is a multivariate central limit theorem for all the simple eigenvalues of this operator, after centering and rescaling. The limiting covariances are expressed in terms of the limiting homogenized eigenvalue problem; more precisely, they are equal to the integral of the product of the squares of the eigenfunctions of that problem times the variance function

Eigenvalue fluctuations for lattice Anderson Hamiltonians

We consider the random Schrödinger operator on a large box in the lattice with a large prefactor in front of the Laplacian part of the operator, which is proportional to the square of the diameter of the box. The random potential is assumed to be independent and bounded; its expectation function and variance function is given in terms of continuous bounded functions on the rescaled box. Our main result is a multivariate central limit theorem for all the simple eigenvalues of this operator, after centering and rescaling. The limiting covariances are expressed in terms of the limiting homogenized eigenvalue problem; more precisely, they are equal to the integral of the product of the squares of the eigenfunctions of that problem times the variance function

Stability and superconductivity of light-atom systems under extreme pressure

The use of high pressure in physics provides access to unusual chemistry, rich phase behaviour, and various interesting phenomena. One of the most sought after phenomena of recent years is high-temperature superconductivity, which has been predicted in solid hydrogen and experimentally verified in numerous metal hydrides. This thesis adds to the knowledge of these high-pressure light-atom systems and introduces new tools for predicting their superconducting properties. It showcases the calculation of an anharmonic phase diagram of solid hydrogen, demonstrates that current theoretical techniques can produce structures and superconducting critical temperatures (Tc) in agreement with experiment for the record-holding binary hydride LaH10, and reveals a metastable hexagonal phase of this material that provides an explanation for recent experimental observations. It also addresses the real need to reduce the operational pressure of superconducting hydrides and offers a solution through the use of machine learning methods, leading to the discovery of several superconductors inhabiting favourable regions of P-Tc space. It is common for papers in this field to focus on the stability and superconductivity of a limited number of metal hydrides, largely because the electron-phonon calculations involved are computationally expensive and because it is not clear which hydrides are potential high-Tc candidates before performing these calculations. This drastically slows down the rate of discovery. The work presented in this thesis provides a solution to this problem; by identifying physically motivated descriptors from scattering theory and density of states calculations, we are able to construct a model for Tc and therefore obtain a method for cheaply identifying the most promising candidate structures. Incorporating this screening step into a high-throughput workflow allows us to study superconductivity in binary hydrides from across the whole periodic table, resulting in one of the most comprehensive studies of superconductivity in binary hydrides ever produced and leading to the identification of several above- and near-room-temperature candidates. The methods developed in this thesis could be expanded to other classes of materials, including ternary hydrides and other light binaries, and used as a guide to designing high-throughput workflows for other material properties. The findings may bring us closer to the ultimate goal of first-principles material design.PhD studentship provided by the Engineering and Physical Sciences Research Council (EPSRC

Atomic and electronic structure studies of nano-structured systems : Carbon and related materials

Modeling in the framework of density functional theory has been conducted on carbon nanotubes and graphene nano-structures. The results have been extended to non-carbon systems such as boron nanostructures. Computational studies are complemented by experimental methods to refine the structural models and obtain a better understanding of the electronic structure. It is observed that the zigzag edged bilayered graphene nanoribbons are highly unstable as compared to their armchair counterparts. A novel approach has been proposed for the patterning of chirality/diameter controlled single walled carbon nanotubes. Nanotube formation is found to be assisted by edge ripples along with the intrinsic edge reactivity of different types of bilayered GNRs. The effect of bundling on the electronic structure of single walled carbon nanotubes in zigzag single walled carbon nanotubes has been studied. Hydrostatic pressure effects were examined on bundled single walled carbon nanotubes. Nanotubes with chiral indices (3n + 3, 3n + 3) acquire hexagonal cross-sections on application of hydrostatic pressures. The formation of a novel quasi two-dimensional phase of carbon during hydrostatic compression of small and large nanotubes under extreme conditions of pressure is modeled and is understood to be dictated by breaking of symmetry during compression. Nanoscale materials with anisotropic compressibility do not exhibit symmetric compression as in bulk materials. Structural stability of boron nanoribbons derived from \u27α-sheet\u27 and reconstructed {1221} sheets was studied. Antiaromatic instabilities were found to destabilize nanoribbons constructed from reconstructed {1221} sheets when compared to those obtained from the \u27α-sheet\u27. The stability of the nanoribbons was found to increase with increasing width and increase in the hole density (η) of the boron nanoribbons. The study of electronic structure reveals the presence of semiconducting nanostructures. The presence of nanoscale crystalline domains due to random functionalization has made it difficult to resolve the chemical structure of graphene oxide and it remains a much debated topic to date. A combination of analytical, spectroscopic and density functional techniques have been used to determine the structure and properties of such nano materials. Graphene oxide has unusual exotic properties and belongs to this class of materials. Investigations reveal that the chemical structure of graphene oxide can be visualized as puckered graphene sheets linked by oxygen atoms. Density functional theory has been used to calculate the site projected partial density of states for carbon and oxygen atoms involved in different types of bonding. A comparison of these simulations with carbon and oxygen K-edge absorption spectra has led to an understanding of the basic electronic structure of this material

