<p>Quantum chemistry methods nowadays reach its maturity with various robust ground state correlation methods. However, many problems related to response do not have satisfactory solutions. Chemical reactivity indexes are some static response to external fields and number of particle change. These chemical reactivity indexes have important chemical significance, while not all of them had analytical expressions for direct evaluations. By solving coupled perturbed self-consistent field equations, analytical expressions were obtained and verified numerically. In the particle-particle (pp) channel, the response to the pairing field can describe <italic>N&plusmn;2</italic> excitations, i.e. double ionization potentials and double electron affinities. The linear response time-dependent density-functional theory (DFT) with pairing fields is the response theory in the density-functional theory (DFT) framework to describe $N\pm 2$ excitations. Both adiabatic and dynamic kernels can be included in this response theory. The correlation energy based on this response, the correlation energy of the particle-particle random phase approximation (pp-RPA), can also be proved equivalent to the ladder approximation of the well-established coupled-cluster doubles. These connections between the response theory, <italic>ab initio</italic> methods, and Green's function theory would be beneficial for further development. Based on RPA and pp-RPA, the theory of second RPA and the second pp-RPA with restrictions can be used to capture single and double excitations efficiently. We also present a novel methods, variational fractional spin DFT, to calculate singlet-triplet energy gaps for diradicals, which are usually calculated through spin-flip response theories.</p> / Dissertation

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Carbon nanotubes have extraordinary mechanical, electrical, thermal andoptical properties. They are harder than diamond yet exible, have betterelectrical conductor than copper, but can also be a semiconductor or evenan insulator. These ranges of properties of course make carbon nanotubeshighly interesting for many applications. Carbon nanotubes are already usedin products as hockey sticks and tennis rackets for improving strength and exibility. Soon there are mobile phones with exible screens made fromcarbon nanotubes. Also, car- and airplane bodies will probably be mademuch lighter and stronger, if carbon nanotubes are included in the construction.However, the real game changers are; nanoelectromechanical systems(NEMS) and computer processors based on graphene and carbon nanotubes.In this work, we study Young's modulus in the axial direction of carbonnanotubes. This has been done by performing density functional theorycalculations. The unit cell has been chosen as to accommodate for tubes ofdierent radii. This allows for modelling the eect of bending of the bondsbetween the carbon atoms in the carbon nanotubes of dierent radii. Theresults show that Young's modulus decreases as the radius decreases. Ineect, the Young's modulus declines from 1 to 0.8 TPa. This eect can beunderstood because the bending diminishes the pure sp^2 character of thebonds.These results are important and useful in construction, not only when usingcarbon nanotubes but also when using graphene. Our results point towardsa Young's modulus that is a material constant and, above a certain criticalvalue, only weakly dependent on the radius of the carbon nanotube.Graphene can be seen as a carbon nanotube with innite radius.

The aim of this thesis is to investigate the effects of additives, reactive elements and impurities, on the lifetime of thermal barrier coatings. The thesis consists of a number of studies on interface adhesion, impurity diffusion, grain boundary sliding and cleavage processes and their impact on the mechanical behaviour of grain boundaries. The effects of additives and impurity on interface adhesion were elaborated by using total energy calculations, electron localization and density of states, and by looking into the atomic separations. The results of these calculations allow the assessment of atomic level contributions to changes in the adhesive trend. Formation of new bonds across the interface is determined to improve the adhesion in reactive element(RE)-doped structures. Breaking of the cross interface bonds and sulfur(S)-oxygen(O) repulsion is found responsible for the decreased adhesion after S segregation. Interstitial and vacancy mediated S diffusion and the effects of Hf and Pt on the diffusion rate of S in bulk NiAl are studied. Hf is shown to reduce the diffusion rate, and the preferred diffusion mechanism of S and the influence of Pt are revealed to be temperature dependent. Finally, the effects of reactive elements on alumina grain boundary strength are studied. Reactive elements are shown to improve both the sliding and cleavage resistance, and the analysis of atomic separations suggest an increased ductility after the addition of quadrivalent Hf and Zr to the alumina grain boundaries.

