Here, we use and develop first-principles methods based on density functional theory (DFT) and beyond to understand and predict charge transport phenomena in the novel class of nanostructured devices: molecular junctions. Molecular junctions, individual molecules contacted to two metallic leads, which can be systematically altered by modifying the chemistry of each component, serve as test beds for the study of transport at the nanoscale. To date, various experimental methods have been designed to reliably assemble and mea- sure transport properties of molecular junctions. Furthermore, theoretical methods built on DFT designed to yield quantitative agreement with these experiments for certain classes of molecular junctions have been developed. In order to gain insight into a broader range of molecular junctions and environmental effects associated with the surrounding solution, this dissertation will employ, explore and extend first-principles DFT calculations coupled with approximate self-energy corrections known to yield quantitative agreement with experiments for certain classes of molecular junctions.

To start we examine molecular junctions in which the molecule is strongly hybridized with the leads: a challenging limit for the existing methodology. Using a physically motivated tight-binding model, we find that the experimental trends observed for such molecules can be explained by the presence of a so-called “gateway” state associated with the chemical bond that bridges the molecule and the lead. We discuss the ingredients of a self-energy corrected DFT based approach to quantitatively predict conductance in the presence of these hybridization effects.

We also develop and apply an approach to account for the surrounding environment on the conductance, which has been predominantly ignored in past transport calculations due to computational complexity. Many experiments are performed in a solution of non-conducting molecules; far from benign, this solution is known to impact the measured conductance by as much as a factor of two. Here, we show that the dominant effect of the solution stems from nearby molecules binding to the lead surface surrounding the junction and altering the local electrostatics. This effect operates in much the same way adsorbates alter the work function of a surface. We develop a framework which implicitly includes the surrounding molecules through an electrostatic-based lattice model with parameters from DFT calculations, reducing the computational complexity of this problem while retaining predictive power. Our approach for computing environmental effects on charge transport in such junctions will pave the way for a better understanding of the physics of nanoscale devices, which are known to be highly sensitive to their surroundings.

The accurate prediction of electronic excitation energies in molecules is an area of intense research of significant fundamental interest and is critical for many applications. Today, most excited state calculations use time-dependent density functional theory (TDDFT) in conjunction with an approximate exchange-correlation functional. In this dissertation, I have examined and critically assessed an alternative method for predicting charged and low-lying neutral excitations with similar computational cost: the \textit{ab initio} Bethe-Salpeter equation (BSE) approach. Rigorously based on many-body Green's function theory but incorporating information from density functional theory, the predictive power of the BSE approach remained at the beginning of this work unexplored for the neutral and charged electronic excitations of organic molecules. Here, the results and implications of several systematic benchmarks are laid out in detail.

Electronic structure theory enables fundamental understanding of material properties. Using first-principles based methods, several different classes of complex materials are studied including perovskite oxide heterostructures, halide perovskites, alkali metals under pressure, and high-throughput screening of multiferroic materials.

• In Chapter 2 we discuss the basis of electronic structure methods used in this thesis and introduce the calculation of topological properties from first-principles.

• In Chapter 3 the properties of lithium, an ostensibly simple metal, under pressure are introduced and our explorations into the emergence of nontrivial topological features at high pressures are shown.

• Halide perovskites have emerged as a promising material class for solar energy con- version due to their optoelectronic properties. We explore three different halide per- ovskite materials and, in collaboration with experiment, develop an understanding of how their properties change through chemical substitutions and structural manipula- tions. This includes the optoelectronic properties of Sn–alloyed Cs2AgBiBr6 (Chapter 4) and Cs8Au4XCl23 (X = In; Bi) (Chapter 6); and the increase in conductivity of (EA)2CuBr4 through pressure (Chapter 5).

