This thesis is part of an effort to enable large-scale Hartree-Fock/Kohn-Sham (HF/KS) calculations. The objective is to model molecules and materials containing thousands of atoms at the quantum mechanical level. HF/KS calculations are usually performed with the Self-Consistent Field (SCF) method. This method involves two computationally intensive steps. These steps are the construction of the Fock/Kohn-Sham potential matrix from a given electron density and the subsequent update of the electron density usually represented by the so-called density matrix. In this thesis the focus lies on the representation of potentials and electron density and on the density matrix construction step in the SCF method. Traditionally a diagonalization has been used for the construction of the density matrix. This diagonalization method is, however, not appropriate for large systems since the time complexity for this operation is σ(n3). Three types of alternative methods are described in this thesis; energy minimization, Chebyshev expansion, and density matrix purification. The efficiency of these methods relies on fast matrix-matrix multiplication. Since the occurring matrices become sparse when the separation between atoms exceeds some value, the matrix-matrix multiplication can be performed with complexity σ(n). A hierarchic sparse matrix data structure is proposed for the storage and manipulation of matrices. This data structure allows for easy development and implementation of algebraic matrix operations, particularly needed for the density matrix construction, but also for other parts of the SCF calculation. The thesis addresses also truncation of small elements to enforce sparsity, permutation and blocking of matrices, and furthermore calculation of the HOMO-LUMO gap and a few surrounding eigenpairs when density matrix purification is used instead of the traditional diagonalization method. / <p>QC 20101123</p>

This thesis describes an accurate and scalable computational method designed to perform nanoelectronic structure calculations. Built around the FEAST framework, this method directly addresses the nonlinear eigenvalue problem. The new approach allows us to bypass traditional approximation techniques typically used for first-principle calculations. As a result, this method is able to take advantage of standard muffin-tin type domain decomposition techniques without being hindered by their perceived limitations. In addition to increased accuracy, this method also has the potential to take advantage of parallel processing for increased scalability. The Introduction presents the motivation behind the proposed method and gives an overview of what will be presented for this thesis. Chapter 1 explains how electronic structure calculations are currently performed, including an overview of Density Functional Theory and the advantages and disadvantages of various numerical techniques. Chapter 2 describes, in detail, the method proposed for this thesis, including mathematical justification, a matrix-level example, and a description of implementing the FEAST algorithm. Chapter 3 presents and discusses results from numerical experiments for Hydrogen and various Hydrogen molecules, Methane, Ethane, and Benzene. Chapter 4 concludes with a summary of the presented work and its impact in the field.

TiP4N8 was obtained from the binary nitrides TiN and P3N5 upon addition of NH4F as a mineralizer at 8 GPa and 1400 °C. An intricate interplay of disorder and polymorphism was elucidated by in situ temperature- dependent single-crystal X-ray diffraction, STEMHAADF, and the investigation of annealed samples. This revealed two polymorphs, which consist of dense networks of PN4 tetrahedra (degree of condensation k= 0.5) and either augmented triangular TiN7 prisms or triangular TiN6 prisms for α- and β-TiP4N8, respectively. The structures of TiP4N8 exhibit body-centered tetragonal (bct) framework topology. DFT calculations confirm the measured band gaps of α- and β-TiP4N8 (1.6–1.8 eV) and predict the thermochemistry of the polymorphs in agreement with the experiments.

No description available.

In this paper we formulate a nonlocal density functional theory of inhomogeneous water. We model a water molecule as a couple of oppositely charged sites. The negatively charged sites interact with each other through the Lennard–Jones potential (steric and dispersion interactions), square-well potential (short-range specific interactions due to electron charge transfer), and Coulomb potential, whereas the positively charged sites interact with all types of sites by applying the Coulomb potential only. Taking into account the nonlocal packing effects via the fundamental measure theory, dispersion and specific interactions in the mean-field approximation, and electrostatic interactions at the many-body level through the random phase approximation, we describe the liquid–vapour interface. We demonstrate that our model without explicit account of the association of water molecules due to hydrogen bonding and with explicit account of the electrostatic interactions at the many-body level is able to describe the liquid–vapour coexistence curve and the surface tension at the ambient pressures and temperatures. We obtain very good agreement with available in the literature MD simulation results for density profile of liquid–vapour interface at ambient state parameters. The formulated theory can be used as a theoretical background for describing of the capillary phenomena, occurring in micro- and mesoporous materials.

