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\begin{document} |
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%Title |
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\title{Investigation of the Pt and Au 557 Surface Reconstructions |
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under a CO Atmosphere} |
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\title{Molecular Dynamics simulations of the surface reconstructions |
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of Pt(557) and Au(557) under exposure to CO} |
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\author{Joseph R. Michalka, Patrick W. McIntyre and J. Daniel |
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Gezelter\footnote{Corresponding author. \ Electronic mail: gezelter@nd.edu} \\ |
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Department of Chemistry and Biochemistry,\\ |
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University of Notre Dame\\ |
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Notre Dame, Indiana 46556} |
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%Date |
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\date{Dec 15, 2012} |
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\date{Dec 15, 2012} |
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%authors |
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% make the title |
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\section{Simulation Methods} |
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The challenge in modeling any solid/gas interface problem is the |
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development of a sufficiently general yet computationally tractable |
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%where did you actually get the functionals for citation? |
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%scf calculations, so initial relaxation was of the four layers, but two layers weren't kept fixed, I don't think |
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%same cutoff for slab and slab + CO ? seems low, although feibelmen had values around there... |
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The Au-C and Au-O interaction parameters were also fit to a Lennard-Jones |
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and Morse potential respectively, to reproduce Au-CO binding energies. |
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These energies were obtained from quantum calculations carried out using |
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the PBE GGA exchange-correlation functionals\cite{Perdew_GGA} for gold, carbon, and oxygen |
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constructed by Rappe, Rabe, Kaxiras, and Joannopoulos. \cite{RRKJ_PP}. |
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All calculations were run using the {\sc Quantum ESPRESSO} package. \cite{QE-2009} |
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First, a four layer slab of gold comprised of 32 atoms displaying a (111) surface was |
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converged using a 4X4X4 grid of Monkhorst-Pack \emph{k}-points.\cite{Monkhorst:1976} |
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The kinetic energy of the wavefunctions were truncated at 20 Ry while the |
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cutoff for the charge density and potential was set at 80 Ry. This relaxed |
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gold slab was then used in numerous single point calculations with CO at various heights |
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to create a potential energy surface for the Au-CO interaction. |
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The Au-C and Au-O cross-interactions were fit using Lennard-Jones and |
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Morse potentials, respectively, to reproduce Au-CO binding energies. |
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The fits were refined against gas-surface calculations using DFT with |
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a periodic supercell plane-wave basis approach, as implemented in the |
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{\sc Quantum ESPRESSO} package.\cite{QE-2009} Electron cores are |
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described with the projector augmented-wave (PAW) |
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method,\cite{PhysRevB.50.17953,PhysRevB.59.1758} with plane waves |
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included to an energy cutoff of 20 Ry. Electronic energies are |
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computed with the PBE implementation of the generalized gradient |
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approximation (GGA) for gold, carbon, and oxygen that was constructed |
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by Rappe, Rabe, Kaxiras, and Joannopoulos.\cite{Perdew_GGA,RRKJ_PP} |
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Ionic relaxations were performed until the energy difference between |
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subsequent steps was less than 0.0001 eV. In testing the CO-Au |
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interaction, Au(111) supercells were constructed of four layers of 4 |
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Au x 2 Au surface planes and separated from vertical images by six |
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layers of vacuum space. The surface atoms were all allowed to relax. |
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Supercell calculations were performed nonspin-polarized, and energies |
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were converged to within 0.03 meV per Au atom with a 4 x 4 x 4 |
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Monkhorst-Pack\cite{Monkhorst:1976,PhysRevB.13.5188} {\bf k}-point |
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sampling of the first Brillouin zone. The relaxed gold slab was then |
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used in numerous single point calculations with CO at various heights |
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(and angles relative to the surface) to allow fitting of the empirical |
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force field. |
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%Hint at future work |
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The fit parameter sets employed in this work are shown in Table 2 and their |
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reproduction of the binding energies are displayed in Table 3. Currently, |