• Similarly, perovskite oxides are a highly tunable class of materials which display a wide range of interesting phenomena. Here we exploit the fact that experimentalists can control the synthesis of perovskite oxide heterostructures at the precision of single atomic layers. Given this level of control, we use first-principles calculations to de- sign monolayers and bilayers that would tune the work function of bulk SrRuO3 for thermionic applications in Chapter 7

• In Chapter 8, we discuss our work developing a high throughput workflow based on symmetry and first-principles calculations to screen tens of thousands of materials for candidates which are both magnetic and ferroelectric.

• Finally, Chapter 9 presents an overview of the work.

The interaction between excitons and phonons is fundamental to the nature and fate of photoexcitatons in solids, with important implications for spectroscopy and transport measurements, and for applications in optoelectronics and clean energy. In this dissertation, we present recent advances in computing exciton-phonon interactions from first principles. We implement a recently proposed linear-response reciprocal space-based framework which involves contracting electron-phonon matrix elements computed from density functional perturbation theory (DFPT) with exciton expansion coefficients obtained after building and diagonalizing the ab initio Bethe-Salpeter Hamiltonian, which is built on density functional theory and the GW approximation. We apply this formalism in unique ways to study phenomena related to exciton-phonon interactions, namely the nature of exciton diffusion in acene crystals, the dynamical screening of excitons in halide perovskites due to lattice vibrations, and the asymmetric lineshapes in MoS2 stemming from off-diagonal exciton-phonon coupling.

The development of the physical principles underlying novel materials to power the technological needs of the modern world is dependent on having a detailed knowledge of the electronic and structural properties of these materials. First-principles electronic structure theory methods are used here to calculate the structural and electronic properties of complex functional materials with an eye toward applications in artificial photosynthesis and "Beyond Moore's Law" information technology. The details of the methods employed are discussed in Chapter 2.

Artificial photosynthesis, the photocatalytic conversion of water and carbon dioxide into solar fuels such as hydrogen gas and hydrocarbons, is a critical technology for future green energy applications. There are numerous challenges to be overcome in the development of high performing photocatalyst materials. Here, first-principles calculations are used to understand and tune the electronic structure of complex materials for artificial photosynthesis catalysis, in particular ternary metal oxides and layered two-dimensional materials.

- In Chapter 3 we present the results of an experimental collaboration investigating n-type FeWO4 as a high photovoltage photoanode material. We perform electronic structure calculations to shed light on the potential mechanism driving this high photovoltage.

- In Chapter 4 we perform absolute band edge energy calculations on a series of MoS_{2(1-x)}Se_{2x} alloys to corroborate the results obtained from experimental collaborators. We find that the band edges of these alloys can be tuned between the band edges of pristine MoS2 and those of pristine MoSe2 when the alloys assume certain crystal structures. We identify one form of these alloys that does not behave as expected upon incorporation of Se into MoS2 and perform a deeper analysis of the properties of these systems.

- In Chapter 5 we study the effect that biaxial in-plane and uniaxial out-of-plane strain have on heterostructures of monolayer Janus WSSe and monolayer ZnO, both polar materials. We find that the absolute band edges of these heterostructures can be tuned to higher and lower energies via application of different types of strain.

Quantum information is a broad field that encompasses novel ways of storing information, both via beyond-transistors forms of storing binary quantities and via quantum computing. Here, first-principles calculations are performed to study two-dimensional materials for use in valleytronics and in tunable exchange bias.

- In Chapter 6 we develop general design principles for maximizing valley splitting in transition metal dichalcogenides (TMDs) via magnetic substrates. We perform a systematic analysis of the effects of proximity, alignment, and magnetic moment of the magnetic ions in a magnetic substrate and the degree to which these factors affect the magnitude of the calculated valley splitting. We then develop a superexchange model to rationalize these calculated values and elucidate the mechanism driving valley splitting in TMDs via magnetic substrates.

- In Chapter 7 we study the magnetic ordering of a novel, layered metal-organic framework that our experimental collaborators found to exhibit tunable exchange bias. Our calculations support the experimental results indicating that this material is a frustrated antiferromagnet and is a spin glass at low temperatures.

