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The work presented in this dissertation focuses on the study of post deposition spatial and temporal evolution of adatom islands and molecules on surfaces using ab initio and semiemperical methods. It is a microscopic study of the phenomena of diffusion and reaction on nanostructured surfaces for which we have developed appropriate computational tools, as well as implemented others that are available. To map out the potential energy surface on which the adatom islands and molecules move, we have carried out ab initio electronic structure calculations based on density functional theory (DFT) for selected systems. For others, we have relied on semiempirical interatomic potentials derived from the embedded atom method. To calculate the activation energy barriers, we have employed the "drag" method in most cases and verified its reliability by employing the more accurate nudged elastic band method for selected systems. Temporal and spatial evolution of the systems of interest have been calculated using the kinetic Monte Carlo (KMC), or the more accurate (complete) Self Learning kinetic Monte Carlo (SLKMC) method in the majority of cases, and ab initio molecular dynamics simulations in others. We have significantly enhanced the range of applicability of the SLKMC method by introducing a new pattern recognition scheme which by allowing occupancy of the "fcc" and "hcp" sites (and inclusion of "top" site in the pattern recognition as well) is capable of simulating the morphological evolution of iii three dimensional adatom islands, a feature not feasible via the earlier - proposed SLKMC method. Using SLKMC (which allows only fcc site occupancy on fcc(111) surface), our results of the coarsening of Ag islands on the Ag(111) surface show that during early stages, coarsening proceeds as a sequence of selected island sizes, creating peaks and valleys in the island-size distribution. This island size selectivity is independent of initial conditions and results from the formation of kinetically stable islands for certain sizes as dictated by the relative energetics of edge atom detachment/attachment processes together with the large activation barrier for kink detachment. On applying the new method, SLKMC-II, to examine the self diffusion of small adatom islands (1-10 atoms) of Cu on Cu(111), Ag on Ag(111) and Ni on Ni(111), we find that for the case of Cu and Ni islands, diffusion is dominated by concerted processes (motion of island as a whole), whereas in the case of Ag, islands of size 2-9 atoms diffuse through concerted motion whereas the 10-atom island diffuses through single atom processes. Effective energy barriers for the self diffusion of these small Cu islands is 0.045 eV/atom, for Ni it is 0.060 eV/atom and for Ag it is 0.049 eV/atom, increasing almost linearly with island size. Application of DFT based techniques have allowed us to address a few issues stemming from experimental observations on the effect of adsorbates such as CO on the structure iv and stability of bimetallic systems (nanoparticles and surfaces). Total energy calculations of Ni-Au nanoparticles show Ni atoms to prefer to be in the interior of the nanoparticle. CO molecules, however, prefer to bind to a Ni atom if present on the surface. Using ab initio molecular dynamics simulations, we confirm that the presence of CO molecule induces diffusion of Ni atom from the core of the Ni-Au nanoparticle to its surface, making the nanoparticle more reactive. These results which help explain a set of experimental data are rationalized through charge transfer analysis. Similar to the case of Ni-Au system, it is found that methoxy (CH3O) may also induce diffusion of inner atoms to the surface on bimetallic Au-Pt systems. Our total energy DFT calculations show that it is more favorable for methoxy to bind to a Pt atom in the top Au layer than to a Au atom in Au-Pt system thereby explaining experimental observations. To understand questions related to the dependence of product selectivity on ambient pressure for ammonia decomposition on RuO2(110), we have carried out an extensive calculation of the reaction pathways and energy barriers for a large number of intermediate products. On combining the reaction energetics from DFT, with KMC simulations, we show that under UHV conditions, selectivity switches from N2 ( ∼ 100 % selectivity) at T = 373K to NO at T = 630K, whereas under ambient conditions, N2 is still the dominant product but maximum selectivity is only 60%. An analysis based on thermodynamics alone shows a contradiction between experimental data at UHV with those under ambient pressure. Our calculations of the reaction rates which are essential for KMC simulations removes this apv parent inconsistency and stresses the need to incorporate kinetics of processes in order to extract information on reaction selectivity.