Restructuring and Hydrogen Evolution on Pt Nanoparticle

Dynamic catalyst structuring and the hydrogen evolution activity enhancement at nanoscale, as predicted by a first principles global optimization method.


Introduction
Nanoparticles are common forms or carriers of heterogeneous catalysts 1-3 and also of wide application in many other elds, e.g. as biomedical drug delivery agents 4 and for energy conversion and storage devices. 5 Special physicochemical properties emerged at the nanoscale adding a new complexity in understanding and optimizing reactions on nanoparticles. Compared to chunky crystalline materials, nanoparticles are more exible in morphology and under reaction conditions, the reshaped nanocatalyst may exhibit a completely different activity, either poisoned or promoted aer a so-called induction period. [6][7][8][9] Despite the vast amount of research on nanoparticle synthesis and morphology control, major gaps in our knowledge still exist, especially with regard to our molecular level understanding on the in situ dynamic restructuring of nanoparticles: this is reected in our inability to predict whether such restructuring is benecial or detrimental to catalyst activity. Controlling the nanostructure dynamics for the desirable property, e.g. catalytic activity, is paramount for rational catalyst design and is a general goal in nanomaterial applications. 10,11 Pt is a unique metal with high catalytic performance for a wide range of reactions, and it is perhaps the most efficient HER catalyst in electro-and photocatalytic water splitting. 12,13 It has been constantly pursued in research to reduce the Pt usage by identifying the optimum particle size for activity. On model single crystalline surfaces, it was however found that HER is only weakly dependent on the crystal facet: the ridged Pt(110) is about two times more active than the (111) and (100) terraces. [14][15][16][17] On going to the nanoscale, there is no consensus on the particle size effect. [18][19][20][21] The presence of the particlesupport interaction further complexes the understanding of the particle size effect on activity. 22 A very recent study by Schweinberger et al. using size-selected Pt nanoparticles supported on CdS nanorod shows that the particle of a critical particle size $46 atoms (1 nm) can achieve the maximum H 2 production, whilst the mass activity is the highest when the particle size shrinks down to the subnanoscale with only 8 atoms (Pt 8 ). 23 To date, there is much uncertainty on the physical origin of the HER activity on small nanoparticles. The nature of the active site and the dynamic structure evolution are two key issues that need to be resolved rst.
Here we present the rst quantum mechanics simulation on the structure dynamics of Pt nanoparticles during HER and quantify its catalytic consequence. The Pt nanoparticle considered in this work is represented by a Pt cluster of $1 nm diameter, Pt 44 , which is identied as a magic number size with O h symmetry. Signicant restructuring-induced promotion is revealed on the Pt 44 nanoparticle at the HER condition, and theory further predicts that such a promotional effect due to restructuring is prominent only for nanoparticles below $1.8 nm. In general, the restructuring as driven by the exothermicity of the adsorption of reaction intermediates may or may not increase the active site concentration that depends on the nature of the reaction and also the particle size.
As both nanoparticle restructuring and catalytic reactions are rare events with high barriers, it presents a challenge to computer simulation since the long simulation times of molecular dynamics, or even the use of enhanced sampling techniques, may not be able to capture the desired reaction patterns. For example, in HER on Pt(111), the barrier of H-H coupling to form H 2 can be as high as 0.92 eV at the working conditions. 24 The approach we adopt here is to use the rst principles density functional theory (DFT) based stochastic surface walking (SSW) global optimization method, 25-27 SSW-DFT, to explore the Pt nanoparticle morphology at the HER condition. The recently-developed SSW method is able to visit the minima on PES by following likely pathways, and therefore is a powerful tool for both structure prediction and pathway search. 25 Using the new technique, we are able to stepwise follow the particle restructuring in a H 2 atmosphere and determine the HER activity.

DFT calculation
All SSW calculations and the reaction modelling were performed in combination with the DFT calculations as implemented in the SIESTA package 28,29 with Troullier-Martins norm conserving pesudopotentials. 30 The exchange-correlation functional utilized was at the generalized gradient approximation level, known as GGA-PBE. 31 The optimized double-z plus polarization (DZP) basis set with extra diffuse function was employed for metal. The orbital-conning cut-off was determined from an energy shi of 0.010 eV. The energy cut-off for the real space grid used to represent the density was set at 150 Ry. The Quasi-Newton l-BFGS method is used for geometry relaxation until the maximal force on each degree of freedom is less than 0.01 eVÅ À1 . To correct the zero-point energy for the reaction barrier, the vibrational frequency calculations were performed via the nite-difference approach. Transition states (TSs) of the catalytic reaction were searched using the Constrained-Broyden-based TS-searching methods. 32,33 For all the Pt clusters from Pt 12 to Pt 46 (see Fig. S1 †), at least four lowest-lying isomers obtained from the SSW-DFT/SIESTA search were further checked using the spin-polarized plane wave calculations with ultraso pseudo-potentials 34 or projected augmented wave 35,36 pseudo-potentials, as implemented in VASP. 37 The plane-wave kinetic energy cut-off of 400 eV was used and the exchange-correlation functional utilized was at the generalized gradient approximation level, GGA-PW91 (ref. 38) and GGA-PBE. 31 Although small Pt clusters in the gas phase are generally spin polarized, the energy contribution of spin polarization is diminished for clusters above 39 atoms (< 0.03 eV).

