The inherent properties of PuO2, such as its toxicity and radioactivity, make computational study beneficial when studying the surface speciation of PuO2 surfaces. This thesis aims to investigate the surface structure and energetics with small molecules relevant to the radiolytically driven dispersal of actinide material (H2O, H2O2 and CO2) to understand the surface specification of PuO2. The thesis begins with an introductory chapter to introduce the nuclear industry in the UK, its significant challenges, and how computational modelling is a valuable tool to assist in tackling some of these challenges. Literature reviews that focus on each topic are presented at the beginning of each results chapter, and the underlining background theory to the simulations performed within this study is provided in the methodology chapter. The first results chapter aims to determine the surface speciation of CeO2 surfaces in the presence of three molecules; H2O, H2O2 and CO2. The chapter aims to explore concepts of the temperature of desorption, surface phase diagrams and to predict the shapes of thermodynamically accessible nanoparticles at pressures of the adsorbed species and temperature. These methodologies are then implemented for PuO2. In the second results chapter, the most-to-date DFT method for PuO2, accounting for the spin-orbit interactions and noncollinear magnetism, is used to model the surface speciation of PuO2 with H2O, H2O2 and CO2 adsorbed to the surface. Finally, as surface defects influence surface speciation, the final result chapter aims to study simple defects (i.e., Frenkel and Schottky defects) in ThO2 (as an actinide, but it does not require simulation of the complex magnetic properties of PuO2). Therefore, the chapter aims to decouple the effect of each defect aims by studying the vibrational analysis alongside an understanding of thermal transport. This will allow for the identification of a defect through spectral analysis and estimate the influence of the defect on thermal transport. The results in this thesis provide insight into the effect of the surface speciation of PuO2 surfaces and the impact this may have on the radiolytically driven dispersal of actinide materials.