Solid-to-liquid phase transitions of sub-nanometer clusters enhance chemical transformation

Understanding the nature of active sites is crucial in heterogeneous catalysis, and dynamic changes of catalyst structures during reaction turnover have brought into focus the dynamic nature of active sites. However, much less is known on how the structural dynamics couples with elementary reactions. Here we report an anomalous decrease in reaction free energies and barriers on dynamical sub-nanometer Au clusters. We calculate temperature dependence of free energies using ab initio molecular dynamics, and find significant entropic effects due to solid-to-liquid phase transitions of the Au clusters induced by adsorption of different states along the reaction coordinate. This finding demonstrates that catalyst dynamics can play an important role in catalyst activity.

These papers (amongst MANY others for these groups and others ) clearly also show the liquid like behavior of supported Au clusters and the impact of entropy and dynamics upon catalysis . This body of work though well cited is completely ignored by the authors despite the similar perspective, method etc. For this alone I believe the paper has a lot less novelty than the authors claim as they have either ignored or are unaware of the earlier work by many other groups even on very similar systems. . We regret that due to length limit, we could not cite all computational publications in this topical area even though we've tried to cite the most relevant ones.
In respect for the reviewer's suggestions, we have accordingly cited these references in the revised manuscript (Refs. 14-15 and 17-19 on page 1).
Secondly, we respectfully disagree with the reviewer's statement "the paper has a lot less novelty than the authors claim as they have either ignored or are unaware of the earlier work by many other groups even on very similar systems". We emphasize that the novelty of our work doesn't lie at ab initio molecular dynamics (AIMD) simulations of structural dynamics of Au clusters, which is the focus of most of previous computational studies, but on the systematic investigation of temperature dependence of reaction free energies (barriers) on dynamical clusters, which enables us to correctly extract reaction entropies due to cluster dynamics, most importantly 3 leading to the discovery of solid-to-liquid phase transitions of Au clusters during the course of elementary reactions that can facilitate chemical transformations. We are very confident that this discovery is new, and has never been proposed before. Our claim is also supported by the second reviewer who, after summarizing three of our main findings, concluded that "the general concept is very interesting..." and our studies "highlight the potential impact of the effect on predicted reaction and activation free energies".
More specifically, previous computational studies on cluster dynamics concern the diversity of structural configurations of given sizes of clusters, and AIMD (e.g. the work of Jun Li et al. as indicated by the reviewer) and global optimization techniques (e.g. the work of Alexandrova) have been applied to exploring the configuration spaces to search for (meta-)stable structures. Once stable structures are obtained, reaction barriers and energies are calculated on given cluster structures using 'static' geometry optimization methods (e.g. transition state optimization methods, etc.). Thus, as far as elementary reactions are concerned, the cluster structures remain 'static'. In this sense, structural dynamics of clusters just brings in many stable structures and 'static' reaction paths on each one of them. For this reason, we have argued, as described in Lines 32-34, Page 1 in the original manuscript, "the "static" perspective has been still taken in identifying the active sites under environmental conditions and monitoring the transformation of one type of active sites into another". This approach can be justified if the time scale of structural evolution of catalysts is much longer than the time scale of elementary reaction steps.
Our work however goes beyond this common view in literature, aiming to address a fundamental question, what if the timescale of the dynamic evolution of catalyst structures overlaps with that of chemical reactions? Thus, we take a distinctly different standpoint from previous publications, as also indicated by Review 2 stating that "the authors correctly argue that most in the field do not consider active site dynamics on the time scales of reaction events" and "the methodology of huge numbers of AIMD simulations is pushing the boundaries of studying the dynamic behaviour of catalytic systems". In our work, we have carried out extensive AIMD simulations to calculate reaction free energy profiles by using constrained MD and thermodynamic integration, fully accounting for cluster dynamics during the course of 4 elementary reactions. Moreover, careful investigations of temperature dependence of the reaction free energies enable us to quantify the entropic contributions due to cluster dynamics, which eventually leads to the discovery of the new catalytic effect that solid-to-liquid phase transitions of the Au clusters induced by the change of adsorption states of reaction species facilitate chemical transformations.
To avoid any confusion, we have added some sentences to clarify the advance and novelty of our work citing previous computational studies as suggested.
On Page 1, we now write: "Although in recent years the advent of in situ spectroscopic and microscopic techniques [9][10][11][12][13] and electronic structure calculation methods has allowed for investigating the dynamic evolution of the structures of catalysts under reaction conditions [14][15][16][17][18][19] , the "static" perspective has been still taken  Regarding the statistical errors in our free energy calculations, we would like to first point out that we usually run several ps AIMD simulations to equilibrate the systems, followed by production periods of about 5-15 ps for data analysis. For the size of systems studied in this work, the time scale of ~10ps is sufficient to obtain well Taking O 2 dissociation on Au 13 at 330K for example, the error bars of PMF and free energy profile are shown in Figure R1a   As for the numerical differentiation of temperature dependent reaction free energies, it is indeed not straightforward, as pointed out by the reviewer. It is worth mentioning: (i) to obtain converged PMF at one fixed O-O distance, it usually takes 10-20 ps, i.e.
20000-40000 AIMD steps; (ii) to obtain accurate a free energy profile and integrated reaction free energy (barrier), we have calculated 15 distances from reactant to product states, with denser sampling around the transition states (TS), as shown in Figure R1a,c. This amounts to about half million AIMD steps for one free energy profile; (iii) to further study the temperature effect, we have investigated 7 temperatures well covering the temperature range of the solid, solid-liquid coexistence and liquid phases. Thus, it overall takes about 4-5 million AIMD steps to obtain sufficient data to assess the temperature dependence of the reaction free energies ( Figure R2a). The error bar in the entropies, obtained by differentiating free energies with respect to the temperature, is however not straightforward to estimate.
Note that it is not a statistical error, but a fitting error. The fitting at low and high temperature ranges are certainly more accurate, because of slowly varying of free energies, than that at the transition temperature range where free energies change more dramatically (see Figure R2 below). The fitting in the transition range will benefit from calculating more free energy points. If simply taking the two points at 273 K and 373 K and assuming a linear fit, the free energy change (i.e. points and curves in red) is about 1.2 eV, giving an average entropy change of ~1200 J/mol/K. This is of similar magnitude to the peak in the curve fitting. Most importantly, the sharp entropy change with such a magnitude clearly indicates the occurrence of phase transitions, irrespective of the fitting procedure of temperature dependent free energies. To clarify this, we have added some discussion in the revised manuscript (Method section, highlighted in yellow).

