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21 May 2026

Mechanistic Insights into the Formation of Hydrogen Cyanide on Cu-SSZ-13 Zeolites During Ammonia-Assisted Selective Catalytic Reduction in the Presence of Formaldehyde: A Perspective from Ab Initio Energetic Span Modelling

,
,
and
1
Junior Professorship of Multi-Scale Modeling of Heterogenous Catalysis in Energy Systems, The Integrated Fuel & Chemical Science Center, Rheinisch-Westfälische Technische Hochschule Aachen, Schinkelstraße 8, 52062 Aachen, Germany
2
National Engineering Laboratory for VOCs Pollution Control Technology and Equipment, Guangzhou 510006, China
3
Guangdong Provincial Key Laboratory of Atmospheric Environment and Pollution Control, School of Environment and Energy, South China University of Technology, Guangzhou 510006, China
*
Author to whom correspondence should be addressed.
Catalysts2026, 16(5), 484;https://doi.org/10.3390/catal16050484
This article belongs to the Special Issue Advanced Catalytic Technologies for NOx Abatement and Environmental Sustainability
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Abstract

The emission of hydrogen cyanide (HCN) from formaldehyde (CH2O) during ammonia-assisted selective catalytic reduction (NH3-SCR) remains a critical challenge for aftertreatment of bio-hybrid fuel combustion exhaust. The mechanistic details of HCN formation are still poorly understood, especially on widely deployed commercial catalysts like Cu-SSZ-13. In this work, we employed density functional theory calculations in combination with the Energetic Span Model to elucidate HCN formation pathways from CH2O in the presence of NO2 and H2O over Cu-SSZ-13. The results revealed the HCN formation pathway with intermediate methylene imine as the dominant one under typical reaction conditions. These findings resonate very well with reports of hexamethylenetetramine (HMT) formation during NH3-SCR with CH2O, for which methylene imine is a critical intermediate. Turnover frequency (TOF) estimations highlighted the strong influence of NO2 and H2O: higher NO2 concentrations promoted CO selectivity and suppressed HCN by oxidizing CH2O to HCOOH, while lower H2O enhanced HCN formation. These findings establish a detailed mechanistic framework for HCN emission on Cu-SSZ-13 and suggest that controlling NO2/NOx ratios and water content can mitigate HCN formation during NH3-SCR.

1. Introduction

Bio-hybrid fuels derived from biomass and renewable electricity are promising candidates to replace traditional fossil-based fuels in combustion processes for cleaner and more sustainable power generation. However, their combustion leads to the emission of many harmful gases, including nitrogen oxides (NOx), CO, and soot, all of which require after-treatment [1]. A standard technology to reduce NOx emissions is selective catalytic reduction (SCR) [2]. Commercially, SCR using NH3 as reducing agent has been implemented with catalyst materials ranging from Cu-exchanged zeolites [3] to titania-supported vanadium-tungsten oxides [4]. The overall NH3-SCR mechanism includes the Standard-SCR, Fast-SCR, and NO2-SCR pathways, wherein the NO2/NOx ratio is a key factor determining the dominant pathway [3,4]. Over the last decade, the detailed mechanism of NH3-SCR has been extensively investigated for both zeolite- and vanadium-based catalysts [5,6,7,8]. The ideal case involves an equimolar amount of NO and NO2 for Fast-SCR, whereas Standard-SCR follows a similar reaction mechanism to Fast-SCR, with an additional NO oxidation step [5,8,9].
In addition to soot, CO, and NOx, the combustion of bio-hybrid fuels also produces other species in significant amounts, such as formaldehyde (CH2O) [1,10,11,12]. Multiple studies investigating the effect of CH2O in the exhaust gas stream during NH3-SCR have reported the formation of hydrogen cyanide (HCN), a well-known hazardous chemical [13,14,15,16,17,18]. Several mechanistic pathways for HCN formation have been proposed, along with various factors that influence this process [1].
Zengel et al. [14] performed NH3-SCR experiments on various catalysts for NOx removal in the presence of CH2O under standard SCR conditions. They reported higher HCN emissions at 500 °C compared to 250 °C over V2O5/WO3-TiO2 (VWTi), Fe-ZSM-5, and Fe-BEA, whereas the opposite trend was observed over Cu-SSZ-13 [14]. Elsener and Nuguid et al. [13,17] conducted similar experiments over VWTi to investigate the effect of water on HCN emissions and found that increasing the water concentration decreases the selectivity of CH2O conversion toward HCN while increasing selectivity toward COx. They also reported that when formic acid (HCOOH) was used instead of CH2O, HCN formation occurred only in the absence of water. Ngo et al. [18] reported small amounts of adsorbed hexamethylenetetramine (HMT, (CH2)6N4) below 250 °C. They further performed experiments over VWTi by bypassing CH2O and instead using formamide (HCONH2) and still observed HCN formation. These results suggest the role of HCONH2 as a key intermediate.
Unlike VWTi, the formation of HCN on Cu-SSZ-13 catalysts is less explored and less well understood [14,15,19]. NH3-SCR experiments with CH2O on Cu-SSZ-13 conducted by Schönberger et al. [15] reported that HCN emissions can be tuned by the NO2/NOx ratio in the temperature range of 200–250 °C. They also observed the presence of adsorbed HMT and smaller amounts of HCONH2. They suggested that HMT is a key intermediate for HCN formation, and that the introduction of NO2 can intercept these intermediates, thereby decreasing HCN formation. While HCN formation had previously been reported to occur only at lower temperatures [14,15], Barth et al. [19] recently demonstrated that HCN emissions in NH3-SCR with CH2O can also occur at relatively higher temperatures (>350 °C), depending on the Si/Al ratio and Cu loading. Based on current evidence, HCN formation occurs differently over VWTi and Cu-SSZ-13 in terms of temperature dependence and key intermediates. Thus, the mechanistic understanding of HCN formation on VWTi does not directly apply to Cu-SSZ-13 catalysts. In addition, an increase in the NO2/NOx ratio has been shown to reduce HCN emissions [15], which could provide an opportunity to tune engine-out conditions for low NOx as well as HCN emissions.
While some adsorbed species (HCONH2 and HMT) common to VWTi have also been detected on Cu-SSZ-13 [15], their relevance as either spectator species or rate-determining intermediates remains unclear. Therefore, it is important to elucidate the HCN formation mechanism on Cu-SSZ-13 catalysts and to investigate the role of the NO2/NOx ratio. Elsener et al. [13] proposed three pathways for HCN formation over VWTi, as well as its decomposition to CO (Figure 1). These pathways provide a useful starting point for further investigations to determine their relative contributions over Cu-SSZ-13.
Figure 1. Reaction pathways for HCN and CO formation from formaldehyde, with NO2 as the oxidizing agent [13].
In this work, we performed quantum chemical simulations using a cluster model of the Cu-SSZ-13 catalyst to investigate various HCN formation pathways during NH3-SCR in the presence of CH2O. A primary objective of this study is to determine whether Cu sites catalyze HCN formation compared to a simple gas-phase reaction. Another objective is to understand the role of NO2, which we assume, without any loss of generality, to be the primary oxidant in the intermediate steps. The free energies and activation barriers for the various pathways were calculated and subsequently employed to estimate overall turnover frequencies (TOFs) using the Energetic Span Model [20,21]. Comparison of these TOFs provides detailed insights into the factors affecting HCN formation, such as NO2 concentration, H2O concentration, and the oxidation state and coordination of the Cu sites. Our results elucidate the important role of H2O in HCN formation and partially capture the effect of high NO2 content in decreasing HCN emissions.

