Orbital-free density functional theory requires accurate approximations for the noninteracting kinetic energy as a functional of the ground-state electron den- sity. For explicit functionals in real space, it has proved difficult to supersede the quality of the gradient expansion, truncated at second order. This is partly because the gradient expansion diverges for atomic and molecular densities. In an effort to include information about higher-order terms in the gradient expansion but avoid divergences, we consider resummations for the series using Padé approximants and Meijer-G functions. To regularize terms that appear in the denominator, we consider various damping functions, which introduces parameter(s) that can be fit to atomic data. These results improve upon the second-order truncation, but do not achieve the exquisite accuracy that would be required for practical orbital-free density-functional theory calculations. / Thesis / Master of Science (MSc)

Nowadays, studying materials for renewable energy applications are highly de- manded. Hybrid halide perovskites have proven to be promising materials for such technology since their first application in solar cells in 2008, with a power conversion efficiency of 2.7%. Since then, hybrid halide perovskites have proven their superior properties for light-absorbing devices. In this scope, studying the optical properties is ultimately essential. This work investigates the tempera- ture dependence of the optical spectra for formamidinium lead iodide/bromide perovskites (FAPb[IxBr1-x]3 (0 ≤ x ≤ 1) using spectroscopic ellipsometry mea- surements, empirical optical modeling, density functional theory, and molecular dynamics. Five FAPb[IxBr1-x]3 perovskite samples were fabricated by a hybrid processing technique. External Quantum Efficiency measurements reported an energy bandgap range between 1.58 eV and 1.77 eV for the resulted samples. Next, multi-angle spectroscopic ellipsometry measurements were applied with a temperature-controlled stage, allowing the variance of temperature from 25 ◦C to 75 ◦C. The results show a blue shift in the optical spectra at elevated tempera- tures. We then conducted a temperature-dependent empirical model that predicts the optical spectra for the sample of study at higher temperatures using input data of the spectra at room temperature. The model reports low mean squared errors which are less than ≈ 2 around the bandgap, and further development can be applied for better utilization. First-principles investigations were conducted on four FAPb[IxBr1-x]3 per- ovskite unit cells. Structural optimization was applied with assuming fixed angles of the lattice. Atomic configuration was chosen to achieve minimal ground state energies. Ab initio molecular dynamics simulations were applied to each opti- mized structures at target temperatures of 300 K and 350 K using Berendsen thermostat. The simulation time was 4ps with 1fs time step, and the electronic energy bandgap was calculated at each step using PBE functional. The simula- tions reported a rotational motion for the FA molecule that showed to be faster at 350 K, along with higher mean energy bandgap compared to the reported value at 300 K. The optical spectra were extracted using a snapshot from the resulted structures. Similar to the spectroscopic ellipsometry measurements, a temperature induced blue shift was reported. Overall, this work detects and predicts the temperature-dependent optical spectra and confirms the role of the atomic thermal motion. With further devel- opment, higher accuracy can be achieved along with broadening the materials of study for photovoltaic and optoelectronic applications.

Understanding the phase behaviour of colloidal systems is relevant to designing new colloid-based nanostructured materials. One common platform for studying the colloidal system is the model of hard spheres. Over the last few decades, different hard-sphere models have been developed. We study the phase behaviour of three hard-sphere models: the lattice gas model, the local density approximation model, and the white bear version of the fundamental measure theory, with short-range attractive and long-range repulsive (SALR) interactions. The competition between the attraction and repulsion results in the formation of clusters composed of many particles, whereas the spatial arrangement of these clusters leads to the formation of long-range ordered phases. Phase diagrams containing the commonly observed body-center-cubic (BCC) and hexagonally close-packed (HCP) phases, as well as the novel Frank-Kasper $\sigma$ and A15 phases, have been constructed using the density functional theory applied to hard spheres with SALR interactions. Similar phase transition sequences have been predicted for the three hard-sphere models, implying a universality of the observed phase behaviour for hard spheres interacting with SALR potentials. However, the details of the phase diagrams could vary significantly. The results obtained from our study shed light on understanding the emergence of complex phases from simple systems. / Thesis / Master of Science (MSc) / Soft condensed matter physics, a sub-field of condensed matter physics, primarily concerns the investigation of physical properties of pliable, deformable materials such as plastics, gels, and colloidal suspensions. One particularly intriguing feature of these soft materials is their ability to self-assembly, leading to the spontaneous formation of ordered structures, including but not limited to body-centered cubic and face-centered cubic phases. In particular, a group of complex spherical phases, known as the Frank-Kasper phases, has been identified in various soft matter systems, encompassing polymeric blends, colloidal suspensions, and more. Notably, in colloidal systems, when nanoparticles are grafted with polymer chains, the Frank-Kasper phases could become stable. However, the emergence of these complex phases from the diverse soft matter systems have not been fully understood. In this thesis, we employ the classical density functional theory based on three different hard-sphere models to probe the formation of the Frank-Kasper phases in colloidal systems. Our results provide insights into the formation mechanism of the Frank-Kasper phases in a simple system and demonstrate the universality of different hard-sphere models.