Response:
We thank the reviewer for the positive comments. Especially, the reviewer agrees that "most in the field do not consider active site dynamics on the time scales of reaction events", and thus our work is distinct from literature that our AIMD simulations assess "the configuration entropy of the cluster along the reaction pathway". More importantly, the reviewer thinks that the method of AIMD simulations is pushing the boundaries of studying the dynamic behavior of catalytic systems and the general concept we discover is very interesting. We also appreciate the constructive comments on technical details of our calculations and potential impact of the discovered concept on real catalytic processes, which would certainly help improving the manuscript. Our point-by-point responses to the comments are given as follows.
1. The authors must do a better job of explaining how the AIMD simulations were done/justified and how the "static" geometry optimization calculations were done. (b) The AIMD simulations seem also to be "static" just from a different reference point -the molecular bond distance. Here the molecule structure was fixed in space, while the cluster was allowed to move around the molecule into an optimum structure at each bond distance. Is this correct? Is there any evidence that this approach well represents the case where the whole system is allowed to evolve without any fixed coordinate species? The second approach would require much too long of a simulation to be reasonable, but there must be some argument that the approach used (fixed molecular bond distance) can represent a real bond breaking event.
Response: We thank the reviewer for the comments. We calculate the reaction free energies by performing constrained molecular dynamics to compute the potential of mean forces (PMF) for a specific reaction coordinate, followed by thermodynamic integration of the mean forces along this reaction coordinate. It is worth mentioning that the free energy calculation methods are well established and have been widely used to study solution chemistry 1-4 and biological processes 5   run as the initial configuration for the next run. The free energies were then obtained by integrating the average forces with respect to the distance." (d) In many cases in Extended Data Figure 3d the Force curves are quite noisy. How were these fits to obtain free energy profiles that are smooth?

Response:
We thank the reviewer for the comment. It should be mentioned that our calculated PMF are well converged with very small statistical uncertainty, i.e. Figure   R1 as given in the response to the comment of reviewer 1. The bumpy features in the PMF profile such as the one at 600 K (see Figure R3 below), simply indicate the fine structures in the corresponding free energy profile. Note also that the free energy change is obtained by integrating the mean force against distance, i.e. the integral area of the force-distance curve, resulting in a rather smooth free energy curve as shown in Figure R3b. In addition, we have calculated overall 15 points with small increments along the reaction coordinate of the O-O distance, well populating the free energy profile to achieve accurate free energies.  2. Next the potential importance of these results in the context of catalytic processes is considered. It makes good sense in general that the fluxional nature of clusters must be considered to couple with reactions, but exactly how important this will be in real catalytic systems is questionable.