2. Results

Figure 2 shows the free energy diagram of HCN pathway P-1 (CH2O > NH2CH2OH > CH2NH > HCN), which is described schematically in Figure 1 and in mechanistic detail in the Supporting Information (SI). Figure 2a presents the reactions in the gas phase, while Figure 2b (2c) shows the corresponding catalyzed reactions on Z2-1 (Z-1) sites, starting from NH3 adsorption and ending with HCN desorption. Z2-1 represents the Cu2+ site with two Al atoms and one adsorbed NH3, Z2-2 represents the Cu2+ site with two Al atoms and two adsorbed NH3, whereas Z-1 represents the Cu+ site with one Al atom and one adsorbed NH3. Without loss of generality, the oxidation steps in all pathways are assumed to proceed via NO2. In the mechanism proposed here, the oxidation of CH2NH to HCN involves an initial H abstraction leading to the formation of HONO, followed by a second H abstraction resulting in the release of H2O and NO. It should be noted that there is substantial experimental evidence supporting HONO as an intermediate species in NH3-SCR [6,22].
Figure 2. Free energy diagram (at 473 K) for HCN formation via pathway P-1 CH2O > NH2CH2OH > CH2NH > HCN, (a) in the gas phase, (b) on Z2-1 sites, (c) on Z-1 sites. Atom colors: Cu, yellow; H, white; O, red; C, brown; N, gray.
Comparing our results with the 0 K energies reported in the literature [23] (in parentheses), the enthalpic reaction barriers in the gas phase are TS1 [CH2O > NH2CH2OH] = 1.34 (1.43) eV, and TS2 [NH2CH2OH > CH2NH] = 2.33 (2.43) eV. The small differences of ~0.1 eV likely arise from the use of the M06-2X functional with the 6-311++G(3df,3pd) basis set for geometry optimization, followed by single-point energy calculations at the CCSD(T)/6-311++G(3df,3pd) level in the literature [23]. Despite employing a relatively less computationally demanding exchange-correlation functional in this work, similar values are obtained.
As shown in Figure 2a for the gas phase reaction, I1 [NH3 + CH2O] is the TDI and T2 [NH2CH2OH*] is the TDTS. For the catalyzed reaction on Z2-1, however, I2 [*NH3 + CH2O] is the TDI and T4 [*CH2N…HONO] is the TDTS (Figure 2b). Similarly, on Z-1, I2 [*NH3 + CH2O] is the TDI and T4 [*CH2N…HONO] is the TDTS (Figure 2c). It can be seen that the energy span (i.e., GTDTS-GTDI) is 2.51 eV for the gas-phase reaction, compared to 2.28 eV on Z2-1 and 1.93 eV on Z-1 for the catalyzed reactions. Clearly, catalysis affects not only the reaction barriers and energy spans but also the identities of the TDIs and TDTSs. In the gas phase, the dehydration of [NH2CH2OH*] limits the TOF of the overall reaction, whereas for the catalyzed reaction on Z2-1 and Z-1, NH2CH2OH dehydration is comparably faster, and CH2NH oxidation becomes the TOF-determining transition state. This provides the first theoretical indication that HCN formation via pathway P-1 can indeed be catalyzed on both Z2-1 and Z-1 sites.
Next, to estimate the reaction rate in terms of the TOF, the effect of the species concentrations was considered. Within the energetic span approximation, only the concentrations of species that enter or exit the reaction cycle between the TDI and TDTS need to be taken into account. For the gas-phase reaction, NH3 and CH2O enter the reaction cycle, while no species exit the cycle. In contrast, for the catalyzed reaction on Z2-1, Z2-2, and Z-1, CH2O and NO2 enter the reaction cycle, while H2O exits between the TDI and TDTS.
The TOFs for this HCN formation pathway, accounting for species concentrations in the gas phase and on the Z2-1 and Z-1 sites, can be expressed by Equations (1) and (2), respectively.
T O F g 1 = k B T h e − ∆ G k B T ∏ N H 3 [ C H 2 O ]
T O F Z 2 1 = T O F Z 1 = k B T h e − ∆ G k B T ∏ C H 2 O [ N O 2 ] [ H 2 O ]
