Effect of Framework Composition and NH3 on the Diffusion of Cu+ in Cu-CHA Catalysts Predicted by Machine-Learning Accelerated Molecular Dynamics

Cu-exchanged zeolites rely on mobile solvated Cu+ cations for their catalytic activity, but the role of the framework composition in transport is not fully understood. Ab initio molecular dynamics simulations can provide quantitative atomistic insight but are too computationally expensive to explore large length and time scales or diverse compositions. We report a machine-learning interatomic potential that accurately reproduces ab initio results and effectively generalizes to allow multinanosecond simulations of large supercells and diverse chemical compositions. Biased and unbiased simulations of [Cu(NH3)2]+ mobility show that aluminum pairing in eight-membered rings accelerates local hopping and demonstrate that increased NH3 concentration enhances long-range diffusion. The probability of finding two [Cu(NH3)2]+ complexes in the same cage, which is key for SCR-NOx reaction, increases with Cu content and Al content but does not correlate with the long-range mobility of Cu+. Supporting experimental evidence was obtained from reactivity tests of Cu-CHA catalysts with a controlled chemical composition.

rings accelerates local hopping, and demonstrate that increased NH 3 concentration enhances long-range diffusion. The probability of finding two [Cu(NH 3 ) 2 ] + complexes in the same cage -key for SCR-NOx reaction -increases with Cu content and Al content, but does not correlate with the long-range mobility of Cu + . Supporting experimental evidence was obtained from reactivity tests of Cu-CHA catalysts with controlled chemical composition.
Copper-exchanged zeolites play a crucial role as redox catalysts for some environmentally relevant processes, like the partial methane oxidation to methanol or the selective catalytic reduction of nitrogen oxides with ammonia (NH 3 −SCR−NOx). In both cases, the small pore Cu-SSZ-13 zeolite with the CHA structure has been reported as an efficient catalyst. [1][2][3][4][5][6][7][8][9][10][11] The NH 3 −SCR−NOx reaction is currently employed for the removal of nitrogen oxides (NOx) from exhaust gases in diesel vehicles and stationary plants, through a redox catalytic cycle in which Cu + is oxidized to Cu 2+ by NO 2 or NO+O 2 , and then reduced to Cu + by reaction of NH 3 and NO forming harmless N 2 + H 2 O (Scheme 1). [12][13][14][15] This understanding of the reaction mechanism has enabled development of optimized catalysts by tuning framework topology, composition and copper speciation. In the as-prepared catalysts, Cu + and Cu 2+ cations are directly coordinated to the zeolite framework forming heterogeneous active sites, while under reaction conditions NH 3 solvates the Cu + cations forming mobile [Cu(NH 3 ) 2 ] + complexes that act as dynamic active sites, resembling homogeneous catalysts but within the confinement of the zeolite pores. At low temperature (T < 523 K) the oxidation step involves transient dimeric Cu + (NH 3 ) 2 −O 2 −Cu + (NH 3 ) 2 species whose formation requires the simultaneous presence of two [Cu(NH 3 ) 2 ] + monomers in the same cha cage.
The hops between adjacent cha cages are modulated by size exclusion effects and also by the attractive interaction between the positively charged [Cu(NH 3 ) 2 ] + complexes and the negatively charged framework Al sites. 8,9,[15][16][17] Thus, structural properties like Al content and distribution, Cu loading or Brønsted acid site density, as well as the interaction of the Cu active sites with the reactants, in particular NH 3 , might affect the mobility of Cu cations and consequently the NH 3 −SCR−NOx reaction rate. This has been evidenced by recent studies combining catalytic activity tests with operando XAS or EPR spectroscopy, [18][19][20][21][22] and ab initio molecular dynamics (AIMD) simulations have been successfully applied to provide atomistic insight into the dynamic nature of the Cu + cations under reaction conditions. 9,16,17 Scheme 1: Illustration of the low temperature SCR-NOx redox cycle.
The cost of AIMD simulations limits their applicabiltiy to a few selected systems at a time, at small length-and time-scales. The timescale limitation may be partially bypassed with enhanced sampling methods, such as umbrella sampling (US), which have been used to study the slow diffusion of copper complexes in CHA. 9,17 However, the systematic exploration of parameters such as Si/Al ratio, Al distribution, Cu/Al ratio, NH 3 concentration or the presence of Brønsted acid sites and compensating NH + 4 cations has not been yet possible.

