Supplemental material for The electronic structure of Ni-Pd particles: a clue to their special catalytic properties

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1 Electronic Supplementary Material (ESI) for Physical Chemistry Chemical Physics. This journal is the Owner Societies 2015 Supplemental material for The electronic structure of Ni-Pd particles: a clue to their special catalytic properties Linn Leppert,a,b, Rhett Kempe,c and Stephan Ku mmela] In this supplemental material we discuss the effects of the exchange correlation (xc) functional approximation in greater detail and present the cluster structures and magnetic moments. We start by discussing the influence of the xc functional approximation on the structure of 13-atom Nix Pd13 x (x = 0 13) clusters. Starting point of our considerations are three stable Pd13 clusters taken from Ref. 1 which are depicted in Fig. 1: an icosahedral cluster Pd13 (ico), a bilayered geometry Pd13 (bi) and a cluster with c3v symmetry Pd13 (c3v). For the clusters Ni1 Pd12 and Ni2 Pd11 we determined further stable geometries by simulated annealing. In Fig. 1, these geometries are labeled Ni1 Pd11 (ico), Ni1 Pd12 (geo4), Ni1 Pd12 (bcc), Ni2 Pd11 (ico), Ni2 Pd11 (geo2) and Ni2 Pd11 (geo3). For Ni13 two structures are reported in the literature: the icosahedron, which is the established ground state structure, and a bilayered structure with a binding energy around 50 mev higher than that of the icosahedron 2. The binding energies of these systems as calculated with the PBE0 xc functional 3 used in the generalized Kohn-Sham framework 4 can be found in Tab. 1. The energetic ordering of the isomers is different when, e.g., the PBE 5 functional is used. This, Ni13 Ni12Pd1 Ni11Pd2 Ni10Pd3 Ni9Pd4 Ni8Pd5 Ni6Pd7 Ni2Pd11 Ni1Pd12 Pd13 geo3 geo4 bi geo2 bcc c3v ico bi Figure 1 The structures of the 13-atom Nix Pd13 x (x = 0 13) clusters that were used in this work. however, is no reason for concern in the present study as we are interested in electronic properties of NiPd systems that are independent of the specific geometry and can be generalized over a wide size range as shown in the main manuscript. Furthermore, as argued in the main manuscript, studying the clusters magnetic properties allows for a sensitive test of the xc functional. 0a Theoretical Physics IV, University of Bayreuth, Bayreuth, Germany Present address: Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA 0c Inorganic Chemistry II, University of Bayreuth, Bayreuth, Germany 0 ] Corresponding author: stephan.kuemmel@uni-bayreuth.de 0b 1

2 Table 1 PBE0 binding energies and magnetic moments of Ni 13, Ni 2 Pd 11, Ni 1 Pd 12 and Pd 13 isomers. The binding energy is defined as xe Ni + (13 x)e Pd E Nix Pd 13 x. system structure binding magnetic energy (ev) moment (µ B ) ico Ni 13 bi Ni 2 Pd 11 geo ico geo Ni 1 Pd 12 bcc ico geo Pd 13 bi ico c3v a) b) magnetic moment/atom (µb) DOS at FL (states/atom) DOS at FL dband center εd εf (ev) Pd atoms Pd atoms Figure 2 a) spin magnetic moment per atom of icosahedral 13-atom clusters as calculated with PBE0. The black dotted line marks the magnetic moment of Ni bulk calculated using the HSE06 functional. b) d-band center with respect to Fermi level (FL) and density of states at the Fermi level, obtained by integrating the total density of states from the Fermi level to 1 ev below it. All numbers refer to the unrelaxed icosahedral 13-atom clusters. We determined the magnetic moment of all clusters by performing a set of geometry optimizations with fixed spin magnetic moments between 0 and 10 for x = 0 2,6,8,9 and between 8 and 18 for x = The resulting magnetic moments per atom are shown as orange triangles in Fig. 2a) for the icosahedral clusters. The moments of all other isomers can be found in Tab. 1. Icosahedral Ni x Pd 13 x clusters with x = 0 9 have magnetic moments of 8 µ B, whereas for x = the moment increases by 2 µ B per Ni atom up to 16 µ B for Ni 13. Note that this value, which is in excellent agreement with a recent experiment 6, is not obtained when the xc functional is approximated by a generalized gradient expression such as PBE. In 2