TOF estimation is highly sensitive to the calculated free energies and activation barriers due to the exponential dependence. The B3LYP/DEF2-SVP level of theory was employed in this study to achieve convergence in barrier calculations within a reasonable computational time. However, this approach is prone to systematic errors, as shown by comparison with the more accurate DLPNO-CCSD(T) level of theory in Figure S1. Consequently, our calculations may overestimate the binding energies (i.e., more negative adsorption energies) of molecules on Cu sites and may therefore systematically underestimate the TOFs. For this reason, we report relative TOF values, taking the lowest TOF as the reference (Table 1). The estimated relative TOFs of the reaction cycles increase from 2.95 × 106 in the gas phase to 8.52 × 108 on the Z2-1 and 3.56 × 1012 on the Z-1 catalyst model. These relative TOFs further confirm that the reaction is catalyzed. It is also evident that the oxidation state of Cu has a significant effect, with Cu in the +1 state (Z-1) catalyzing the reaction approximately 103 times faster than in the +2 state.
Table 1. TDI, TDTS, energy span, important species and relative TOF results of different pathways and active sites.
Following the same methodology as described above, we performed calculations for all other pathways and catalyst models. Pathways P-2 and P-3 both involve the key intermediate HCONH2, which has been reported in several NH3-SCR studies on HCN formation [13,14,15,17,18]. In line with previous computational studies [24,25], we modeled the decomposition of formamide (HCONH2) via an additional intermediate step involving NHCHOH (HCONH2 > NHCHOH > HCN), with H2O acting as a catalyst. The detailed mechanisms are provided in the SI.
Comparing our results with literature [24,25], the enthalpic reaction barrier for HCONH2 decomposition to HCN in the gas phase, with one H2O molecule acting as a catalyst, is 2.44 (2.42 [25], 2.46 [24]) eV. These literature results were obtained using B3LYP/6-31++G(d,p) calculations [25] and MP2/aug-cc-pVTZ optimizations followed by CCSD(T)/CBS single-point calculations [24]. Despite the use of different levels of theory, our results show good agreement with the reported values. For the same reaction over catalysts, no direct literature values were found. However, the free energy barrier reported over silica is 2.13–2.27 eV [26], which is comparable to our value of 2.27 eV on the Z2-1 catalyst. Finally, our calculated gas-phase reaction barrier for the HCOOH decomposition process catalyzed by H2O is 1.94 eV, which differs from literature values of 2.09 [27] and 2.14 [28] eV. This discrepancy likely arises from the use of the def2-SVP basis set in our calculations, as opposed to the 6-311G(d,p) basis set used in the referenced studies.
The free energy diagrams of HCN formation via pathways P-2 (CH2O > NH2CH2OH > HCONH2 > HCN) and P-3 (CH2O > HCOOH > HCONH2 > HCN) are shown in Figure 3 and Figure 4, respectively. The TDIs, TDTSs, energy spans and relative TOFs of all three pathways in the gas phase and over the two catalyst models are summarized in Table 1. As shown in Table 1, even for the same reaction pathway, different catalyst models exhibit different TDI and TDTS, and consequently, different relative TOFs.
Figure 3. Free energy diagram (at 473 K) for HCN formation via pathway P-2 CH2O > NH2CH2OH > HCONH2 > HCN, (a) in the gas phase, (b) on Z2-1 sites, and (c) on Z-1 sites. Atom colors: Cu, yellow; H, white; O, red; C, brown; N, gray.
Figure 4. Free energy diagram (at 473 K) for HCN formation via pathway P-3 CH2O > HCOOH > HCONH2 > HCN, (a) in the gas phase, (b) on Z2-1 sites, and (c) on Z-1 sites. Atom colors: Cu, yellow; H, white; O, red; C, brown; N, gray.
Figure 3 (Table 1) shows that HCN formation along P-2 has an energy span of 2.58 eV, which increases to 3.11 eV and 3.05 eV on the Z2-1 and Z-1 sites, respectively. Correspondingly, the relative TOF in the gas phase along P-2 is 9.98 × 106, which decreases to 2.40 × 101 and 6.92 × 101 on the Z2-1 and Z-1 sites, respectively. These estimates indicate that the gas-phase P-2 pathway is preferred over the catalyzed P-2 pathway.
Figure 4 (Table 1) shows that the energy span of 3.48 eV for P-3 in the gas phase changes to 3.60 eV and 3.19 eV on the Z2-1 and Z-1 sites, respectively. The relative TOF of 1 in the gas phase increases to 3.47 × 103 and 6.62 × 107 on Z2-1 and Z-1, respectively. Notably, although the energy span for Z2-1 is not lower than that of the gas phase, the relative TOF on Z2-1 is significantly higher. These estimates highlight the importance of including concentration effects in relative TOF calculations. Furthermore, both Z2-1 and Z-1 exhibit higher relative TOFs along P-3 compared to the gas phase.