SSW calculation
In all SSW simulation, the key parameters utilized are the same with those utilized previously for exploring the PES of carbon and boron clusters, [25][26][27] i.e. the Gaussian width being 0.6Å, the number of Gaussian potential being 10.
To identify the global minimum structure of Pt x (x ¼ 12 to 46) (see Fig. S1 †), we set the temperature utilized in Metropolis Monte Carlo as being 3000-5000 K. The higher temperature is used to verify the obtained global minimum structure. In the SSW search, we performed four to ten parallel runs and up to 300 minima are collected at the rst stage, from which the most stable conguration is obtained. Next, we veried the result from the most stable conguration of the rst stage and collected another 300 minima. This process was repeated until no more further stable congurations were identied at the stage of verication.
For the grand canonical Monte Carlo (GCMC) simulation for Pt 44 H x system, the basic procedure of the SSW simulation at each xed H concentration was the same as that described above for pure Pt clusters. In the GCMC simulation, the major difference was that every 300 SSW steps, we evaluated the chemical potential of adsorbed H atom with respect to that of H in the gas phase DG H (see below in eqn (2)) based on the current most stable conguration. According to the value DG H < or >0, we were able decide to accept or refuse the current most stable conguration. To speed up the structure search for reaching the DG H ¼ 0 equilibrium, the newly-arrived H atoms will be always added to the vacant surface sites, e.g. vacant bridge site; the removal of H atoms will always choose the atop H atoms or subsurface H atoms, if present, which are calculated to have the poorest adsorption energy.

The exothermicity of restructuring under HER condition
In HER, the nanoparticle is in the H 2 atmosphere and an equilibrium of H chemical potential needs to be achieved at the steady state. The exothermicity of the H adsorption on the bare nanoparticle provides the driving force of the restructuring. This is measured by DG per Pt atom with reference to Pt 44 octahedron and H 2 gas (the standard condition is utilized here), as shown in eqn (1).
Here G(Pt 44 H x ) and G(Pt 44 ) can be computed from DFT directly by including the zero point energy (ZPE) correction, and G(H 2 ) is the free energy of the gas phase H 2 that can be obtained from standard thermodynamics data. 39

Pt 44 octahedron
In this work, we utilize Pt 44 as the model catalyst for investigating the HER on $1 nm Pt nanoparticles. Pt 44 is predicted to a magic number size based on the unbiased SSW-DFT global structure search (see ESI discussion and Fig. S1 †), which was also suggested previously 40 Fig. 1 to provide insights into the PES of Pt nanoparticle in general. The structures of typical less stable minima are also shown. In general, the conformation of the Pt nanoparticle is discrete at the energy window 0-0.5 eV above GM and becomes continuous-like above 0.5 eV. Most of the low lying structures have a common core-shell feature as the GM with 6 core atoms and 38 shell atoms. The continuous energy spectrum appears just 0.5 eV above GM, indicating that the Pt nanoparticle is highly mobile and the reconstruction of the shell is kinetically allowed even at ambient conditions.

Structure evolution under HER condition
To simulate the structure evolution dynamics at the HER conditions, we consider the Pt 44 /H 2 system as a grand canonical ensemble where the chemical potential of the adsorbed H atoms will eventually reach equilibrium with that in the gas phase, i.e. DG H / 0. DG H can be calculated as follows, where DE DFT and ZPE are the differential adsorption energy and the zero point energy of the newly-arrived H atom on particle; and G(H 2 ) is the free energy of H 2 in the gas phase at the standard state.  (Fig. 2b), although the core-shell structure still remains: Pt 44 H 50 has 7 core atoms and 37 shell atoms.  The GCMC/SSW-DFT simulation conveys two important messages for the HER-driven nanoparticle restructuring: (i) adsorbed H atoms are always more stable on the surface even when the equilibrium coverage is above 2 ML. Importantly, the subsurface H atoms inside the Pt nanoparticle is found to be unstable (see ESI Fig. S2 †) since the stronger Pt-Pt bond is energetically preferred compared to the Pt-H bond in forming the particle core. This implies a high stability of Pt nanoparticles under HER conditions. (ii) The restructuring is driven to maximally expose {100} while the core-shell structure of Pt nanoparticles is always kept to minimize the total energy. Only {100} and {111} facets are present at the GM of Pt 44 H 80 . Overall, the core Pt atoms increase from 6 to 8 and the shell Pt atoms decrease from 38 to 36 (the surface density drops) aer the restructuring, which is consistent with the typical surface reconstruction observed in surface science studies. 41