<p> Surface probes are producing a huge variety of spatially resolved images of materials during phase transitions. These images have complex pattern formation present across a variety of length scales. Here, I apply image cluster scaling analysis and machine learning to several such images. First, I apply cluster analysis techniques to charge stripe orientations in Bi2−zPbzSr2−yLayCuO6+x. Our experimental collaborators observe stripes with period 4a0 in Bi2−zPbzSr2−yLayCuO6+x. [1] The local orientation of these stripes forms complex patterns from which we extract relationships involving cluster sizes. We compare these experimental exponents to those computed at a phase transition in the following models: 2D percolation and the 2D and 3D clean and random field Ising models. We find that only the 3D clean and random field Ising models are consistent with the data. Combined with the stability of these exponents across the superconducting region, we conclude that the system is in the random field Ising model universality class. We apply these same cluster techniques to period-4 antiferromagnet order in NdNiO3. [2] Our experimental collaborators observed the intensity for 2 of 8 possible directions for period-4 antiferromagnetic order in NdNiO3 and find complex pattern formation that remains after a temperature cycle past the hysteresis loop. We threshold this experimental data and extract cluster exponents for this system. We then compare these models to the 4-state clean and random field clock models. This exponent comparison shows that the 4-state random field clock model is a match for the experimental data. We then train a convolutional neural network to distinguish the 4-state clean and random field clock models. The fit neural net is capable of labeling our entire testing dataset of 16000 images with 100% accuracy. This gives us a 95% confidence interval of (0.9998, 1) by the rule of three. [3] We then split the field of view into 52 sliding windows of the original experimental data which we feed into the trained model. The model classifies every input window as a 2D random field clock model which gives us a 95% confidence interval of (0.94, 1). The observed hysteresis in the experimental data, the cluster analysis and the machine learning prediction clearly show the observed patterns are in the random field 4-state clock model universality class. </p>

No description available.

Covariant density functional theory (CDFT) is one of the modern theoretical tools for the description of finite nuclei and neutron stars. Its performance is defined by underlying covariant energy density functionals (CEDFs) which depend on a number of parameters. Several investigations within the CDFT framework using the relativistic Hartree-Bogoliubov (RHB) approach are discussed in this dissertation. Statistical errors in ground state observables and single-particle properties of spherical even-even nuclei and their propagation to the limits of nuclear landscape have been investigated in the covariant energy density functionals with nonlinear density dependency. The parametric correlations are studied in different classes of CEDFs; the elimination of these correlations reduces the number of independent parameters to five or six without affecting the performance of CEDFs on a global scale. Moreover, this study reveals the need to include information on deformed nuclei for the improvement of fitting protocols. A new technique for incorporating deformed nuclei data into the fitting protocol is described. Different CEDFs are optimized using this approach, resulting in a significant improvement in the nuclear mass description. A systematic investigation of the ground state and fission properties of even-even actinides and superheavy nuclei with proton numbers Z = 90 - 120 located between the two-proton and two-neutron drip lines has been performed. These results provide a necessary theoretical input for the modeling of the nuclear astrophysical rapid neutron capture process (r-process) taking place in the mergers of neutron stars. The state-of-the-art CEDFs, namely, DD-PC1, DD-ME2, NL3*, and PC-PK1, are employed in this study. Theoretical systematic uncertainties in the physical observables and their evolution as a function of proton and neutron numbers have been quantified and their major sources have been identified. The extension of the nuclear landscape to hyperheavy nuclei is investigated. The transition from ellipsoidal-like nuclear shapes to toroidal shapes is crucial for the potential expansion of the nuclear landscape to hyperheavy nuclei. The physical reasons for the stability of toroidal nuclei in the Z ~ 134 region are discussed.

No description available.

A molecule can crystallise in more than one crystal structure, a common phenomenon in organic compounds known as polymorphism. Different polymorphic forms may have significantly different physical properties, and a reliable prediction would be beneficial to the pharmaceutical industry. However, crystal structure prediction (CSP) based on the knowledge of the chemical structure had long been considered impossible. Previous failures of some CSP attempts led to speculation that the thermodynamic calculations in CSP methodologies failed to predict the kinetically favoured structures. Similarly, regarding the stabilities of co-crystals relative to their pure components, the results from lattice energy calculations and full CSP studies were inconclusive. In this thesis, these problems are addressed using the state-of-the-art CSP methodology implemented in the GRACE software. Firstly, it is shown that the low-energy predicted structures of four organic molecules, which have previously been considered difficult for CSP, correspond to their experimental structures. The possible outcomes of crystallisation can be reliably predicted by sufficiently accurate thermodynamic calculations. Then, the polymorphism of 5- chloroaspirin is investigated theoretically. The order of polymorph stability is predicted correctly and the isostructural relationships between a number of predicted structures and the experimental structures of other aspirin derivatives are established. Regarding the stabilities of co-crystals, 99 out of 102 co-crystals and salts of nicotinamide, isonicotinamide and picolinamide reported in the Cambridge Structural Database (CSD) are found to be more stable than their corresponding co-formers. Finally, full CSP studies of two co-crystal systems are conducted to explain why the co-crystals are not easily obtained experimentally. / University of Bradford