Nano-scale structures are increasingly applied in the design of catalysts and electronic devices. A theoretical understanding of the basic properties of such systems is enabled through modern electronic structure methods such as density functional theory. This thesis describes the development of efficient approaches to density functional theory and the application of these methods to metal nanoparticles. We describe the formalism and implementation of localized atom-centered basis sets within the projector augmented wave method. Basis sets allow for a dramatic increase in performance compared to plane-wave or real-space methods, but sacrifice accuracy in doing so. This approach is implemented in the GPAW code where it complements the existing real-space approach. For both the real-space and basis set methods we implement parallel code to adapt GPAW for large-scale calculations on the BlueGene/P architecture. Real-space calculations are performed to investigate the convergence of chemical properties of Au and Pt clusters toward the bulk limit. Specically we study chemisorption of O and CO on cuboctahedral clusters up to 1415 atoms using up to 65536 CPU cores. Small clusters almost universally bind more strongly than large ones. This can be understood mostly as a geometric eect. Convergence of chemisorption energies within 0.1 eV of bulk values happens at about 200 atoms for Pt and 600 atoms for Au. Particularly for O on Au, large variations due to electronic effects are seen for smaller clusters. The basis set method is used to study the electronic effects for the contiguous range of clusters up to several hundred atoms. The s-electrons hybridize to form electronic shells consistent with the jellium model, leading to electronic magic numbers for clusters with full shells. Large electronic gaps and jumps in Fermi level near magic numbers can lead to alkali-like or halogen-like behaviour when main-group atoms adsorb onto gold clusters. A non-self-consistent NewnsAnderson model is used to more closely study the chemisorption of main-group atoms on magic-number Au clusters. The behaviour at magic numbers can be understood from the location of adsorbateinduced states relative to the Fermi level. The relationship between geometric and electronic eects in Au is studied by rough first-principles simulated annealings with up to 150 atoms. Non-magic clusters are found to deform considerably, reducing the total energy through the creation of gaps. Clusters larger than 100 atoms can elongate systematically by up to 15 %. This demonstrates a complex interdependence between electronic and geometric structure in a size regime which in most cases has been studied semiempirically.
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Thygesen, Kristian Sommer, Jacobsen, Karsten Wedel
Technical University of Denmark, Center for Atomic-Scale Materials Physics, 2011