Finally, an overview and outlook are provided in Chapter 8.

Metal-organic frameworks (MOFs) are a class of crystalline materials with broad diversity in their chemical compositions and geometries which give rise to a high degree of tunability of their properties, and many possible applications. Because a broad range of synthetic modifications to MOFs are possible, computational methods are invaluable in guiding experimental studies to understand the relationship between a given structure and chemistry and its material properties. In this work, we use first principles electronic structure calculations to calculate low energy geometries, nuclear magnetic resonance (NMR) chemical shifts, and binding energetics of MOFs that adsorb CO$_2$ and O$_2$. Our calculations explain experiments indicating that the presence of SO$_2$ degrades the performance of diamine-appended Mg$_2$(dobpdc), a promising class of MOF for carbon capture, with some appended diamines but not others. Additionally, we show that we can capture trends in O$_2$ binding in a computationally challenging family of MOFs, the BTTri MOFs, that contain open-shell transition metal atoms. We predict that by modifying the halide in BTTri we can obtain binding energies that are ideal for industrial separations of O$_2$.

In order to better understand the mechanism of cooperative CO$_2$ adsorption in diamine-appended Mg$_2$(dobpdc), we extend a statistical mechanics model to understand the role of defects, steric hindrance, and mixtures of diamines on CO$_2$ adsorption isotherms and isobars. This work shows that cooperative uptake is robust in the presence of defects as long as the cooperative interaction which promotes CO$_2$ binding at adjacent diamine sites is sufficiently strong. We also rationalize experimentally observed double stepped isotherms, and develop a way of understanding how the ratio of mixed diamine systems can be chosen to target a specific pressure at which CO$_2$ will be bound to the MOF.

We benchmark the performance of van der Waals corrected density functionals in layered MOFs and layered perovskites, showing that recently developed functionals are able to accurately predict lattice constants for hybrid layered materials. Our calculations also highlight the impact of the lattice constants on calculated observables like the exfoliation energy and the fundamental gap, and demonstrate that care must be taken in including van der Waals corrections in these challenging systems.

Finally, with ab initio many-body perturbation theory we predict the structure and spectroscopic properties of Zn-MFU-4l including electron-hole interactions and accounting for zero-point vibrational effects, and show how modifications to the anion in the framework can reduce both the fundamental gap and the optical gap, and we provide an explanation for previously seen trends in optical experiments on Zn-MFU-4l.

This dissertation studies the persistence of localization and nonergodicity in quantum many-body systems upon collectively coupling a localized bath to a central degree of freedom. Our work sits at the crossroads between two branches of inquiry that are currently under intense theoretical and experimental scrutiny: the existence of robust nonequilibrium phases of matter afforded by external driving or strong disorder, and how one can develop new computational approaches to study dynamics in large systems to long times. The latter is particularly poignant now that we have entered the age of ``noisy intermediate-scale'' quantum computers, scalable analog quantum simulators, and strongly correlated materials, all of which test the limits of what our current toolbox of numerical simulations can achieve. In this respect, centrally coupled systems offers a useful playground for designing new methods for dynamics due to its highly nonlocal geometry, which should generically lead to the rapid growth of entanglement.

In Chapter 2, we show how to avoid this scenario by ensuring that the bath stays localized even with finite central coupling. While one would intuitively expect that the presence of a central degree of freedom would mediate infinite ranged interactions between different parts of the localized bath and thereby destroying it, we demonstrate through analytical arguments and numerical simulations that this is not always true. This crucially relies on being able to suppress the effects of the mediated interactions by making the internal level spacing of the central degree of freedom large enough, at the same time that the number of internal levels is sufficiently large compared to the size of the bath. We give numerical evidence linking a small number of internal levels to the suppression of localization by examining eigenstate and spectral properties of a generic model with bath sizes up to 14 sites.