The results in Table 1 show that, irrespective of the catalyst model, the relative TOFs for the catalyzed pathways follow the trend P-1 > P-3 > P-2. From a mechanistic perspective, the lower relative TOFs for P-2 and P-3 can be attributed to the high relative stability of the TDIs, namely HCONH2 (P-2) and HCOOH (P-3). For P-2, on the Z2-1 (Z-1) site, adsorbed HCONH2 exhibits a significantly lower free energy of −3.03 eV (−3.11 eV) relative to the initial state, as shown in Figure 3b (3c). Similarly, for P-3, on the Z2-1 (Z-1) site, HCOOH has a low free energy of −3.43 eV (−3.01 eV) relative to the initial state, as shown in Figure 4b (4c). These calculations help explain, at least in part, why formamide and formic acid are routinely detected in experiments using diffuse reflectance infrared Fourier transform (DRIFT) spectroscopy [14,15,17].
Next, we consider P-CO, a competing pathway to HCN formation starting from CH2O (CH2O > HCOOH > CO). The P-CO involves formaldehyde oxidation to formic acid, followed by formic acid decomposition to CO and H2O. The detailed mechanism is provided in the SI. In this work, all formic acid decomposition reactions were modeled with H2O acting as a catalyst. In the gas phase at 0 K, formic acid decomposition without H2O as a catalyst has an energy barrier of 3.03 eV, whereas in the presence of H2O, the barrier decreases to 2.15 eV (Figure 5a). Experimental studies report that although formic acid is abundant during NH3-SCR with CH2O, HCN formation from formic acid occurs only in the absence of water [13,17]. This observation can be rationalized by the fact that formic acid decomposition to CO is significantly more favorable in the presence of water, as demonstrated by our calculations. The effect of water concentration is revisited in the following sections.
Figure 5. Free energy diagram (at 473 K) for the CO formation pathway CH2O > HCOOH > CO, (a) in the gas phase, (b) on Z2-1 sites, (c) on Z-1 sites. Atom colors: Cu, yellow; H, white; O, red; C, brown; N, gray.
The free energy diagrams of P-CO are shown in Figure 5. For this pathway, the TDI and TDTS are I1 [CH2O + NO2] and T1 [CH2O…NO2] in the gas phase; I4[*HCOOH + H2O] and T1[*CH2O…NO2] on Z2-1, and I5[*HCOOH + H2O] and T3[*HCOOH…H2O] on Z-1. As shown in Figure 5a, the gas-phase reaction has an energy span of 2.44 eV, whereas over the Z2-1 and Z-1 sites (Figure 5b,c), the energy spans decrease to 1.97 eV and 2.33 eV, respectively. Accordingly, the relative TOFs increase from 3.87 × 104 in the gas phase to 1.39 × 1018 and 6.77 × 1017 on the Z2-1 and Z-1 sites, respectively. From a mechanistic perspective, the CH2O oxidation barrier of 2.44eV in the gas phase is significantly reduced to 1.42eV (Z2-1) and 1.36 eV (Z-1) on the catalysts, enabling a much faster reaction.
Lastly, the Z2-2 catalyst model shows results similar to those of the Z2-1 model, as the relative TOFs for all three HCN pathways are within one order of magnitude, as shown in Table 1. The free energy diagrams for the Z2-2 catalyst model are provided in Figures S2–S5 in the SI. Compared to the Z2-1 model, however, the relative TOF of the CO pathway on the Z2-2 model decreases from 1.39 × 1018 to 5.31 × 1014. This indicates that the presence of an additional co-adsorbed NH3 molecule on Cu2+ sites has a limited effect on HCN formation pathways but significantly slows down CO formation.
We also considered the dynamically solvated and mobile Cu(NH3)2 moiety as an active site for HCN formation and compared it with the equivalent tethered Z2-2 model. It was found that the binding energies of all intermediates on the Cu(NH3)2 moiety (Table S1) are more negative than those on the Z2-2 model. Under the assumption that the transition states remain unchanged, the relative TOFs for the mobile Cu(NH3)2 and Z2-2 models are compared in Table S2. As can be clearly observed, irrespective of the pathway, the reaction rates are several orders of magnitude lower on the solvated and mobile Cu(NH3)2 moiety. This behavior is consistent with Sabatier’s principle.