Response:
We thank the reviewer for the helpful comments. We have to admit that this conceptually new catalytic effect of dynamic clusters presented in our work is on the basis of sole theoretical calculations, but using computational methods with solid foundation. The experimental realization or validation is however not yet possible because it has just been discovered theoretically. However, we want to argue that the importance of our work lies at exactly where the concern of the reviewer is, i.e., how significantly does this new theoretically proven concept impact real catalytic processes? Addressing this question will certainly stimulate future experimental studies. More importantly, our work also clearly shows the direction how experiment which would not react simultaneously with any reasonable probability, the adsorbates would further act to "pin" the structure. Thus, while the case presented where the entropic effect is maximized (Au 13 in gas phase with 1 adsorbate) certainly highlights the importance of cluster dynamics on the reaction pathway, whether this effect exists under realistic catalytic conditions seems questionable.

Response:
We are grateful for the constructive comments of the reviewer. Firstly, we absolutely agree that the support will have strong effect on the cluster dynamics and phase transition temperature. In this work, we compare the Au clusters in gas phase and on MgO support, and the results indeed suggest that MgO support constrains the dynamic effect of Au cluster, leading to smaller entropy changes in transition temperature range compared to the free standing cluster. However, it should be noted that the estimate of entropy change due to phase transition is still on the order of 500 J/mol/K, which is very significant for surface reactions. On the other hand, there is some evidence that shows the support effect is not just reducing the cluster dynamics and screening the adsorbate influence on the phase transition behaviour of the cluster along the reaction coordinate. On some active support such as TiO 2 , CeO 2 and FeO x , structural fluctuation of clusters can even be boosted [8][9][10][11] , especially when oxygen vacancies are present 8 . We therefore believe that the support has non-trivial effects on cluster dynamics, which will surely simulate future investigations.
With regard to the influence of adsorbate coverage, it is usually thought that the increase of coverage will actually enhance the dynamic effect 9,10 . As shown in our present work, with the adsorption of one molecule, the Au cluster becomes more dynamical, as evident by the decrease in the melting temperature. It is therefore reasonable to argue that in practical catalytic reaction conditions the dynamic effect will become even more dramatic at high surface coverage. [Redacted] (b) From a similar perspective, there should be cluster size dependence for these effects. I imagine clusters below 3-4 atoms become more "rigid" and present less configurational entropy, and likely a similar phenomenon occurs at larger cluster sizes (>15 -20 atoms) where crystal structures begin to develop. Some comments on the size dependence would be useful, as any real catalyst will have a range of sizes and the reactivity would be of the collective behavior of these species. there is a possibility that this effect may have been observed in some experimental studies without being realized. In the following, we list some experimental observations that may suggest our discovered effect.
It is generally believed that the activity of Au cluster are highly size dependent, and only the Au clusters with a size less than 3 nm exhibit enhanced catalytic activity 14 .
The fundamental reason however is not clear. Taking ultra-small (<3nm) supported Au clusters for example, Tsukuda and coworkers found the activity of Au clusters Au n (n=10,18,25,39,89) for cyclohexane oxidation, increases with the increase of size, reaching the highest at n = 39, and thereafter decreases 15 . Other experiment also 18 showed that for clusters Au n (n<7), the activity is very low 16,17 . The volcano-shaped size dependence cannot be explained solely by geometric factors, such as the density of under-coordinated Au atoms. Interestingly, it was found that the larger the cluster size, the higher the temperature required for the reaction 14 . Considering the cluster dynamics is also size and temperature dependent, the size dependent phase transition behavior of clusters may offer a possible explanation to these observations, i.e.
volcano-shaped size dependence and increase of reaction temperature with cluster size.
In heterogeneous catalysis, many factors of catalysts such as cluster sizes 14,18 , support oxides 14,19 , and co-adsorption effects 20 , have been proven to have significant impact on catalytic reactivity. Conventionally, they are often explained by geometric or electronic effects. As the reviewer has also suggested, these factors could also change the behavior of cluster dynamics 8,10 , and thus the activity. Our proposed concept connecting phase transition of clusters and chemical reactions, therefore add a new dimension in understanding the factors relevant to catalytic activity.
Finally, we would like to stress again that our work also shows how the proposed effect could be realized in experiment, i.e. looking into the interplay between factors that affect cluster dynamics (e.g. cluster size, support, coverage and co-adsorption) and temperature. We have added some discussion in the revised manuscript to discuss this (Discussion section, highlighted in yellow).
3. Lastly there were a few recent papers on AIMD for the dynamic behaviour of clusters coupling to reaction pathways and supported liquid metal catalysts that I was surprised weren't cited or discussed. See Nature Chemistry 9, 862-867 (2017) and Nature Communications 6, 6511 (2015).

Response:
We thank the reviewer for the suggestion. We have added these citations and some discussion accordingly in the revised manuscript (Refs. 14 and 16 in the revised manuscript).