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During the last decades the specific manipulation of matter on the (sub-) nanometer scale, also known as nanoscience, became possible by technologies such as the scanning tunneling microscope. Nanocatalysts, i.e. catalytic active structures of up to a few nanometers in size, belong to this rather new class of materials. Unlike ordinary ’macroscopic’ catalytic materials, the performance of nanocatalysts does not simply scale, for instance, with the surface to volume ratio of the active material. In this Thesis model nanocatalysts are investigated by means of ab-initio density functional theory calculations. In paper I, we explain the experimentally observed catalytic characteristics of small gold clusters, Au1-4, on a regular magnesium oxide terrace towards the oxidation of carbon monoxide by thoroughly studying the adsorption of CO and O2 on these clusters. In the subsequent paper II, we study the feasibility of a catalytic water-mediated CO oxidation reaction on Au1-4/MgO and find that this reaction mechanism is not assessable for Au2,4/MgO and unlikely for Au1,3/MgO. Papers III and IV concentrate on the reactivity of clusters in the gas phase. Particularly, we focus on the relative stability of Au13 isomers and its potential for O2 dissociation (paper III). We find the lowest energy isomers, which contain a triangular prism at their center surrounded by a ring of the remaining seven atoms, to be generally stable upon O2 adsorption. The dissociation of O2 at certain sites of Au13 is found to be exothermic. In paper IV we performed scans of the Born-Oppenheimer potential energy surfaces of neutral and charged Cu3, Ag3, and Au3 to explore the thermally excited vibrations of these trimers. While the Born-Oppenheimer surface of Cu3 exhibits one fairly deep energy minimum, it is comparatively flat with two shallow minima in the case of Ag3. Hence for Ag3 there exist many thermally accessible geometries in a wide range of angles and bond lengths. For Au3, two distinct energy minima appear, being well-separated by a barrier of 180 meV. Already at room temperature, we find bond lengths changes of up to 5% for the studied trimers. Choosing Au3 as a case study for the changed reactivity of thermally excited modes, we find CO to bind up to 150 meV stronger to the excited cluster. Gold deposited on graphene and graphite was observed to form larger aggregates. In paper V, we study the electronic structures, high mobility, and substrate-mediated clustering processes of Au1-4 on graphene. Already in the 1970s is was speculated that dispersion forces, i.e. van der Waals forces, significantly contribute to the adsorption energies of gold atoms on graphite. We accounted for van der Waals interactions in our density functional theory calculations (paper VI) and investigated the influence of these dispersion forces on the binding of copper, silver, and gold adatoms on graphene. While copper and gold show a mixed adsorption mechanism, i.e. chemical binding plus attraction due to the van der Waals forces, silver is purely physisorbed on graphene. Felaktigt tryckt som Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 719