3. Discussion

A comparative summary of the relative TOFs for all pathways is shown in the bar plot in Figure 6. As expected, TOF estimation is highly sensitive to the calculated free energies and activation barriers due to the exponential dependence. Nevertheless, based on reasonable assumptions regarding the uncertainty in energy calculations, several clear conclusions can still be drawn from their comparison.
Figure 6. Relative TOFs of different pathways in the gas phase and over different active sites at a temperature of 473 K.
Assuming a typical DFT error of ~10 kcal/mol in the estimation of energies and barriers, this corresponds to a difference in relative TOFs of approximately 104 at 473 K, according to Equation (3). Therefore, relative TOFs that differ by ~104 can still be compared with a reasonable degree of confidence.
Another source of uncertainty arises from the fact that only pathways involving intermediates and reaction steps proposed in experimental studies (Figure 1) [13] were considered. If alternative pathways involving other intermediates (e.g., HMT) or more complex reaction mechanisms (e.g., on the [(NH3)4Cu2O2]2+ complex [29]) are operative, the relative TOFs may differ. An additional source of uncertainty is that the current analysis treats all pathways independently, whereas in reality, the reactions occur simultaneously. However, given the large differences in relative TOFs between certain pathways, even if the absolute values change with the inclusion of additional intermediates or parallel pathways, the mechanistic roles of NO2 and H2O, as well as their influence on product selectivity, are expected to remain valid.
First, considering only the gas-phase reactions (blue bars), pathway P-2 exhibits the highest relative TOF. It is higher than CO formation (via P-CO), although not beyond the estimated error margin (~104). Therefore, in the absence of a catalyst, it is difficult to conclusively determine whether HCN formation from CH2O dominates over its decomposition to CO.
When the effect of catalysis is considered, the results indicate that HCN formation on the Z-1 site is significantly faster along pathways P-1 and P-3 compared to the gas phase. Furthermore, catalyzed CH2O decomposition to CO is substantially faster than even the most favorable HCN formation pathways, irrespective of the catalyst model.
These observations help rationalize the experimental findings. Schoeneberger et al. [15] reported that increasing the NO2 concentration decreases HCN emissions. Table 2 details the effect of NO2 on HCN emissions, comparing experimental emission data [15] with calculated relative TOF values. Across the NO2/NOx ratio range of 0–100%, pathway P-CO consistently exhibits significantly higher relative TOFs than P-1 for HCN formation (by ~106). Although the relative TOF for HCN formation also increases with increasing NO2 concentration, the simultaneous increase in CH2O decomposition to CO occurs at much higher relative TOFs, thereby reducing the availability of CH2O for HCN formation. This implies that HCN formation is strongly suppressed with increasing NO2. In addition, as shown in Table 1, both gas-phase and catalyzed (on Z2-1) P-CO pathways are directly proportional to the NO2 concentration. These findings are in good qualitative agreement with the reported experimental data [15].
Table 2. Comparison of the experimental data [15] and calculated rel. TOF values of the NO2 effect on CO and HCN formation during NH3-SCR on Cu-SSZ-13 catalysts.
It is important to reiterate that NO2 is assumed to be the oxidizing agent in all pathways considered, rather than O2 or atomic O, and it is a key intermediate in both Fast- and Standard-SCR. The presence of alternative oxidants may alter the relative TOFs, which will be addressed in future work. However, (i) O-O bond activation on mononuclear Cu sites in SSZ-13 involves additional steps with NO participation, (ii) it incurs a relatively high energy penalty at low temperatures (e.g., 1.45 eV at 0 K [30], 1.08 eV at 473 K [8], 0.89 eV at ~623 K [7]), and (iii) previous studies indicate that NO- and O2-assisted NH3 activation via NO2 intermediates is more favorable than direct O2-assisted activation on Cu-SSZ-13 [31], supporting the validity of our assumption.
Although the exact relative TOF values may change if oxidants other than NO2 are considered, the trends, particularly the effect of H2O concentration, are expected to remain similar. Finally, a comparative analysis of all results highlights a strong influence of the Cu oxidation state and a relatively minor effect of additional NH3 coordination on the Z2-1 site.
Our finding that pathway P-1 is the most dominant route for HCN formation is consistent with experimental observations of HMT formation, which has been reported during NH3-SCR with CH2O over Cu-SSZ-13 zeolites [15] and other catalysts [18,32]. This is because the P-1 intermediates, NH2CH2OH and CH2NH, are known precursors for HMT formation at low temperatures, as demonstrated in both experiments [33] and simulations [34].
Next, we examine the important effect of H2O on HCN formation, which has been studied in detail over VWTi catalysts [13,17]. A comparison of experimental data with our relative TOF analysis is presented in Table 3. When the H2O concentration increases from 0 to 2.5%, the selectivity toward CO rises rapidly from 2% to 23%, as reported experimentally [13]. This trend can be correlated with a substantial increase in the relative TOF (~104) or in the P-CO/P-1 TOF ratio (~105) predicted by our calculations. These results are again in good qualitative agreement with the reported experimental data [13].
Table 3. Comparison of the experimental data [13] and rel. TOF values on the H2O effect on CO and HCN formation during NH3-SCR on V2O5/WO3-TiO2 catalysts.
According to our reaction models, the relative TOFs of all catalyzed pathways across all catalyst models are influenced by the H2O concentration. Furthermore, with the exception of P-CO on Z-1, all relative TOFs are inversely proportional to [H2O]. Notably, the relative TOFs for P-3 exhibit a stronger inverse dependence on [H2O] than those for P-1 and P-2, as shown in Table 1.
To investigate the effect of a dry atmosphere, we considered [H2O] = 1 ppm and re-evaluated the TDIs and TDTSs for all pathways. Within the Energetic Span Model, incorporating species concentrations can alter the identities of the TDI and TDTS. Table S3 summarizes the TDIs, TDTSs, energy spans, relevant species entering or exiting the cycle, and the resulting relative TOFs for different pathways and active sites. At 1 ppm H2O, the TDI-TDTS combinations change for all pathways except P-2. These changes in TDIs and TDTSs lead to corresponding variations in energy spans and, consequently, in the relative TOFs.
A summary of relative TOF enhancement by water (TOFw), comparing conditions with and without water ([H2O] = 80,000 ppm and 1 ppm), is shown in Figure 7. The ratios of TOFs in the presence of water (80,000 ppm H2O) to those in its absence (1 ppm H2O) are presented in the bar plot. Positive and negative values indicate that increasing H2O concentration increases or decreases the TOF, respectively.
Figure 7. Relative TOFw indicating the effect of water on different pathways at 473 K. Results are expressed as the ratio of TOF with water (80,000 ppm H2O) to TOF without water (1 ppm H2O). Positive and negative values indicate that increasing the H2O concentration increases or decreases the relative TOF, respectively.
The TOFw values for HCN formation are generally negative across all pathways and catalyst models. In the gas phase, however, these values fall within the previously discussed error margin. On the catalyst models, the TOFw for HCN formation is significantly reduced (<10−4) across multiple pathways and catalyst configurations. In contrast, the TOFw values for CH2O decomposition to CO on the catalyst models are positive.
Taken together, these trends clearly indicate that increasing H2O concentration inhibits HCN formation while promoting decomposition to CO. Similar behavior has been reported for NH3-SCR with CH2O over V2O5/WO3-TiO2 catalysts [13]. Notably, pathways involving HCOOH as an intermediate (P-3 and P-CO) are strongly influenced by H2O concentration. These findings are consistent with experimental observations over V2O5/WO3-TiO2, where HCN formation from HCOOH—an important intermediate in P-CO—occurs only in the absence of water [13,17]. Furthermore, in the absence of H2O, pathway P-3 becomes as dominant as P-1 for HCN formation.

