Hydrogen Promotes the Growth of Platinum Pyramidal Nanocrystals by Size-Dependent Symmetry Breaking

The growth of pyramidal platinum nanocrystals is studied by a combination of synthesis/characterization experiments and density functional theory calculations. It is shown that the growth of pyramidal shapes is due to a peculiar type of symmetry breaking, which is caused by the adsorption of hydrogen on the growing nanocrystals. Specifically, the growth of pyramidal shapes is attributed to the size-dependent adsorption energies of hydrogen atoms on {100} facets, whose growth is hindered only if they are sufficiently large. The crucial role of hydrogen adsorption is further confirmed by the absence of pyramidal nanocrystals in experiments where the reduction process does not involve hydrogen.

Shape and faceting of nanocrystals deduced from HR-

TEM images
In Figure S2 we show the pyramidal shape deduced from HR-TEM image of the nanocrystal in Figure 1a in the main text. The shape is shown in different views, and the different type of surface facets (i.e. {111} and {100}) are highlighted.

DFT data for the adsorption of two H atoms
In Figure S3 we schematically show all possible inequivalent adsorption configurations for two H atoms in bridge positions on 3×3 and 2×2 {100} facets. The configurations are ordered with increasing energy from the best one, whose energy is set to zero.
We studied the simultaneous adsorption of two H atoms also on the {111} facets and on the edge between two large {111} facets. In all cases, we considered the most favorable sites as found for the adsorption of a single H atom, i.e. on-top sites on the {111} facets   Figure S3) is reported below each configuration. and bridge sites on the edge (see Figure 3 and Table 1 in the main text). The considered configurations and their corresponding energies are reported in Figure S4. Our results show that the {111} facets and the long edge are less favorable for the adsorption of two H atoms compared to the 3×3 {100} facet. Indeed, six configurations with H atoms adsorbed on the 3×3 facet (configurations from c1 to c6 in Figure S3) are lower in energy.
Hydrogen adsorption behavior on a Pt nanocrystal of larger size  Figure S5. In each case the configurations are oredered with increasing energy from the best one, whose energy is set to zero.
bridge sites on the edge of the 4×4 facet (see Figure 6a). For the adsorption of two H atoms, we checked the two inequivalent configurations with the H atoms adsorbed on bridge sites of the same edge of the 4×4 facet (see Figure 6b), which are expected to be the most favorable ones according to the results for H adsorption on the 3×3 facet (configuration c1 in Figure   4 of the main text). In both cases, configurations with H atoms adsorbed on the 4×4 facet are close in energy, and much more favorable than configurations with H adsorbed on the 2×2 facet. The same trend is found for the adsorption of four H atoms. We note that, in all cases, the energy difference between adsorption sites on the 2×2 and on the 4×4 facet is even larger than the one between 2×2 and 3×3 facets, as evaluated for the 75-atom cluster (see Table 1 and Figures 4 and 5 in the main text). Therefore, the overall picture arising from the calculations on the 75-and 127-atom clusters is that {100} facets of size 2×2 are by far the least favourable for hydrogen adsorption, followed by the 3×3 ones and then by the 4×4 ones. The comparison of the {100} facets of different sizes is summarized in Table   S1.  Figure 4 and Figure 5 of the main text and from Figure S6.

Effect of hydrogen on the adsorption of Pt atoms
We studied the effect of hydrogen on the adsorption of one Pt atom on the surface of the Pt cluster of size 75 atoms, shown in Figure 2 of the main text. Firstly, we considered the bare cluster, i.e. with no H atoms on its surface, and we evaluated all inequivalent adsorption  Table   S3. The presence of H atoms strongly affects the adsorption of Pt. For each given site type, sites closer to the H atoms are more energetically unfavorable. We especially note the two adsorption sites on the 3×3 facet have very different energy. The site far from the H atoms is equivalent to the corresponding site in the bare cluster, since we have calculated basically the same energy difference compared to the site on the 2×2 facet. On the other hand, the energy difference is almost doubled for the site close to the H atoms, which is therefore much more unfavorable, and in close competition with adsorption sites on the nearby {111} facets.
The same behavior is found when four H atoms are adsorbed on the 3×3 facet. Sites and corresponding energies are shown in Figure S7 c and in Table S4. In this case, one of the sites on the small {111} facet (site 2, far from the H atoms) is slightly more favorable than the site on the 3×3 facet. We recall that, in bare clusters, the adsorption of metal atoms is always more favorable on surface facets of {100} type compared to {111}, due to the higher  Figure 2 in the main text, with one Pt atom adsorbed on its surface, in the sites of Figure S7a. ∆E is the energy difference (in eV) with respect to adsorption in the best site, i.e. on the 2×2 {100} facet.  Figure  4(c1) in the main text), and with one further Pt atom adsorbed on its surface, in the sites of Figure S7b. ∆E is the energy difference (in eV) with respect to adsorption in the best site, i.e. on the 2×2 {100} facet.  Figure  5 of the main text), and with one further Pt atom adsorbed on its surface, in the sites of Figure S7b. ∆E is the energy difference (in eV) with respect to adsorption in the best site, i.e. on the 2×2 {100} facet.