Graphene, the first two-dimensional crystal ever found, is a material that has attracted fervent and sustained interest from condensed matter researchers from around the world. It has a unique and unprecedented band structure in a bulk material: the bands near the Fermi level are linear, leading to massless charge carriers that propagate at the speed of light. However, graphene does not possess a band gap, and as such, it cannot be used to process information in any electronic device that uses digital logic. Graphene is oxidized when several different basic functional groups like hydroxyls, carboxyls, and epoxides bond to the hexagonal carbon basal plane to make graphene oxide (GO). The result is a nonstoichiometric and highly disordered system that, according to the results shown in this thesis, consists of zones of densely-packed functional groups interspersed between zones of relatively small functional group concentration. This has been confirmed by DFT calculations presented here, which is the first time that a successful simulation of the GO density of states has been compared to X-ray data. Contrary to many assumptions in the literature, many of the features in the density of states of GO are due not to carbon sites bonded to functional groups, but are due to nearby non-functionalized carbon sites. The band gap of graphene oxide is principally controlled by oxidation level. Reduction, followed by heating, will regenerate the near-Fermi states and close the band gap significantly as has been seen by others. However, heating non-reduced graphene oxide can also result in a much-reduced band gap, which occurs because intercalated water can react with the heated GO sample to remove functional groups by creation and eventual expulsion of carbon dioxide. The band gap of GO is further complicated by stacking effects if it is multilayered, because residual pi-conjugated states in neighboring planes interact. The two major types of stacking in graphite are AA-stacking and AB-stacking. AA-stacking interactions cause the pi * resonance to broaden and push states to lower energy, which means that AA-stacking determines the width of the gap in highly oxidized samples. However, direct oxidation of graphene is not the only way that one alter the electronic structure of GO. Other results presented here also show that non-covalent functionalization of graphene oxide by amorphous solid water is a powerful, reversible way to dramatically change the GO electronic structure.

In this dissertation we discuss the electronic properties, structural configurations, and reaction mechanisms of chemically functionalized graphene and charged atomic metals. In general, we analyze fundamental atomic scale and nanoscale systems with density functional theory in order to investigate chemical reaction energetics for peroxide synthesis as well as methanol production without carbon emission. These systems were found to be tunable via the addition of cationic and anionic charges, change in transition metal type, and modification through chemical functionalization. Furthermore, transition state theory was used to predict an optimal configuration for chemically functionalized graphene, efficient use of anionic atomic gold and palladium for synthesis of water to peroxide, and clean conversion of methane to methanol without carbon dioxide emission utilizing anionic gold.

Density-functional theory has become an indispensible tool for studying matter on the atomic level, being routinely applied across diverse disciplines from solid-state physics to chemistry and molecular biology. Its failure to account for dispersion interactions has spurred intensive research over the past decade. In this thesis, a semilocal density-functional approximation including dispersion is developed by combining standard functionals for exchange and correlation with the nonempirical “exchange-hole dipole moment“ (XDM) dispersion model of Becke and Johnson. With a minimum of empiricism, the method accurately describes all types of noncovalent interactions, from the extremely weak dispersion forces in rare-gas systems to the hydrogen bonding and stacking interactions responsible for the structure and function of biological macromolecules such as DNA and proteins. The method is compatible with a wide variety of standard Gaussian basis sets, and is easily applied to any system that can be modeled with density-functional theory.

The behavior of sp-valent solids and liquids under compression is a field of intense re- search. At high pressure, they often undergo phase transitions to new structures with novel properties such as superconductivity, high-energy density, and superhardness. Furthermore, knowledge of these materials is essential for understanding the structure and evolution of planets. Molecular systems such as nitrogen and carbon dioxide are particularly interesting as energetic materials: their strong molecular bonds break under compression spawning transformations to exotic polymeric phases. We have used first-principles theory and molecular dynamics to make predictions for the properties of dense nitrogen, carbon dioxide, magnesium silicate, and magnesium oxide. For nitrogen, we provide evidence for a rare first-order liquid-liquid phase transition; only the second such transition seen in an elemental fluid. New finite-temperature structure search techniques have been developed and applied to predict a thermodynamically stable polymeric metal phase of solid nitrogen. Regarding carbon dioxide, we have computed its high-pressure liquid phase diagram over a broad pressure-temperature range, revealing rich structural diversity. We have also designed new free energy methods to explore the stability of free CO2 under deep mantle conditions. Lastly, first-principles molecular dynamics and finite-temperature free energy methods were used to predict a high-pressure phase separation transition in liquid MgSiO3 and also characterize the high-pressure phase diagram of MgO, including its melting curve.