The growth of the Si(001) surface from gas sources such as disilane is technologically important, as well as scientifically interesting. The aspects of growth covered are: the clean surface, its defects and steps; the action of bismuth, a surfactant; the diffusion behaviour of hydrogen in different environments; and the entire pathway for formation of a new layer of silicon from adsorption of fragments of disilane to nucleation of dimer strings. The theoretical methods used, density functional theory and tight binding, are described. Four linear scaling tight binding methods are compared. The construction of the tight binding parameterisations used is also explained. The structure of the most common defect on the Si(001) surface is identified by comparison of the electronic structure with scanning tunneling microscopy (STM) images. The energy and structure of steps is calculated, and their kinking behaviour is modelled, achieving good agreement with experimental results. Two unusual features which form when bismuth is placed on the surface and annealed are investigated. The first has possible applications as a quantum wire, and its structure and growth are described. The second relates to a controversial area in the field; a structure is proposed which fits all available experimental evidence. The behaviour of hydrogen is vital to understanding growth, as large amounts are deposited during disilane growth. After validating the tight binding parameterisation against DFT and experiment for the system of a single hydrogen diffusing on the clean Si(001) surface, the barriers for diffusion on the saturated surface, down a step and away from a defect are found, and prove to be in good agreement with available experimental data. The pathway for the formation of a new layer of silicon from disilane is described step by step, giving barriers and structures for all events. The interaction with experiment is highlighted, and demonstrates that great benefit accrues from such close work, and that the atomistic modelling techniques used in the thesis produce results in close agreement with reality.

There has been growing demands towards the efficient production of enantiopure compounds through either asymmetric synthesis or separation from racemic mixtures. Recent studies have examined numerous different methods that may address this challenge. One of these methods involved the interaction of chiral molecules on achiral metal surfaces such as copper to create chiral templates while another method utilizes the interaction of chiral molecules on intrinsically chiral surfaces. Earlier studies using nonhybrid Density Functional Theory (DFT) functional has provided some insights into the geometric structures and relative energies of some of these interactions, but it failed to achieve quantitative agreement with experimental studies. Using dispersion corrected DFT functionals, this thesis present a study of chemisorbed dense adlayers of glycine and alanine on Cu(110) and Cu(3,1,17), physisorbed R-3-methycyclohexanone (R-3MCHO) on Cu(100), Cu(110), Cu(111), Cu(221), and Cu(643)R, and the hydrogenation of formaldehyde and methoxide on Zn or Zr heteroatoms promoted Cu surfaces. In the dense glycine and alanine adlayer study, we have resolved a disagreement between experimental observation made on LEED, STM, and XPD, and we showed that heterochiral and homochiral glycine adlayer coexist on Cu(110). Our model failed to show the minute enantiospecificity for dense alanine adlayer on Cu(3,1,17) which indicated a numeric limitation for computational modeling of surface adsorption. In the physisorbed system, the dispersion corrected methods calculated adsorption energies were in better quantitative agreement with the experimentally observed values than the nonhybrid functionals, but it also created a significant overestimation of total adsorption energies. On the other hand, our model had indicated a previously unexpected adsorbate-induced surface reconstruction on Cu(110). This is promising news in term of computational modeling's capability in examining surface-adsorbate interaction on an atomic scale. As for the hydrogenation of formaldehyde and methoxide on copper surfaces, the model showed that the increased binding strength between the reaction intermediates and the heteroatom promoted copper surfaces to be the primary contributor of the increased reaction rates. Furthermore, our model had also indicated that while clustered heteroatoms are relatively rare, a significant portion of reaction takes place near these clustered structures. It is our hope that the results and techniques presented in this thesis can be used to better understand and predict the interaction of more complex surface-adsorbate interactions.

The detrimental effects of rising CO₂ levels on the global climate have made carbon abatement technologies one of the most widely researched areas of recent times. In this thesis, we first present a techno-economic analysis of a novel approach to directly capture CO₂ from air (Air Capture) using highly selective adsorbents. Our process modeling calculations suggest that the monetary cost of Air Capture can be reduced significantly by identifying adsorbents that have high capacities and optimum heats of adsorption. The search for the best performing material is not limited to Air Capture, but is generally applicable for any adsorption-based separation. Recently, a new class of nanoporous materials, Metal-Organic Frameworks (MOFs), have been widely studied using both experimental and computational techniques. In this thesis, we use a combined quantum chemistry and classical simulations approach to predict macroscopic properties of MOFs. Specifically, we describe a systematic procedure for developing classical force fields that accurately represent hydrocarbon interactions with the MIL-series of MOFs using Density Functional Theory (DFT) calculations. We show that this force field development technique is easily extended for screening a large number of complex open metal site MOFs for various olefin/paraffin separations. Finally, we demonstrate the capability of DFT for predicting MOF topologies by studying the effect of ligand functionalization during CuBTC synthesis. This thesis highlights the versatility and opportunities of using multiscale modeling approach that combines process modeling, classical simulations and quantum chemistry calculations to study nanoporous materials for adsorptive separations.