4. Methods

4.1. Catalyst Model

The Cu atom located in the six-membered (6M) ring, as shown in Figure 8a–c, where Al atoms replace the original Si atoms, represents one of the most widely used models of the active site in Cu-SSZ-13 catalysts in the literature [35]. The full periodic unit cell model of Cu-SSZ-13 (Figure 8d) contains 109 atoms (36 T sites + Cu). Reaction barrier calculations on this model are computationally demanding and difficult to converge, particularly when using the Nudged Elastic Band (NEB) method [36].
Figure 8. Cu-SSZ-13 zeolite catalyst model: (a) Cu-tethered 6-membered ring with 2 Al and 1 adsorbed NH3 (Z2-1), (b) Cu-tethered 6-membered ring with 2 Al and 2 adsorbed NH3 (Z2-2), (c) Cu-tethered 6-membered ring with 1 Al and 1 adsorbed NH3 (Z-1), (d) periodic model showing the unit cell, (e) cluster model, (f) cluster model with fixed atoms.
To enable the application of advanced NEB techniques, such as free-end NEB and zoom NEB, which are only implemented in specific software packages, we employed a cluster model of the catalyst (Figure 8e). Atoms were removed from the periodic structure such that only the active site 6M ring, along with all connected 4M and 8M rings, was retained. To maintain charge balance, the outermost O atoms bonded to Si were terminated with H atoms. This cluster model effectively includes at least four bonds extending from the Cu active site.
This approach is comparable to the low-error cluster model (MAE < 5 kJ/mol) reported by Goncalves et al. [37], which includes up to five bonds from the active site. The difference in the number of bonds used for cluster termination arises from the different Cu site locations considered, as their study focused on a Cu atom in a 4M ring rather than the more stable 6M ring examined here. In this work, we considered Cu in both the Cu+ (Z-1) state, obtained by substituting one Si atom with Al (Figure 8c), and the Cu2+ (Z2-1) state obtained by substituting two diametrically opposite Si atoms with Al (Figure 8a). To prevent spurious structural distortions, the atoms in the upper and lower “layers” were fixed to mimic their positions in the periodic lattice, as shown in Figure 8f.
In the temperature range of 200–550 °C and at an NH3 concentration of 750 ppm—conditions consistent with a recent experimental study on NH3-SCR with CH2O [15]—singly and doubly NH2-coordinated Cu species have been identified as the most stable [38]. Accordingly, three starting models were considered in this work: Z-1 (corresponding to Cu+), and Z2-1 and Z2-2 (corresponding to Cu2+). The model Z-2 (Cu+) was not considered, as it is stable only within a narrow low-temperature range [38].
A commonly used catalyst model for NH3-SCR on Cu-SSZ-13 zeolites in the literature [6,38,39] is the dynamically solvated and mobile Cu(NH3)2 moiety. This model is briefly considered in our analysis; however, detailed simulations were not performed due to the very strong binding of reaction intermediates.