Results
Neural network potential NNPs are highly accurate but they struggle to extrapolate outside their training data. In order to ensure robust and accurate production simulations, our NNP was trained on data gathered through multiple generations of active learning (AL) using a query by-committee approach. [61][62][63][64][65][66][67][68][69] A committee (ensemble) of NNPs was trained on the available labeled data at each iteration, and new data was collected based on the disagreement (variance) of the prediction of the committee members on newly generated geometries, as described in Computational Details Section and illustrated in Figure 1a. The last generation of the NNP was trained on a complete dataset containing 42k revPBE+D3 force calculations on structural models with a diverse set of atomic local environments, ranging from 290 to 323 atoms per supercell, summarized in Table S1 (see structural models in Figure S1). The chemical compositions in the dataset ( Figure 1b)   The active learning strategy was capable of automatically adding new, diverse, and informative chemical environments to the training pool at each of the pre-selected compositions through a combination of MD and uncertainty quantification. It generated informative training data for a number of chemical processes that occur during the reaction, but were not present in the initial training data. These include adsorption and protonation of NH 3 on the Brønsted acid sites to form NH + 4 cations, exchange between a gas phase NH 3 molecule and one of the two NH 3 ligands of the [Cu(NH 3 ) 2 ] + complex, and proton transfer from NH + 4 to NH 3 . The diffusion of [Cu(NH 3 ) 2 ] + complexes through the 8R windows that connect adjacent cha cages has a higher activation barrier. Therefore representative training data was obtained through the same enhanced sampling approach as the production simulations ( Figure S2).
This strategic combination of biased MD with uncertainty quantification allowed efficient sampling of the relevant regions on the PES with a small and diverse number of DFT evaluations. Figure S3 illustrates the structural diversity in the final dataset by means of a 2D projection of the local chemical environments around each Al atom in our data using UMAP 73 on the feature vectors learned by the NNP. 74    For the systems with two Al atoms in the same 8R (orange profiles in Figure 3), ∆G act values range from 3.9 to 5.4 kcal/mol and the reaction is slightly endergonic with ∆G values between 0.4 and 2.3 kcal/mol. In all other cases, ∆G act are higher than 6 kcal/mol and ∆G are larger than 3 kcal/mol, with the only exception of the DR4 system for which the process is slightly exergonic. The Al distribution in the DR4 model is the same as in SR1, but the diffusion occurs through different 8R windows (see snapshots in Figure 3).    Figure 4 show that the NH + 4 cation has been displaced from its initial position in the plane of the 8R to a position relatively close to one of the   To explore this hypothesis, two additional MD simulations of 5 ns were run using two modified M20 models, one of them containing 30 protons as compensating cations, labeled M20-H+, and another one with 60 additional NH 3 molecules added to the system, labeled   Bimolecular complexes and mechanistic implications for the NH 3 -

SCR-NOx reaction
According to the proposed mechanism, 9 the reaction rate depends directly on the probability of finding simultaneously two [Cu(NH 3 ) 2 ] + complexes in the same cage, which we analyzed separately from the mobility calculations.

Experimental validation for the low-T NH 3 -SCR-NOx reaction catalyzed by Cu-CHA zeolites with controlled composition
To experimentally validate the computational predictions, three CHA samples with different Si/Al molar ratios ranging from 7.3 to 23.3, which translates to a broad range of 1.4 to 0.5 Al sites per cha (see Table S4 in the Supporting Information) were synthesized as described in Methods. Then, the same Cu loading (∼1.5%wt Cu) was introduced within the three CHA materials, which resulted in a similar amount of initial Cu atoms per cha cage, ∼0.17, but different Cu/Al ratios (from 0.11 to 0.35, see Table S5). In addition, the CHA sample with Si/Al ratio ∼7.3 was also loaded with 3.0%wt Cu resulting in an additional sample with increased amount of initial Cu atoms per cha cage (0.3).
The catalytic tests to evaluate the low-temperature SCR-NOx activity of the different Cu- .9 ± 0.3 kcal/mol. The catalytic activity measured by the TOF and normalized by Cu content, however, increases in parallel with the calculated likelihood of two-copper encounters in the same cage (Fig 8a). This supports the argument that the formation of [Cu(NH 3 ) 2 ] + pairs in the same cha cage is responsible for the generation of the binuclear active sites that catalyze the reaction, although copper diffusion may not necessarily be the rate-determining step of the global process.

Catalyst Models
The Cu-CHA catalytic system was modeled using three different supercells of increasing size (see Figure S1).  Table S1. For the systems with 3 and 7 Al atoms, ten random Al distributions were generated. For the systems with two Al atoms ten different Al distributions were generated, one with 2 Al in the same 4R, one with two Al in the same 6R, four of them  Table S3 in the Supporting Information. In the models with low and medium Al content, two Cu loadings were considered, 4 and 20 atoms per unit cell, corresponding to Cu spatial densities of 0.08 and 0.4 Cu/1000Å 2 respectively and 0.5% and 2.6% Cu/Si ratios (systems labeled L4, L20, M4 and M20, Figure 5). In the models with high Al content, the Cu loading was always 20 atoms per unit cell, and the labels in Figure 5   The acquisition of training data was performed using active learning (AL) with a queryby-committee approach 61-68 as illustrated in Figure 1a. In this approach a committee (ensemble) of NNPs is trained on the available labelled data and new data is collected based on the maximum disagreement (variance) of the prediction the committee members.
The first generation of the potential was trained on a randomly collected subset of the DFT data generated from a previous study 17 and from three biased simulations performed with DFT at 423 K, used as reference ground truth. In total, there were ∼9000 geometries in the initial dataset. This pretrained potential was then retrained in 4 active learning loops using the 2x2x2 triclinic supercell described in previous section (see Figure S1.

Characterization
Powder X-ray diffraction (PXRD) measurements were performed with a multi sample Philips X'Pert diffractometer equipped with a graphite monochromator, operating at 40 kV and 35 mA, and using Cu Kα radiation (λ = 0.1542 nm). The PXRD patterns reveal the good crystallization of the CHA materials (see Figure S7 in the Supporting Information), all of them presenting particle sizes within the sub-micron scale (below 1 µm, see Figure S7 and From the low temperature NO conversion results, the rate constants (k) can be calculated using a first-order kinetic equation, as described previously in the literature: 88 where F 0 is the molar NO feed rate, [N O] 0 is the molar concentration at the inlet, W is the catalyst amount (gr) and X is the NO conversion. The Arrhenius equation was employed to estimate the apparent activation energies (Ea) after its linearization as follows: where A is the pre-exponential factor, R is the universal gas constant and T denotes the absolute temperature associated with the reaction (in Kelvin).

Data availability
The experimental and computational data that support the findings of this study are available from the corresponding author upon reasonable request. The datasets generated during this study are available at https://figshare.com/projects/Dataset_and_machine_ learning_potential_Cu-CHA/167645. The code used for this study can be downloaded from https://github.com/learningmatter-mit/NeuralForceField.