Computational techniques based on density functional theory (DFT) and experimental methods based on electrochemistry (EC), electrochemical scanning tunneling microscopy (EC-STM), and high-resolution electron energy loss spectroscopy (HREELS) were employed to study the adsorption of (i) sulfuric acid on Pd(111), (ii) benzene on Pd(111), (iii) hydroquinone/benzoquinone on Pd(111), (iv) hydroquinone sulfonate/benzoquinone sulfonate on Pd(111), (v) 2,3-dimethylhydroquinone/2,3-dimethylbenzoquinone on Pd(111) and polycrystalline Pd, (vi) hydrogen on 1-6 monolayers (ML) of Pd deposited on a Pt(111) substrate, and (vii) a thiolated iron hydrogenase model complex on polycrystalline Au. In situ EC-STM and DFT investigations of sulfuric acid on a Pd(111) surface indicated that two layers of water molecules and hydronium ions are assembled, non-co-planar with one another, between the rows of surface-coordinated sulfate anions; the layer that is slightly elevated is composed of hydronium counter cations. The STM images of benzene chemisorbed on a Pd(111) electrode surface were simulated and the results suggested that, when the potential of the Pd electrode is held at 0.3 V, benzene is chemisorbed on a 3-fold site; while at 0.55 V, the molecule is adsorbed on a position between a 3-fold and a 2-fold site. Computational and experimental results implied that at low concentrations, hydroquinone sulfonate undergoes oxidative chemisorption forming benzoquinone sulfonate (BQS) on the Pd(111) surface, BQS adopts a flat orientation in which the quinone ring is centered over a 2-fold site, and the C–H and C–S bonds are no longer co-planar with the quinone ring and are slightly tilted, directed away from the surface. At very dilute concentrations, when hydroquinone (H_(2)Q) undergoes oxidative chemisorption producing benzoquinone oriented flat, albeit with a slight tilt, on the Pd(111) surface, the flat-adsorbed quinone ring is centered on a bridge site where the C_(2) axis is rotated 30degree from the [110] direction of the metal substrate, the p-oxygen atoms are located above two-fold sites, and the ring is slightly puckered with the C–H bonds tilted away from the surface at approximately 20degree. When 2,3-dimethylH_(2)Q is chemisorbed on the Pd surface, at low concentrations, 2,3-dimethylH_(2)Q is oxidatively chemisorbed producing 2,3-dimethyl-1,4-benzoquinone oriented flat on the surface, the flat-adsorbed rings are centered above 2-fold sites wherein the C=O bonds are pointing 30degree from the [110] direction of the substrate, the para-oxygen atoms are located above bridge sites, the peripheral bonds are tilted away from the surface at ca. 20degree, and at higher concentrations, oxidative chemisorption occurs through activation of the ring’s C–H bonds yielding edge-oriented 2,3-dimethylH_(2)Q. Electrochemistry and DFT results also implied that at 1-2 ML of Pd on Pt(111), hydrogen is only adsorbed on a hollow site while at 3 ML of Pd or more, atomic hydrogen may be chemisorbed on the 3-fold site or absorbed in the octahedral hole underneath the hollow site. Using Au electrodes, an unbound iron hydrogenase analogue complex studied was found to slightly catalyze the H_(2) evolution process. However, when the complex was immobilized unto the Au surface, the electrocatalytic activity was greatly improved.

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Cerium dioxide (ceria) is an excellent catalytic material due to its ability to both facilitate oxidation/reduction reactions as well as store/release oxygen as an oxygen buffer. The traditional approach to assess and improve ceria's catalytic behavior focuses on how efficiently O-vacancies can be generated and/or annihilated within the material, and how to extend established understandings of "bulk" ceria to further explain the greatly enhanced catalytic behavior of ultra-small ceria nanoparticles (uCNPs) with sizes less than 10 nm. Here, using density functional theory (DFT) calculations, we reexamine the atomic and electronic structures of uCNPs, especially their surface configurations. A unique picture dissimilar to the traditional point of view emerges from these calculations for the surface structure of uCNPs. uCNPs similar to those obtained by experimental synthesis and applied in catalytic environments exhibit core-shell like structures overall, with under-stoichiometric, reduced CNP "cores" and over-stoichiometric, oxidized surface "shell" constituted by various surface functional groups, e.g.,-Ox and/or -OH surface groups. Therefore, their catalytic behavior is dominated by surface chemistry rather than O-vacancies. Based on this finding, reaction pathways of two prevalent catalytic reactions, namely CO oxidation and the water-gas shift reaction over uCNPs are systematically investigated. Combined, these results demonstrate an alternative understanding of the surface structure of uCNPs, and provide new avenues to explore and enhance their catalytic behavior, which is likely applicable to other transition metal oxide nanoparticles with multivalent ions and very small sizes.

The diverse field of material research has been steadily expanding with a great help from computational physics, especially in the investigation of the fundamental properties of materials. This has driven the computational physics to become one of the main branches of physics, allowing for density functional theory (DFT) to develop as one of the cornerstones of material research. Nowdays, DFT is the method of choice in a great variety of studies, from fundamental properties, to materials modelling and searching for new materials. In this thesis, DFT is employed for the study of a small part of this vast pool of applications. Specifically, the microscopic characteristics of Zn1-xCdxS alloys are studied by looking into the evolution of the local structure. In addition, the way to model the growth of graphene on Fe(110) surface is discussed. The structural stability of silicon nanocrystals with various shapes is analysed in detail, as well. DFT is further used in studying different properties of semiconductor nanocrystals. The size evolution of the character of the band gap in silicon nanocrystals is investigated in terms of changes in the character of the states around the band gap. The influence of various surface impurities on the band gap, as well as on the electronic and optical properties of silicon nanocrystals is further studied. In addition, the future use of silicon nanocrystals in photovoltaic devices is examined by studying the band alignment and the charge densities of silicon nanocrystals embedded in a silicon carbide matrix. Furthermore, the electronic and optical properties of different semiconductor nanocrystals is also investigated. In the case of the CdSe/CdS and CdS/ZnS core-shell nanocrystals the influence of the nanocrystal size and different structural models on their properties is analysed. For silicon nanocrystal capped with organic ligands, the changes in the optical properties and lifetimes is thoroughly examined with changes in the type of organic ligand.

It has been shown recently that high-quality epitaxial graphene (EPG) can be grown on the SiC substrate that exhibits interesting physical properties and has great advantages for varies device applications. In particular, the multilayer graphene films grown on the C-face show rotational disorder. It is expected that the twisted layers exhibit unique new physics that is distinct from that of either single layer graphene or graphite. In this work, by combining density functional and tight-binding model calculations, we investigate the electric field and doping effects on twisted bilayer graphene (TBG), multiple layer effects on twisted triple-layer graphene, and wave packet propagation properties of TBG. Though these studies, we obtain a comprehensive description of the interesting interlayer interaction in this twisted multilayer graphene system.