In Chapter 3, we attempt to probe what happens with much larger bath sizes by studying the dynamics of these localizable, centrally coupled systems using a method based on the time-dependent variational principle. The method is most effective deep in the localized phase, which allows us to study baths of size ~10^2 sites as well as interesting slow dynamics on intermediate timescales reminiscent of logarithmic growth of entanglement in one-dimensional many-body localized systems. Finally, we apply preliminary results on a controlled expansion for the propagator to attempt to understand some of the dynamics revealed by numerical simulations. However, both the numerical and analytical approaches are found to be limited to finite timescales which, in the case of the numerical method, is sometimes due to the rapid growth of entanglement.

In Chapter 4, we strive to push past the limited timescales by focusing on the dynamics of only the system. We study the time-nonlocal memory kernel for the population dynamics of the central degree of freedom, which is again coupled to a localizable bath. We analyze its behavior on short, intermediate, and long timescales to understand what signatures, if any, a localized bath imparts on the memory kernel. From our analysis on the long time behavior, we demonstrate how one can use the memory to directly extract infinite time values for the population from finite time simulations, and potentially serving as a useful approach to obtaining longer time dynamics without directly simulating them.

With first-principles calculations based on density functional theory, we can predict with good accuracy the electronic ground state properties of a fixed arrangement of nuclei in a molecule or crystal. However, the potential of this formalism and approach is not fully utilized; most calculations are performed on experimentally determined structures and stoichiometric substitutions of those systems.

This in part stems from the difficulty of systematically generating 3D geometries that are chemically valid under the complex interactions existing in materials. Designing materials is a bottleneck for computational materials exploration; there is a need for systematic design tools that can keep up with our calculation capacity. Identifying a higher level language to articulate designs at the atomic scale rather than simply points in 3D space can aid in developing these tools.

Constituent atoms of materials tend to arrange in recognizable patterns with defined symmetry such as coordination polyhedra in transition metal oxides or subgroups of organic molecules; we call these structural motifs. In this thesis, we advance a variety of systematic strategies for understanding complex materials from structural motifs on the atomic scale with an eye towards future design.

In collaboration with experiment, we introduce the harmonic honeycomb iridates with frustrated, spin-anisotropic magnetism. At the atomic level, the harmonic honeycomb iridates have identical local geometry where each iridium atom octahedrally coordinated by oxygen hosts a $J_{eff}=1/2$ spin state that experiences interactions in orthogonal spin directions from three neighboring iridium atoms. A homologous series of harmonic honeycomb can be constructed by changing the connectivity of their basic structural units.

Also in collaboration with experiment, we investigate the metal-organic chalcogenide assembly [AgSePh]$_\infty$ that hosts 2D physics in a bulk 3D crystal. In this material, inorganic AgSe layers are scaffolded by organic phenyl ligands preventing the inorganic layers from strongly interacting. While bulk Ag$_2$Se is an indirect band gap semiconductor, [AgSePh]$_\infty$ has a direct band gap and photoluminesces blue. We propose that these hybrid systems present a promising alternative approach to exploring and controlling low-dimensional physics due to their ease of synthesis and robustness to the ambient environment, contrasting sharply with the difficulty of isolating and maintaining traditional low-dimensional materials such as graphene and MoS$_2$.

Automated density functional theory via high throughput approaches are a promising means of identifying new materials with a given property. We automate a search for ferroelectric materials by integrating density functional theory calculations, crystal structure databases, symmetry tools, workflow software, and a custom analysis toolkit. Structural distortions that occur in the structural motifs of ferroelectrics give rise to a switchable spontaneous polarization. In ferroelectrics lattice, spin, and electronic degrees of freedom couple leading to exotic physical phenomena and making them technologically useful (e.g. non-volatile RAM).

We also propose a new neural network architecture that encodes the symmetries of 3D Euclidean space for learning the structural motifs of atomic systems. We describe how these networks can be used to speed up important components of the computational materials discovery pipeline and generate hypothetical stable atomic structures.

Finally, we conclude with a discussion of the materials design tools deep learning may enable and how these tools could be guided by the intuition of materials scientists.