No description available.

No description available.

Metal organic frameworks (MOFs) are nanoporous materials composed of inorganic and organic structural building units (SBUs). Over the last several decades, interest in MOFs has grown considerably partially due to their promising capabilities for carbon capture and storage (CCS) technologies. This is mostly due to their tunable pore chemistry, high internal surface area and unique structural diversity. This thesis focuses on computational methods that were used to analyze and organize a database of hypothetical structures to facilitate MOF discovery. The work done is detailed in two main parts. In the first part of the thesis, a topologically diverse hypothetical MOF database, containing over 300,000 structures, is screened using simplified molecular-input line-entry system (SMILES) strings to identify SBUs in each structure. The structures in the database are then renamed according to the SBUs identified by the SMILES strings algorithm. The renaming of the structures allows users to have a good idea of the geometrical and topological distribution of the database. Furthermore, a quick and reliable test is developed to identify structures with incorrect bonding patterns/missing hydrogen. In the second part of the thesis, density functional theory (DFT) - derived charges are generated for each structure in the hypothetical MOF database. Using these charges, the CO₂/N₂ selectivity is calculated and compared with the selectivity values obtained from another charge generating method, split-charge equilibration (SQE), and it is determined that there is good agreement, r = 0.96, between the two methods. A machine learning model is then developed to identify relationships between geometrical features and CO₂/N₂ selectivity.

In recent decades, machine learning techniques have received an explosion of interest in the domain of high-throughput materials discovery, which is largely attributed to the fastgrowing development of quantum-chemical methods and learning algorithms. Nevertheless, machine learning for catalysis is still at its initial stage due to our insufficient knowledge of the structure-property relationships. In this regard, we demonstrate a holistic machine-learning framework as surrogate models for the expensive density functional theory to facilitate the discovery of high-performance catalysts. The framework, which integrates the descriptor-based kinetic analysis, material fingerprinting and machine learning algorithms, can rapidly explore a broad range of materials space with enormous compositional and configurational degrees of freedom prior to the expensive quantum-chemical calculations and/or experimental testing. Importantly, advanced machine learning approaches (e.g., global sensitivity analysis, principal component analysis, and exploratory analysis) can be utilized to shed light on the underlying physical factors governing the catalytic activity on a diverse type of catalytic materials with different applications. Chapter 1 introduces some basic concepts and knowledge relating to the computational catalyst design. Chapter 2 and Chapter 3 demonstrate the methodology to construct the machine-learning models for bimetallic catalysts. In Chapter 4, the multi-functionality of the machine-learning models is illustrated to understand the metalloporphyrin's underlying structure-property relationships. In Chapter 5, an uncertainty-guided machine learning strategy is introduced to tackle the challenge of data deficiency for perovskite electrode materials design in the electrochemical water splitting cell. / Doctor of Philosophy / Machine learning and deep learning techniques have revolutionized a range of industries in recent years and have huge potential to improve every aspect of our daily lives. Essentially, machine-learning provides algorithms the ability to automatically discover the hidden patterns of data without being explicitly programmed. Because of this, machine learning models have gained huge successes in applications such as website recommendation systems, online fraud detection, robotic technologies, image recognition, etc. Nevertheless, implementing machine-learning techniques in the field of catalyst design remains difficult due to 2 primary challenges. The first challenge is our insufficient knowledge about the structure-property relationships for diverse material systems. Typically, developing a physically intuitive material feature method requests in-depth expert knowledge about the underlying physics of the material system and it is always an active field. The second challenge is the lack of training data in academic research. In many cases, collecting a sufficient amount of training data is not always feasible due to the limitation of computational/experimental resources. Subsequently, the machine learning model optimized with small data tends to be over-fitted and could provide biased predictions with huge uncertainties. To address the above-mentioned challenges, this thesis focus on the development of robust feature methods and strategies for a variety of catalyst systems using the density functional theory (DFT) calculations. Through the case studies in the chapters, we show that the bulk electronic structure characteristics are successful features for capturing the adsorption properties of metal alloys and metal oxides. While molecular graphs are robust features for the molecular property, e.g., energy gap, of metal-organics compounds. Besides, we demonstrate that the adaptive machine learning workflow is an effective strategy to tackle the data deficiency issue in search of perovskite catalysts for the oxygen evolution reaction.

