Activity Self-Optimization Steered by Dynamically Evolved Fe3+@Fe2+ Double-Center on Fe2O3 Catalyst for NH3-SCR

Identification of the active centers dynamically stable under the reaction condition is of paramount importance but challenging because of the limited knowledge of steady-state chemistry on catalysts at the atomic level. Herein, focusing on the Fe2O3 catalyst for the selective catalytic reduction of NO with NH3 (NH3-SCR) as a model system, we reveal quantitatively the self-evolving Fe3+@Fe2+ (∼1:1) double-centers under the in-situ condition by the first-principles microkinetic simulations, which enables the accurate prediction of the optimal industry operating temperature (590 K). The cooperation of this double-center achieves the self-optimization of catalytic activity and rationalizes the intrinsic origin of Fe2O3 catalyzing NH3-SCR at middle-high temperatures instead of high temperatures. Our findings demonstrate the atomic-level self-evolution of active sites and the dynamically adjusted activity variation of the catalyst under the in-situ condition during the reaction process and provide insights into the reaction mechanism and catalyst optimization.

. (a) Hexagonal unit cell of Fe 2 O 3 ; (b) Rhombohedral primitive cell of Fe 2 O 3 with an antiferromagnetic helical spin arrangement, where "↑" and "↓" stands represents the spin up and spin down, respectively. S3 Note S1. NH 3 Dissociation NH3 adsorbed on Fe site ([NH3-Fe-Ol], Eads = -1.08 eV) can not couple with the gaseous or adsorbed NO directly, forming the N-N bond owing to its bond saturation.
Hence, the NH3 dissociation is the fundament for the subsequent reactions. Here, two different lattice oxygen (Ol) were considered to assist the NH3 dissociation, i.e., Ol in [NH3-Fe-Ol] or the adjacent [Fe-Ol] (donated as Ol_1 and Ol_2, Figure S2). The energy profile of Ol_1(or Ol_2)-assisted NH3* dissociation on clean Fe2O3(001) is shown in Figure S2. Comparing the orange (Ol_1) and olive (Ol_2) lines in Figure S2, we can find that Ol_2 is more reactive to facilitate the breaking of the N-H bond in NH3 to form NH2* with a lower barrier of 0.74 eV compared with Ol_2 (Ea = 0.86 eV); in the optimized transition state (TS1, Figure 2a), the N-H bond is elongated to 1.643 Å, and the forming Ol-H bond is 1.075 Å. The further dissociations of NH2* assisted by Ol_2 give a barrier of 0.90 eV and 0.62 eV for the process NH2 + Ol_2 → NH + Ol_2H and NH + Ol_2 → N +Ol_2H, respectively, which is lower than the barriers of the NH3 dissociation by Ol_1(TS2 vs. TS2' and TS3 vs. TS3'). The related transition states are shown in Figure S3. In general, Ol_2 exhibits a more reactivity to dissociate NH3.
Moreover, the further dissociation of NH2 into NH or N has an evidently increased barrier, and gradually becomes more endothermic ( Figure S2). Therefore, on Fe2O3, the deep dissociation of NH3 would be restrained, the formation of NH2 species could be more favored, which is the main intermediate to participate in the following NH3-SCR.  Figure S3, respectively. Figure S3. Transition state structures for NH 3 dissociation, where TS1~TS3 and TS1'~TS3' correspond transition states in Figure S2.