4.2. Computational Details

The cluster model described above was used to perform free energy and NEB calculations using ORCA (v5.0.4) [40]. All calculations were carried out using the B3LYP functional [41,42,43,44] with the Valence double-zeta basis set (def2-SVP) [45,46] and DFT-D3 dispersion correction [47]. NEB calculations were considered converged when the maximum force was below 10−3 Hartree/Bohr and the root-mean-square (RMS) force was below 3 × 10−4 Hartree/Bohr. Single-point free energy calculations were considered converged when the change in energy was less than 10−6 Hartree.
For each mechanistic step, the reactant and product structures were first optimized to their minimum-energy configurations. Using these optimized structures as endpoints, nudged elastic band (NEB) calculations were performed to locate the transition states (TS). The NEB-TS approach was employed, wherein the saddle point was first approximated using the climbing-image NEB (CI-NEB) method and subsequently refined using the Eigenvector Following method [48].
Thermochemical frequency calculations were then carried out to determine the free energies of all states, including reactants, intermediates, products, and transition states. These calculations were performed with all zeolite framework atoms fixed. This approximation is justified by previous literature on zeolite modeling [49], which shows that the entropic and zero-point vibrational energy contributions of distant framework atoms largely cancel when comparing relative reaction barriers; therefore, analyses based on relative TOFs and free energy spans remain reliable without requiring full-cluster Hessians. A temperature of 473 K (200 °C) was used for the entropy contribution to the Gibbs free energy. Although this temperature is relatively low for NH3-SCR, HCN emissions over Cu-SSZ-13 have been observed experimentally under such conditions [14,15,19]. While some studies report increased HCN emissions at higher temperatures (250–350 °C) [14,19], others show that HCN emissions decrease to nearly zero above 250 °C [15]. These discrepancies may arise from differences in Cu loading and Si/Al ratios resulting from varying synthesis procedures. A standard pressure of 1 atm was used during the free energy calculations.
The final reaction pathways presented in Section 2 connect all identified states and summarize the relevant intermediates (local minima) and transition states (saddle points). The cluster model employed in this work remains relatively large (106 atoms for the Z2Cu framework, excluding gas-phase or adsorbed species). To address convergence challenges in NEB calculations, free-end NEB and zoom-NEB methods were applied. These approaches improved the resolution of images near the saddle point along the reaction path, facilitating better convergence.

4.3. Kinetics Modelling

To compare reaction rates of different pathways, the turnover frequency (TOF) was calculated (Equation (3)) using the Energetic Span Model [20,21]. In Equation (3), k B is the Boltzmann constant, h is the Planck’s constant, R is the ideal gas constant, T is the temperature, and Δ G r is the overall free energy change in the reaction cycle. T i and I j denote the free energies of transition states and intermediates, respectively. The term δ G i , j represents the relative free energy between these two states: if T i appears after I j , then δ G i , j = Δ G r ; if T i appears before I j , then δ G i , j = 0 (Equation (4)).
T O F = k B T h e − ∆ G r k B T − 1 ∑ i , j = 1 N e T i − I j + δ G i , j k B T
δ G i , j = ∆ G r       i f       T i   a f t e r   I j 0           i f       T i   b e f o r e   I j
In most cases, the denominator of Equation (4) is dominated by a single term, which corresponds to the turnover frequency determining intermediate (TDI) and turnover frequency determining transition state (TDTS). Accordingly, Equation (4) can be simplified to Equation (5), where ΔG represents the energy span defined by the TDI and TDTS, as given in Equation (6).
T O F = k B T h e − ∆ G k B T
∆ G = G T D T S − G T D I                                 i f   T D T S   a f t e r   T D I G T D T S − G T D I + ∆ G r           i f   T D T S   b e f o r e   T D I
While the scalar influence of species concentration on TOFs is important, it is less significant than the energy span, which affects TOFs exponentially [21]. Nevertheless, concentration effects are included in the TOF calculations according to Equation (7). The full expressions are provided in the SI (Equations (S1)–(S3)).
The identification of the TDI and TDTS follows directly from the Energetic Span Model. In the absence of concentration effects, all intermediates and transition states along a given catalytic cycle are considered, and the TDTS–TDI pair is defined as the combination that maximizes the energetic span ( ∆ G ), i.e., the free energy difference between a transition state and a preceding intermediate (accounting for the cyclic nature of the catalytic pathway). This pair determines the rate-limiting segment of the cycle and thus the TOF.
When concentration effects are included, the free energies of intermediates and transition states are adjusted according to the chemical potentials of reactants and products (as described in Equations (6) and (7)) [21]. The TDI and TDTS are then identified as the intermediate–transition state pair that yields the maximum effective free energy span under these conditions. In practice, this involves evaluating all possible TDTS–TDI combinations along the catalytic cycle and selecting the pair that provides the largest contribution to the denominator of the TOF expression.
This procedure is applied consistently to all pathways analyzed in this work (Figure 2, Figure 3, Figure 4 and Figure 5). Notably, the identified TDI and TDTS do not necessarily correspond to the lowest-energy intermediate or highest-energy transition state, but rather to the states that maximize the (concentration-dependent) energetic span and thus control the overall TOF.
T O F = k B T h e − ∆ G k B T ∏ R P f r o m   T D I   t o   T D T S
The species concentration values assumed in this work are listed in Table 4. These values were taken from recently reported experimental measurements on NH3-SCR with CH2O [15]. For species that were not detectable, a concentration of 1 ppm was assigned instead of 0 to avoid undefined or infinite TOF values. Water is known to have a significant impact on HCN formation [13]. To assess this effect, two H2O concentrations were considered: the experimentally measured value of 8% (80,000 ppm), representative of real exhaust aftertreatment conditions [15], and 1 ppm to approximate dry conditions.
Table 4. Species concentration used for TOF calculation.

