FIRST PRINCIPLES CALCULATIONS TO INVESTIGATE SURFACE AND CATALYTIC PROPERTIES OF MATERIALS FOR GREEN ENERGY GENERATION

Climate change due to greenhouse gas build up in the earth’s atmosphere is an existential threat to humanity. To mitigate climate change, a significant shift from fossil fuels is necessary. Over the years, several renewable energy sources like solar, wind, geothermal etc. have been explored with the aim providing carbon-free energy. In this work, we focus on using density functional theory (DFT) methods to investigate key functional properties of materials of interest for applications in solar cells and catalytic conversion for energy generation. We show geometric effects of carboxylic acid binding on a transition metal surface to impact the deoxygenation reaction mechanism. Using insights from binding energy calculations and transition state theory, we elucidate the reaction pathway. We then use the same methods to investigate the surface of perovskites substituted with organic ligands and show the effect of fluorination of the phenyl ring of anilinium on the relative surface energy, relative binding energy, surface penetration, work function, and surface electronic properties. Lastly, we turn to DFT studies of molecular systems to investigate the impact of a perylene diimide (PDI) chromophore substituted on a rhenium-based organometallic complex. We show that unfolding of the PDI away from the organometallic complex is a key step in the catalytic reduction of CO2 and demonstrate how the PDI acts as an electronic reservoir during this process

Modeling and Analysis of Repeated Ordinal Data Using Copula Based Likelihoods and Estimating Equation Methods

Repeated or longitudinal ordinal data occur in many fields such as biology, epidemiology, and finance. These data normally are analyzed using both likelihood and non-likelihood methods. The first part of this dissertation discusses the multivariate ordered probit model which is a likelihood method based on latent variables. We show that this latent variable model belong to a very general class of Copula models. We use the copula representation for the multivariate ordered probit model to obtain maximum likelihood estimates of the parameters. We apply the methodology in the analysis of real life data examples. Though likelihood methods are preferable, there are computational challenges implementing them. Alternatives are the non-likelihood models. These are partially specified models, that is, in these models only the functional forms of the marginals are known but joint distributions are unknown. In addition, the dependence among the observations is modeled using an appropriate correlation structure. The second part of the dissertation outlines the estimating equations approach for the analysis of longitudinal ordinal data for these non-likelihood models. We study the asymptotic properties of the estimates for both likelihood and non-likelihood methods. Comparisons based on simulations show that the maximum likelihood estimates arising from copula models are more efficient than the estimates obtained from estimating equations. The third part of this dissertation describes how ordinal data can be viewed as multinomial random vectors and points out the theoretical challenges in finding restrictions on the correlation parameters for dependent multinomial random vectors