Note S2. NH 2 NO Formation and Conversion
As the intermediate [NH2-Fe-Ol] forms, it could react with NO into N2 and H2O.It is interestingly found that the NO in the gas phase can readily couple with NH2 in [NH2-Fe-Ol] into [NH2NO-Fe-Ol] (the Eley-Rideal (E-R) mechanism), following an almost barrierless process in terms of total energy; even putting a NO molecule above NH2* at a long distance of 3.225 Å ( Figure S4), the NO gradually descends and bonds with NH2 spontaneously upon a typical structural optimization, forming a monodentate NH2NO configuration with the N-end in NH2 group bonded with Fe site; such an adsorption configuration of NH2NO further tends to transform into a thermodynamically more stable configuration with the N-end from NO anchored at Fe site ( Figure S4). This whole process (NH2* + NO(g) →NH2N*O) is strongly exothermic (ΔH= -2.38 eV).
The coupling between NH2 and NO could be a radical-like reaction, thus resulting in a barrierless process. 1 The formed NH2NO will converse into H2O and N2 easily, a thermodynamic and kinetic favorable pathway (a hydrogen push-pull mechanism, i.e., NH2NO → NHNO → NHNOH → NNOH → N2+OH) has been reported. [1][2][3] Firstly, NH2NO dehydrogenates into NHNO assisted by Ol of the adjacent [Fe-Ol] with a low barrier of 0.10 eV (ΔH = -0.25 eV). In the transition state (TS1, Figure S5), the N-H bond is elongated to 1.141 Å, and the Ol-H bond is shortened to 1.140 Å. Then, the H atom from the NH2NO dehydrogenation transfers back and bonds with the O in NHNO, forming NHNOH with an energy barrier of 0.42 eV (TS2, Figure S5). NHNOH breaks its N-H bond with an energy barrier of 0.41 eV, leading to the formation of NNOH.
The related transition state (TS3, Figure S5) shows that the N-H bond and Ol-H bond are 1.270 Å and 1.260 Å, respectively. For NNOH, its N-O bond is so weak, which can break easily upon simple optimization, leading to the formation of N2 and a hydroxyl, and the similar result has also been found in our previous works. 1, 2 Finally, the formed hydroxyl overcomes a low barrier to a capture a H from Ol to form a H2O molecule (Ea = 0.21 eV, TS4, Figure S5), finishing the whole NH2NO conversion process. Overall, as seen from the energy profile in Figure S5, it can be found that the whole NH2NO S7 conversion into N2 and H2O is a strongly exothermic process and has low barriers, revealing the NH2NO conversion being very easy. Figure S4. Process of the gaseous NO attacking NH 2 on Fe site. Figure S5. Energy profile and the transition states for the NH 2 NO conversion by the hydrogen pushpull mechanism. TS1, TS2, TS3 and TS4 show the optimized transition states of the breaking of N- Accordingly, we resorted the Mars-van Krevelen pathway (Scheme S1, see the detailed energy profile in Figure 1f), 1 with a low barrier of 0.30 eV (TS1, Figure S6). On Ov, O2 adsorbs strongly (Eads = -2.27 eV, see Figure S6), for which two possible channels were examined to remove H atoms, i.e. Path A and Path B.

S9
In Path A, O2 on Ov ([Fe-O2]) dissociates with a barrier of 0.70 eV (TS2, Figure   S6  Scheme S1. Scheme for the possible pathways of H removal pathways on O l on Fer 2 O 3 (001). S12 Figure S6. Optimized transition states and important intermediates involved in the H removal process, which correspond to the energy states in Figure S6.

Note S4. Kinetic Details
According to the De Donder relation 4 , the net rate for elementary step i in terms of the forward rate constant, ki, the coverage of the reactant on active sites, θ(j), and the reversibility, Zi, can be written as where Zi = ∏θ(j) vij /Keq,i, which approaches zero as step i becomes irreversible and approach unity as step becomes in quasi-equilibrium. In order to distinguish the relative importance of each elementary step in the reaction mechanism, i.e. identifying which transition state really controls the net rate, the "degree of rate control" was used here, 5 where the partial derivative is taken by holding the standard state Gibbs free energy of all other transition states for step j ≠ i and all intermediate m constant, which is the same as holding the rate constants, kj, and the equilibrium constant, Kj, content (j ≠ i). Here, keeping Ki,eq constant means that ki+ and ki-must be changed together, whose ratio remains constant. Changing the Gibbs free energy of the transition state of step i while nothing else is changed can determine the influence of step i on the overall reaction rate in whole mechanism. The value of XRC,i for step i is larger, the influence of this step i S14 on the overall reaction rate, ri, is bigger.
To study the importance of an intermediate's stability (thermodynamics) in an overall complex mechanism, the degree of thermodynamic rate control XTRC,n of intermediate n was defined. According to Campbell's report, 6 XTRC,n could be written as: in which the partial derivative is taken holding the standard-state Gibbs free-energy constant of all other intermediates m≠ n (G 0 m≠n) and Gibbs free energy of all transition states i constant (G 0,TS n). Here R is the universal gas constant and T is the absolute temperature. XTRC,n is dimensionless, which describes the relative increase in the reaction rate of per decrease the standard-state free energy for intermediate n when other species' energies hold constant.
Here, we used the collision theory 7 to estimate the barriers (Ea) of gas-phase molecule adsorption process, as well as the barrier of the gas-phase NO coupling with the surface NH2* species. Therefore, according to the transition state theory and collision theory, the reaction rate on a per site basis can be written as: where kB, h, T, Pi and mi are Boltzmann constant, Planck constant, reaction temperature, pressure and the mass of gas molecule, respectively. And, A is the area of the atom which is described as A =πr 2 , in which r is the VDW radius of the atom. Here, we have assumed that the gas behaves ideally, and Si(T), the sticking coefficient, is approximated as 1. Hence we could derive an equation about Ea: In our microkinetic simulation, the experimental condition for NH3-SCR on Fe2O3, PNH3 = 5.00×10 -4 atm, PNO = 5.00×10 -4 atm, PO2 = 0.03 atm, PN2 = 0.8 atm and PH2O = 0.05 atm.