HER activity
We are now at the position to investigate the HER on the Pt 44 H 80 polyhedron. We have considered all the likely reaction patterns for the hydrogen evolution via the coupling of two adsorbed H atoms, H + H / H 2 , the so-called Tafel mechanism in electrocatalytic HER that is preferable at high H coverage conditions (see our recent work on HER kinetics on surfaces 24 where the electrochemical potential and solvation effect have been considered; here we follow the main conclusions obtained there). Fig. 3a shows that the calculated free energy barriers (DG a ) of H-H coupling on Pt 44 H 80 span from 0.47 to 1.07 eV depending on the local sites. Unexpectedly, DG a at the apex sites are 0.47-0.71 eV, which is much lower than that on the {111}, edge and {100} sites, 0.88, 0.88 and 1.07 eV, respectively. We also noticed that the calculated DG a of the H-H coupling on the {111} facets of Pt 44 H 80 (F1) is in fact similar to that on the extended Pt(111) ($0.9 eV). The optimized structures of the transition state (TS) are also similar in two cases (see ESI Fig. S3 †). Similarly, DG a at the apex sites of the unreconstructed Pt 44 H 48 octahedron (AO) is also in the DG a range of the apex sites on Pt 44 H 80 . These results indicate that the HER activity can be assessed largely by the local geometry of the Pt site.
By identifying the critical role of apex sites and the local reactivity in HER, we can discuss their implication to HER catalysis. In Fig. 4, we rst estimated the HER activity of Pt particles on differently sized as-synthesized nanoparticles at the equilibrium shape in solution, i.e. no restructuring due to H 2 (data taken from experiment and our recent study). 42, 43 We then  The sites are as indicated on the right-hand particle. Among 18 apex sites, there are ten A1, four A2, two A3 and two A4 sites. Also shown are DG a on the extended (111), (100) surfaces and the apex sites of the unreconstructed Pt 44 H 48 (AO); (b-d) the reaction snapshots for the lowest barrier reaction channel at the apex A1 site. The reaction features with the atop H reacting with a neighboring bridging H (both H highlighted by yellow color), where the apex Pt atom is coordinated with five H atoms. The color scheme is as in Fig. 2. count the apex, {111} and {100} and edge sites of the particles and sum the overall HER rate (specic activity of HER, SA, mol cm À2 s À1 ) on all the sites based on microkinetics, as shown in eqn (3).
where k B is Boltzmann's constant and h is Planck's constant (k B T/h is 6.25 Â 10 12 at 298.15 K from classic TS theory); DG a is the estimated free energy barrier statistically averaged according to the data in Fig. 3a, i.e. 0.48 eV for apex sites, 0.88 eV for terrace sites and 0.89 eV for edge sites; q site is the number of the active sites on the nanoparticles; S is the surface area. Here we assume the same HER activity at the same type of site based on the fact of local reactivity of HER identied above. The calculated HER rate on the nanoparticle is thus plotted in Fig. 4 (3)), while the estimated DG a utilized in Fig. 4 is 0.48 eV and the difference in the rate is no more than 10 times. Furthermore, we may also consider the situation aer the nanoparticle restructuring at the HER condition. Although we do not know the exact atomic structure, this work does show that {100} is the direction of restructuring and thus the {100}dominated truncated cube would be the preferred shape starting from small particles, where the apex sites can reach 24 per particle. We therefore estimate the HER rate as a possible maximum limit due to restructuring using the same approach above, as plotted in the grey dash curve in Fig. 4. Indeed, the trend for the large increase of HER activity of Pt 44 aer restructuring is correctly reected in the gure (the red arrow). Interestingly, Fig. 4 predicts that for large nanoparticles above 1.8 nm, the restructuring of nanoparticles, although should occur as well, does not enhance the HER activity appreciably. The activity decays very slowly above 3 nm, when the activity can be regarded as insensitive to the particle size.
By contrast, for very small nanoparticles (e.g. 1 nm), the activity can be dramatically higher, which is caused by the dynamic restructuring at the HER condition that creates a high concentration of ve or six coordinated apex sites per surface area. Along this line, we expect that ultrasmall Pt clusters without core atoms have the highest HER activity because all Pt atoms are on the surface with low coordination, where the concentration of apex sites can be maximized at the HER condition. This corresponds to a size of less than $20 atoms (see ref. 40 and also ESI Fig. S1 †), which may rationalize the highest photocatalytic HER activity of Pt 8 observed recently. 23

Conclusions
New DFT-based global optimization theoretical methods allow the observation of the dynamic catalyst structure evolution and the quantication of the activity change of Pt nanoparticles for HER. Unexpectedly, we found that HER occurs preferentially on Pt low-coordinated apex Pt sites, which totally dominates the activity for Pt nanoparticles. The restructuring of nanoparticles can promote HER, but appreciably only below a certain size threshold, $2 nm, where the apex sites dynamically created can reach the maximum concentration. The subnano Pt clusters without core atoms are predicted to have the highest HER activity. Fig. 4 Estimated HER activity (using eqn (3)) of Pt nanoparticles with the equilibrium shape in solution, i.e. no restructuring due to H 2 , (black curve) and with only the {100}-dominated truncated cubic shape (grey dash curve). The nanoparticle equilibrium shape in solution is taken from experiment 42 and our recent work, 43 which exhibits a gradual transition from octahedron at very small particles to truncated octahedron, to cuboctahedron and to the {100}-dominated truncated cube at large particles. The grey dash curve represents the activity limit after the restructuring.