In recent years, deep learning technologies have received huge attention and interest in the field of high-performance material design. This is primarily because deep learning algorithms in nature have huge advantages over the conventional machine learning models in processing massive amounts of unstructured data with high performance. Besides, deep learning models are capable of recognizing the hidden patterns among unstructured data in an automatic fashion without relying on excessive human domain knowledge. Nevertheless, constructing a robust deep learning model for assessing materials' structure-property relationships remains a non-trivial task due to highly flexible model architecture and the challenge of selecting appropriate material representation methods. In this regard, we develop advanced deep-learning models and implement them for predicting the quantum-chemical calculated properties (i.e., formation energy) for an enormous number of crystal systems. Chapter 1 briefly introduces some fundamental theory of deep learning models (i.e., CNN, GNN) and advanced analysis methods (i.e., saliency map). In Chapter 2, the convolutional neural network (CNN) model is established to find the correlation between the physically intuitive partial electronic density of state (PDOS) and the formation energies of crystals. Importantly, advanced machine learning analysis methods (i.e., salience mapping analysis) are utilized to shed light on underlying physical factors governing the energy properties. In Chapter 3, we introduce the methodology of implementing the cutting-edge graph neural networks (GNN) models for learning an enormous number of crystal structures for the desired properties. / Master of Science / Machine learning technologies, particularly deep learning, have demonstrated remarkable progress in facilitating the high-throughput materials discovery process. In essence, machine learning algorithms have the ability to uncover the hidden patterns of data and make appropriate decisions without being explicitly programmed. Nevertheless, implementing machine learning models in the field of material design remains a challenging task. One of the biggest limitations is our insufficient knowledge about the structure-property relationships for material systems. As the performance of machine learning models is to a large degree determined by the underlying material representation method, which typically requires the experts to have in-depth knowledge of the material systems. Thus, designing effective feature representation methods is always the most crucial aspect for machine learning model development and the process takes a significant amount of manual effort. Even though tremendous efforts have been made in recent years, the research process for robust feature representation methods is still slow. In this regard, we attempt to automate the feature engineering process with the assistance of advanced deep learning algorithms. Unlike the conventional machine learning models, our deep learning models (i.e., convolutional neural networks, graph neural networks) are capable of processing massive amounts of structured data such as spectrum and crystal graphs. Specifically, the deep learning models are explicitly designed to learn the hidden latent variables that are contained in crystal structures in an automatic fashion and provide accurate prediction results. We believe the deep learning models have huge potential to simplify the machine learning modeling process and facilitate the discovery of promising functional materials.

A real-space time-domain calculation of the frequency-dependent dielectric constant of nonmetallic crystals is outlined and the integrals required for this calculation are computed. The outline is based on time dependent current density functional theory and is partially implemented in the ab initio density functional theory FIREBALL program. The addition of a vector potential to the Hamiltonian of the system is discussed as well as the need to include the current density in addition to the particle density. The derivation of gradient integrals within a localized atomic-like orbital basis is presented for use in constructing the current density. Due to the generality of the derivation we also give the derivation of the kinetic energy, dipole, and overlap interactions.

No description available.