Note S5. Kinetic analysis of NH 3 -SCR on the pristine Fe 2 O 3 with only Fe 3+ sites
To investigate the importance of the each elementary step in the feasible NH3-SCR pathway on the pristine Fe2O3 catalyst with only Fe 3+ site, the reversibility and degree of rate control (XRT,i) of each elementary step was calculated. From Table S1, one can see that the coupling step of NH2 and NO into NH2NO ( [NH2-Fe-Ol] + NO(g) ⇆ [NH2NO-Fe-Ol]) has a largest XRT (about 6.65×10 -1 ), and is extremely irreversible (Z4 = 4.17×10 -11 ), indicating this step is the critical rate-limiting step. From its rate equation , is a key factor influencing the reaction rate. However, θ([NH2- is small, only 6.51×10 -12 (Table S2), which limits the NH3-SCR rate on the pristine Fe2O3 significantly. Besides, as shown by XRT,i in Table S1, we can find that the adsorption of O2 on the oxygen vacancy (Ov) has a relatively large XRT,i of about 3.35×10 -1 , meaning this step could be the second important step for NH3-SCR on the pristine Fe2O3. The difficult O2 adsorption step could lead to the low coverage of O2 on Ov (only 6.60×10 -16 ), inhibiting the following H removal process to some extent.
Therefore, increasing the NH2 and O2 coverages on Fe2O3 to contribute the NH2NO formation and H removal processes could be effective methods to improve the catalytic activity of Fe2O3 for NH3-SCR. S16 Table S1. Kinetic data, k + r i , Z i , for each elementary reaction step in NH 3 -SCR over the pristine α-Fe 2 O 3 (001) at 600 K.
S t e p i Clean Fe2O3(110)

Note S6. Activity trend of NH 3 -SCR on Fe 2 O 3 as a function of reaction temperature
As show in Figure 3b,  this essentially requires to activate the lattice oxygen, which could be achieved by introducing the more reducible metallic sites.
Driven by the increased temperature, the MvK pathway to remove H species on the catalyst surface is gradually promoted ( Figure S9), reducing the H accumulation on Ol. Accordingly, the activity curve rises significantly with the increase of temperature.
As temperature increases to middle-high one of about 590 K, the activity curve reaches the maximum point, implying the optimal catalytic activity at this time. It is noteworthy that this theoretical optimal temperature predicted is in agreement with the optimum experimental temperature range (~600 K) for NH3-SCR on Fe2O3-based catalysts. From the coverage curves (Figure 3c), it can be found that as the temperature increases, θ(Fe 2+ ) (or θ(Fe 3+ )) decreases (or increases) quickly, and around this optimal temperature (590     As temperature increases, the lattice oxygen on Fe2O3 could be activated for NH3 dissociation and become catalytically active; however, at this time, due to the low Evac of MnO2, its lattice oxygen is very easy to leach out and yields abundant oxygen vacancies on MnO2, which are difficult to be supplied by O2 for its low adsorption energy (-0.50 eV) and high entropy at high temperature (1.28 eV at 600 K), 1 thus MnO2 could exhibit a poor activity for NH3-SCR at high temperature. Therefore, MnO2-based oxides are good basic materials for NH3-SCR at low temperatures, and Fe2O3 prefers to work at a relatively high temperature.