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15
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84931482020
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At a fcc (110) surface, the outer layer atoms have a nearest neighbor directly below them, in the third layer. The bond between these first- and third-layer neighbors cannot shrink farther than electron-electron repulsion will allow. This prevents the first-to-second layer bonds from relieving all their tensile stress.
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18
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84931482019
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The rapid spatial variation of the 3d radial function places strong demands on numerical quadrature meshes. The 4d and 5d pseudo-wave-functions of Pd and Pt vary less rapidly as a consequence of orthogonalization to d-like core orbitals.
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22
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84931507903
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Mol. Phys. 17, 197 (1969).
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(1969)
Mol. Phys.
, vol.17
, pp. 197
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31
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84931482021
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Also, the Hamann LAPW code, which I use to generate standard results, does not compute forces analytically, which makes it inconvenient when geometry optimization is required.
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32
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84931482017
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This method has been found to work well for several transition metals, by P. A. Schultz (unpublished).
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33
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84931482016
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For the radial parts of both the hollow-site s and the atop-site p orbitals I employ a single Gaussian, of attenuation constant 0.19 bohr-2.
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34
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84931482018
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Specifically, I place s-like Gaussians with attenuation constants 0.3 and 0.5 bohr-2 both at the midpoint of the long bridge and also directly above second-layer Pd's, at a height of 3.37 bohrs above the first layer. I also place s Gaussians with attenuation constant 0.19 bohr-2, 2.1 bohrs along the long bridge on either side of each outer layer nucleus and also above the midpoint of the long bridge, 0.37 bohrs above the outermost layer of Pd's.
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35
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0000560659
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quote photoelectric work functions of 5.95, 5.65, and 5.25 eV for the Pd(111), (100), and (110) surfaces, with error bars of +- 0.1 eV.
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(1984)
Surf. Sci.
, vol.140
, pp. 355
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Wandelt, K.1
Gumhalter, B.2
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40
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84931482014
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A calculation in which I include a second radial d orbital on each Pt nucleus, corresponding to a single Gaussian with an attenuation constant of 0.15 bohr-2, yields a Pt(111) surface energy equal to 0.133 eV/ A ang sup 2_ (=0.475 eV/bohr2) and a work function of 6.10 eV.
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41
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84931482013
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To make the concept of ``close to zero'' quantitative, one may ask by how much the lattice parameter would have to dilate to reduce the residual stress to zero, given the bulk modulus of Pt, which is roughly 2.8 Mbar. The answer is that an isotropic stress of 0.03 eV/atom would give rise to a compressive strain of 0.04%, or a contraction of the lattice constant equal to only 0.003 bohr.
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