Computational quantum mechanics in the frame work of density functional theory (DFT) was used to investigate the effect of chemical impurities on high field conduction in polyethylene (PE). The impurity states in the band gap caused by common chemical impurities were characterized in terms of their “depth”, i.e. energy relative to their relevant band edge (valence band or conduction band), and in terms of the extent to which their wavefunctions were localized to a single polymer chain or extended across chains. It was found that impurity states can affect high field phenomena by providing “traps” for carriers, the depths of which were computed from first principle in agreement with estimates in literature. Since the square of the wavefunction is proportional to the spatial electron probability density, transfer of charge between chains requires wavefunctions which are extended across chains. Impurity states which are extended between chains can facilitate the inherently limited interchain charge transfer in PE, as the DFT study of iodine doped PE revealed. The introduction of iodine into PE increases conductivity by several orders of magnitude, increases hole mobility to a much greater extent than electron mobility, and decreases the activation energy of conduction from about 1 eV to about 0.8 eV. These characteristics were explained in terms of the impurity states introduced by iodine and wavefunctions of those states. Understanding the effect of iodine on conduction in PE provided a basis for understanding the effect of common chemical impurities on conduction therein. In particular, carbonyl and vinyl impurities create states which should promote hole mobility in a manner very similar to that caused by iodine. It was demonstrated that in the context of high field conduction in PE, besides the traditional focus on the depth of impurity states, it is important to study the spatial features of the states wavefunctions which are neither discussed nor accounted for in present models.

Computational quantum mechanics in the frame work of density functional theory (DFT) was used to investigate the effect of chemical impurities on high field conduction in polyethylene (PE). The impurity states in the band gap caused by common chemical impurities were characterized in terms of their “depth”, i.e. energy relative to their relevant band edge (valence band or conduction band), and in terms of the extent to which their wavefunctions were localized to a single polymer chain or extended across chains. It was found that impurity states can affect high field phenomena by providing “traps” for carriers, the depths of which were computed from first principle in agreement with estimates in literature. Since the square of the wavefunction is proportional to the spatial electron probability density, transfer of charge between chains requires wavefunctions which are extended across chains. Impurity states which are extended between chains can facilitate the inherently limited interchain charge transfer in PE, as the DFT study of iodine doped PE revealed. The introduction of iodine into PE increases conductivity by several orders of magnitude, increases hole mobility to a much greater extent than electron mobility, and decreases the activation energy of conduction from about 1 eV to about 0.8 eV. These characteristics were explained in terms of the impurity states introduced by iodine and wavefunctions of those states. Understanding the effect of iodine on conduction in PE provided a basis for understanding the effect of common chemical impurities on conduction therein. In particular, carbonyl and vinyl impurities create states which should promote hole mobility in a manner very similar to that caused by iodine. It was demonstrated that in the context of high field conduction in PE, besides the traditional focus on the depth of impurity states, it is important to study the spatial features of the states wavefunctions which are neither discussed nor accounted for in present models.

The reaction mechanism for the Selective Catalytic Reduction (SCR) of NO by NH3 on V2O5 surface was simulated by means of density functional theory (DFT) calculations performed at B3LYP/6-31G** level. As the initiation reaction, ammonia activation on V2O5 was investigated. Coordinate driving calculations showed that ammonia is adsorbed on Br&oslash / nsted acidic V-OH site as NH4 + species by a nonactivated process with a relative energy of -23.6kcal/mol. Vibration frequencies were calculated as 1421, 1650, 2857 and 2900cm-1 for the optimized geometry, in agreement with the experimental literature. Transition state with a relative energy of -17.1kcal/mol was also obtained. At the end of the Lewis acidic ammonia interaction calculations, it was observed that ammonia is hardly adsorbed on the surface. Therefore, it is concluded that the SCR reaction is initiated more favorably by the Br&oslash / nsted acidic ammonia adsorption. As the second step of the SCR reaction, NO interaction with the preadsorbed NH4 + species was investigated. Accordingly, NO interaction results in the formation of gas phase NH2NO molecule with a relative energy difference of 6.4kcal/mol. For the rest of the reaction sequence, gas phase decomposition of NH2NO was considered. Firstly, one of the hydrogen atoms of NH2NO migrates to oxygen. It then isomerizes in the second step. After that, the reaction proceeds with the isomerization of the other hydrogen. Finally, a second hydrogen atom migration to the oxygen leads to the formation of N2 and H2O. Total relative energy for this reaction series was obtained as -60.12kcal/mol, in agreement with the literature.