Dynamics of clusters and fragments in heavy-ion collisions

A review is given on the studies of formation of light clusters and heavier fragments in heavy-ion collisions at incident energies from several tens of MeV/nucleon to several hundred MeV/nucleon, focusing on dynamical aspects and on microscopic theoretical descriptions. Existing experimental data already clarify basic characteristics of expanding and fragmenting systems typically in central collisions, where cluster correlations cannot be ignored. Cluster correlations appear almost everywhere in excited low-density nuclear many-body systems and nuclear matter in statistical equilibrium where the properties of a cluster may be influenced by the medium. On the other hand, transport models to solve the time evolution have been developed based on the single-nucleon distribution function. Different types of transport models are reviewed putting emphasis both on theoretical features and practical performances in the description of fragmentation. A key concept to distinguish different models is how to consistently handle single-nucleon motions in the mean field, fluctuation or branching induced by two-nucleon collisions, and localization of nucleons to form fragments and clusters. Some transport codes have been extended to treat light clusters explicitly. Results indicate that cluster correlations can have strong impacts on global collision dynamics and correlations between light clusters should also be taken into account.Comment: review article, 64 pages, 27 figure

Quantum Chemical Investigation of Electronic and Structural Properties of Crystalline Bismuth and Lanthanide Triborates

The origins of the optical effects and the chemical stability of BiB3O6 are studied by gradient-corrected hybrid B3PW density functional theory within the Gaussian-orbital-based CO-LCAO scheme. Including spin-orbit coupling, B3PW yields an estimate of the indirect band gap of 4.29~4.99 eV which is closer to the experimental value of 4.3 eV than the HF, LDA or GGA results. The crystal orbital overlap population is carried out to give a detailed first-principles analysis of chemical bonding. It is found that the Bi 6s couples with the O 2p in the primary interaction, which eventually forms both bonding and antibonding orbitals below the Fermi level. The Bi 6p is further involved in the secondary interaction with the filled Bi 6s-O 2p antibonding orbitals. The stereochemical activity of the Bi lone-pairs mainly originates from the primary interaction for the occupied Bi 6s-O 2p antibonding orbitals. It is found that the Bi 6p orbitals are not critically responsible for the non-spherical shape of the Bi lone-pairs. The densities of optical absorptions for the total BiB3O6 crystal, [BiO4]5- and [BO3]3- and [BO4]5- subunits are individually calculated by convoluting the total occupied density of states and the virtual densities of states of the corresponding unit. It is found that the [BiO4]5- units are mainly responsible for the optics of BiB3O6 in the long wavelength region. The reason is that the Bi-O covalent bonds lead to large spatial orbital overlappings and thus favor the electronic transfer from the occupied O 2p to the empty Bi 6p orbitals. The relativistic and correlation effects lead to fundamental differences of the band structure, chemical bonds and optical effects for BiB3O6 compared with non-relativistic and uncorrelated calculations. The harmonic frequencies of BiB3O6 are calculated by applying the numerical-difference technique. The complete 13 A and 14 B vibrational modes are assigned, graphically visualized and classified according to the Bi-O and B-O motions. Comparisons with previous experimental reports are discussed in detail. Crystal orbital adapted Gaussian (4s4p3d), (5s5p4d) and (6s6p5d) valence primitive basis sets are derived, in line with relativistic energy-consistent 4f-in-core lanthanide pseudopotentials of the Stuttgart-Köln variety, for calculating periodic bulk materials containing trivalent lanthanide ions, particularly in this thesis for the investigation of the relative stability of C2 and I2 phases of LnB3O6. Different segmented contraction schemes are calibrated on A-type Pm2O3 studying the basis set size effects. Further applications to the geometry optimization of other A-type Ln2O3 (Ln=La-Nd) show a satisfactory agreement with experimental data using the lanthanide valence basis sets (6s6p5d)/[4s4p4d]. The cohesive energies of A-Ln2O3 within both conventional Kohn-Sham DFT and the a posteriori-HF correlation DFT schemes are evaluated by using the corresponding augmented sets (8s7p6d)/[6s5p5d] with additional diffuse functions for the atomic energies of free lanthanide atoms. The I2 phases of LaB3O6 and GdB3O6 crystals are more stable than C2 phases according to both of the calculated energetic data and first-principles bond analysis. This is in agreement with the experimental results. A new method is developed to calculate the optical properties for large systems based on available wavefunction correlation approaches in the framework of the incremental scheme. The convergence behaviors of first- and second-order polarizabilities with respect to the domain distances and incremental expansion orders are examined and discussed for the model system Ga4As4H18

A Spectroscopic and Computational Study of Diacetyl and Water Clusters

Diacetyl, otherwise known as 1,2-butadione or biacetyl, is a flavor additive used in microwave popcorn, and more importantly as of late, e-cigarettes. The compound is known to cause lung disease for those who have been exposed to a large quantity of the buttery smelling molecule. As such, the characterization of diacetyl’s vibrational modes when it interacts with water are pivotal to understanding the effects it has on human lung tissue. In this research, the intermolecular interactions between water and diacetyl and the effects they have on one another’s vibrational modes are explored. While some experimental data is presented, the spectra obtained are not sufficient for extensive comparison to theoretical computations. Therefore, the focus of this work is on the theoretical optimization and simulated spectra of diacetyl and water complexes ranging from 1/1 to 1/5 Diacetyl/Water ratios, with the increase in water molecules assisting in the understanding of how diacetyl behaves when it is solvated in the human body. By using the B3LYP and MP2 methods with aug-cc-pVTZ basis set and tight convergence, a total of three 1/1, ten 1/2, twelve 1/3, twenty-three 1/4, and thirty-nine 1/5 Diacetyl/Water complexes were optimized. Use of rCCSD(T) single-point energy calculations, as well as B3LYP-D3, M06-2X, M06-2X-D3, and -B97XD methods, the energetics of the lowest energy structures were confirmed. The simulated spectra of the lowest energy structures were investigated, and trends were gathered for the lowest energy structures from the one to five water complexes. These simulated spectra showed that the carbonyl stretching frequency of diacetyl shifted to lower energy and increased in the splitting between the symmetric and asymmetric motions as the number of water molecules increased. The stretching motions of the methyl group also increased in the range of frequencies that described their motions