The atomistic origin of the extraordinary oxygen reduction activity of Pt3Ni7 fuel cell catalysts

Optimality of Pt : Ni 30 : 70 fully dealloyed nanoporous Pt particles in terms of size and coordination environment.

Here we provide further computational details and additional structural and ORR catalytic information on the Pt-Ni dealloyed particles.
As described in detail in Ref. [7], the ReaxFF parameters used to describe the interactions in Pt clusters was fitted to reproduce a large set of DFT-derived quantities: the equation-of-state for various bulk Pt phases (fcc, bcc, sc, and A-15), the stability of various surface orientations, finite Pt clusters (up to 35 atoms).
In connection with the nanoparticle structure generation protocol, it is important to note that the initial local minimizations of the nanoparticles after Ni removal are performed to avoid disruption of the original random fcc framework. This is important for a proper description of dealloyed nanoporous systems. Thus, at each conjugate gradient step, we limited the maximum difference in Cartesian coordinates to 0.2 Å, until convergence threshold criteria of 4 10 -6 eV on the energy and 4 10 -8 eV/Å on the gradient thresholds were met.
For convenience of the reader and further analysis, the Cartesian coordinates of the three particles shown in Fig. 1 of the main text are provided as separate text files with names: Pt5Ni5.xyz, Pt3Ni7.xyz, Pt1Ni9.xyz. These structures have been selected from among the several runs of our structure generation protocols and are representative of typical situations. Further information is available upon request.
Analysis of structural features as a function of initial Ni:Pt composition is reported in Fig. S1 and S2.
In Fig. S1, a comparison of the Pt-Pt radial distribution functions for the truncated octahedral particle of Fig. 2(a) of the main text and the nanoporous particle of Fig. 2 Also interesting is information on the coordination environment of surface atoms, which we obtain employing a variant of the Common Neighbor Analysis (CNA), 1 aimed at distinguishing between icosahedral-like and crystalline-like bonding environments. We use the following procedure: for each Pt atom of the particle, we define its first-neighbour coordination shell as the set of Pt atoms lying at a distance smaller than 3 Å. Selecting one atom at a time in the first-neighbour shell, we use its bond distance R from the central atom to create a perfect icosahedron of radius R and we optimally superimpose this icosahedron onto the first-neighbor shell, i.e., we determine the orientation of the icosahedron which minimizes the sum of distances between its atoms and the atoms of the firstneighbour shell, neglecting mismatching atoms if the coordination number is less than 12. We repeat this procedure for each first-neighbour atom and report as 5-fold index in Fig. S2(c) the minimum value of the minimized sum of distances. Clearly, the lower the value of the 5-fold index, the more icosahedral-like the coordination environment of the given atom. From previous work 2 it is known that non-crystalline bonding environments such as icosahedral and poly-icosahedral are common in small Pt clusters, so that amorphous configurations commonly found in these systems can be described as originating from a rosette-like transformations of five-fold icosahedral vertexes. 2 Other analyses propose a transition to fcc-like structures at very small sizes, with a dominating role of (111) facets.   Finally, we conclude our structural analysis by quantifying the smoothness of the nanoporous surfaces.
To this aim, we plot in Fig. S3 the distribution of dihedral angles in the surface rhombi. By defining atoms 1,2 in a rhombus as the farthest ones and atoms 3,4 as those on the diagonal of the rhombus, the dihedral angle is calculated as the angle formed between atoms 1,2 and the middle point between 3 and 4, as illustrated in Fig. S3. This figure clearly shows that in nanoporous particles up to 70:30 Ni:Pt initial composition most dihedral angles lie between 140° and 180°, thus corresponding to smooth particle surfaces and excluding the massive presence of adatoms and surface defects.  We focused on the rate-determining-step (rds) of the ORR in water, as determined in previous work, 6 i.e., the oxygen hydration (or inverse of a hydroxyl disproportionation) step: O ads + H 2 O ads → OH ads + OH ads (1) where O ads , H 2 O ads , and OH ads are an oxygen adatom, a water molecule, and a hydroxyl radical all adsorbed onto the Pt surface.
However for one case we also examined the O 2 dissociation and water formation steps, as reported in Figure 5 of the main text.
We single out a few rhombi on the surface of Pt-Ni dealloyed particles as described in the main text, and report in Table S1 Table S1: Energetics of the ORR on selected sites on the external surfaces of nanoparticles obtained by dealloying truncated octahedra with initial radius of 10 nm and different initial Ni content as predicted by DFT calculations. See text for more details.