5. Conclusions

This work investigated the various reaction pathways of CH2O in NH3-SCR over Cu-SSZ-13 zeolite catalyst using an ab initio kinetics approach. The free energies of different CH2O reaction pathways were further analyzed using the Energetic Span Model to compare their relative TOFs, while accounting for species concentration effects. The results show that HCN formation from CH2O is catalyzed, with the pathway involving methylene imine (CH2NH) being the most favorable under typical reaction conditions. A key role of the Cu sites is to lower the energy barrier for the decomposition of aminomethanol (NH2CH2OH) to CH2NH. These findings are consistent with reports of hexamethylenetetramine (HMT) formation during NH3-SCR with CH2O, for which methylene imine is a critical intermediate [33,34].
Cu in +1 oxidation state is found to be a more effective catalyst for HCN formation than Cu in the +2 state. In the presence of NO2 as an oxidant, CH2O conversion to CO via formic acid formation is significantly faster than any of the HCN formation pathways, consistent with experimentally observed decreases in HCN emissions at higher NO2 concentrations. Mechanistically, this behavior is attributed to the rapid reaction between CH2O and NO2 over Cu sites.
This work also examines the dependence of HCN versus CO selectivity on H2O concentration and finds that CO selectivity decreases with decreasing H2O concentration. From a mechanistic perspective, this trend arises because H2O plays a catalytic role in HCOOH decomposition. In the absence of H2O, the preferred HCN formation pathway is predicted to shift, as lower H2O concentrations facilitate dehydration steps.
While this work explores the effects of NO2 and H2O on HCN formation from CH2O over Cu-SSZ-13, several questions remain to be addressed for a more comprehensive understanding. In particular, the subsequent reactivity of the produced HCN with other components of the gas mixture warrants further investigation. For example, HCN has been reported to react directly with NO2 over Ba-Y type FAU zeolites [50], but this process has not yet been studied at a fundamental level for Cu-SSZ-13.
Furthermore, recent studies highlight the role of the ZCuOH site—an important intermediate in the NH3-SCR mechanism—as particularly active for HCN conversion [19]. Another study reports the hydrolysis of HCN over Fe-BEA catalysts [32]. A detailed atomistic investigation of the subsequent reactions of HCN over Cu-SSZ-13 under NH3-SCR conditions is the focus of our ongoing work.

Supplementary Materials

The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/catal16050484/s1, Figure S1: Comparison of the adsorption energy with different calculation methods; Figures S2–S5: Free energy diagram of reaction pathways over Z2-2; Table S1: Comparison of the adsorption energy between Z2-2 model with Cu in the 6-membered ring and the solvated mobile Cu; Table S2: Comparison of relative TOFs between Z2-2 model with Cu in the 6-membered ring and the solvated mobile Cu; Table S3: TDI, TDTS, energy span, important species and relative TOF results of different pathways and active sites, [H2O] = 1 ppm; Equations (S1)–(S3): TOF calculation with species concentration; Equations (S4)–(S17): Mechanistic details of reaction pathways.

Author Contributions

The manuscript was written through contributions of all authors. S.T. primarily performed the calculations and developed the analysis routines. N.L. contributed by performing part of the DFT calculations and analysis. P.C. and A.K. devised the research plan and supervised the project. A.K. acquired research funding. All authors have read and agreed to the published version of the manuscript.

Funding

The authors gratefully acknowledge funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy—Cluster of Excellence 2186/2 “The Integrated Fuel & Chemical Science Center”—ID: 390919832.

Data Availability Statement

Data for this article, including nudged elastic band trajectories, optimized intermediates, and transition states are available at Science Data Bank at https://doi.org/10.57760/sciencedb.32232.

Acknowledgments

The authors gratefully acknowledge the computing time provided to them at the NHR Center NHR4CES at TU Darmstadt (project number p0021065). This is funded by the Federal Ministry of Research, Technology and Space, and the state governments participating on the basis of the resolutions of the GWK for national high-performance computing at universities (www.nhr-verein.de/unsere-partner (accessed on 1 November 2023)). Part of the computations were also performed with computing resources granted by RWTH Aachen University under project rwth1467.

Conflicts of Interest

The authors declare no conflicts of interest.

Abbreviations

The following abbreviations are used in this manuscript:
NOxNitrogen oxides
TOFTurnover frequency
HMTHexamethylenetetramine
NH3-SCRAmmonia-assisted selective catalytic reduction
VWTiV2O5/WO3-TiO2
TDITurnover frequency determining intermediate
TDTSTurnover frequency determining transition state
Z-1Cu+ site with one Al and one adsorbed NH3
Z-2Cu+ site with one Al and two adsorbed NH3
Z2-1Cu2+ site with two Al and one adsorbed NH3
Z2-2Cu2+ site with two Al and two adsorbed NH3

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