The development of a local orbital method and its applications to aluminum and platinum clusters
Yang, Sang Hoon
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Permalink
https://hdl.handle.net/2142/22530
Description
Title
The development of a local orbital method and its applications to aluminum and platinum clusters
Author(s)
Yang, Sang Hoon
Issue Date
1996
Doctoral Committee Chair(s)
Adams, James B.
Department of Study
Physics
Discipline
Physics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Physics, Condensed Matter
Language
eng
Abstract
We generalized the method of Sankey and co-workers, which is based on the ab initio Harris functional of the local density approximation of density functional theory, by adding d orbitals into the original local orbital basis set of $sp\sp3$ orbitals. This enables the treatment of most elements in the periodic table including all $sp\sp3$ bonding elements and almost all transition metals with $sp\sp3d\sp5$ bondings. The task was a major modification (13,000 new lines of code), which involved almost all subroutines. We have tested this by calculating bandstructures of Si, Al, Fe, Pt and FeSi compound structures. The results are in good agreement with APW calculations. This new method was applied to study Al and Pt clusters. For the Al clusters we used an $sp\sp3$ basis set, and for Pt clusters we used a $sp\sp3d\sp5$ basis set.
Al clusters of 2-6, 13, 55, 147 atoms were studied. These are the largest Al clusters studied with an ab initio method. Equilibrium structures and total energies were calculated and compared with experiment and the predictions of other calculations. 13, 55 and 147 atom clusters are interesting because they represent the first, second and third atomic-shells of both the icosahedral (ICO) and cubo-octahedral (COS) structures. The minimum energy structure of $Al\sb{13}$ and $Al\sb{55}$ are found to be distorted icosahedrons, whereas that of $Al\sb{147}$ appears to be a slightly distorted cubo-octahedron (FCC). The vibrational density of states was calculated for most of these clusters. Most importantly, we found that small clusters prefer the icosahedral (ICO) to the cubo-octahedral (COS), and found the size at which the transition to the bulk-like COS occurs. We also performed EAM calculations for these clusters and compared to the ab initio calculations.
We also studied Pt clusters, and obtained the minimum energy structures of Pt clusters with sizes from 2 to 6 atoms, and also for the Pt$\sb{13}$ cluster. The structures were obtained by a dynamical quenching procedure, so that different structures were obtained depending on the initial configuration. The minimum energy structures for sizes 2 to 6 are found to be planar. In $Pt\sb{13}$, the first closed shell cluster, we found that the COS structure was only slightly lower in energy than the ICO by 0.01 eV/atom. However, our ab initio MD simulations resulted in a variety of amorphous structures with lower energy (as much as 0.16 eV/atom below the COS structure). This result is compared with previous EAM studies.
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