3 contrast, PBE results in a magnetic moment of 8 µ B which is even lower than the moment of bulk Ni. This observation not only emphasizes the importance of choosing a proper xc functional approximation for these systems, but also independently confirms that the icosahedral geometry is most likely the ground state of Ni 13. A Mulliken population analysis relates the size dependence of the magnetic moment to considerable charge transfer from Ni to Pd. For clusters with x = 0 9 the local spin magnetic moments of Pd are reduced by charge transfer from Ni to Pd. The reduced local moments of Pd thus compensate the Ni local moments and the total spin moments remains at 8 µ B. For x > 9 not enough Pd atoms are available for compensation any more and the spin moment begins to build up until it reaches a maximum of 16 µ B in Ni 13. The importance of choosing an xc functional that at least partly cancels the spurious effects of the selfinteraction error becomes evident in several calculations. As a first example we mention that the d-band centers of Ni 13 and Pd 13 calculated with PBE are 1.4 ev and 1.6 ev below the Fermi level, respectively. This means that PBE not only predicts a d-band center much closer to the Fermi level than PBE0, but also reverses the energetic ordering of the d-band centers of Ni 13 and Pd 13. Second, for the Pd 13 (bi) cluster s DOS, see Methods section of main manuscript, using the PBE xc functional results in a value of 5.6 states/atom, whereas PBE0 and ωpbe give 3.5 and 3.4 states/atom, respectively. The DOS at the Fermi level shows a similar behaviour as the d-band center as a function of Ni-Pd ratio, as can be seen in Fig. 2b). There is no minimum for the Ni-Pd ratio for which a maximum of E diss is observed. To determine hydrogen binding on mixed Ni-Pd surfaces, we constructed a mixed Ni-Pd surface model with a Ni:Pd ratio of 1:1. In this surface slab, each surface layer consists of two Ni and two Pd atoms as can be seen in Fig. 3. Figure 3 Ni-Pd(111) surface with Ni:Pd ratio of 1:1. The red rhombus marks the atoms in the top layer of one unit cell. 3

4 Finally, we report the optimized coordinates of our 13-atom (Tab. 2) and 38-atom (Tab. 3) clusters. Pd 13 bilayer ico c3v element x y z x y z x y z Pd Pd Pd Pd Pd Pd Pd Pd Pd Pd Pd Pd Pd Ni 1 Pd 12 ico geo4 bcc element x y z x y z x y z Pd Pd Pd Pd Pd Pd Pd Pd Pd Pd Pd Pd Ni Ni 2 Pd 11 ico geo2 geo3 element x y z x y z x y z Pd Pd Pd Pd Pd Pd Pd Pd Pd Pd

5 Pd Ni Ni Ni 6 Pd 7 ico Ni 8 Pd 5 ico element x y z x y z Pd Pd Pd Pd Pd Pd Pd Pd Pd Pd Pd Ni Pd Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni 9 Pd 4 ico Ni 10 Pd 3 ico element x y z x y z Pd Pd Pd Pd Pd Pd Pd Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni 11 Pd 2 ico Ni 12 Pd 1 ico element x y z x y z Pd Pd Pd Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni

6 Ni Ni Ni Ni Ni Ni Ni Ni Ni 13 ico bilayer element x y z x y z Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Table 2 xyz-coordinates in Ångström of the 13-atom clusters depicted in Fig. 1. 6

7 element x y z Pd Pd Pd Pd Pd Pd Pd Pd Pd Pd Pd Pd Pd Pd Pd Pd Pd Pd Pd Pd Pd Pd Pd Pd Pd Pd Pd Pd Pd Pd Pd Pd Pd Pd Pd Pd Pd Pd Table 3 xyz-coordinates in Ångström of cuboctahedral Pd 38, Ni 5 Pd 33 and Ni 38. To construct Ni 5 Pd 33 the five Pd atoms that are marked by bold letters were replaced by Ni. 7

8 REFERENCES REFERENCES References [1] A. M. Köster, P. Calaminici, E. Orgaz, D. R. Roy, J. U. Reveles and S. N. Khanna, J. Am. Chem. Soc., 2011, 133, [2] P. Błonski and J. Hafner, J. Phys: Cond. Matter, 2011, 23, (1 17). [3] J. P. Perdew, M. Ernzerhof and K. Burke, J. Chem. Phys., 1996, 105, [4] A. Seidl, A. Görling, P. Vogl, J. A. Majewski and M. Levy, Phys. Rev. B, 1996, 53, [5] J. P. Perdew, K. Burke and M. Ernzerhof, Phys. Rev. Lett., 1996, 77, [6] A. Langenberg, K. Hirsch, A. Ławicki, V. Zamudio-Bayer, M. Niemeyer, P. Chmiela, B. Langbehn, A. Terasaki, B. V. Issendorff and J. T. Lau, Phys. Rev. B, 2014, 90, (1 14). 8