A Theoretical Study of NH2 Radical Reactions with Propane and Its Kinetic Implications in NH3-Propane Blends’ Oxidation

The reaction of NH2 radicals with C3H8 is crucial for understanding the combustion behavior of NH3/C3H8 blends. In this study, we investigated the temperature dependence of the rate coefficients for the hydrogen abstraction reactions of C3H8 by NH2 radicals using high-level theoretical approaches. The potential energy surface was constructed at the CCSD(T)/cc-pV(T, Q)//M06-2X/aug-cc-pVTZ level of theory, and the rate coefficients were computed using conventional transition state theory, incorporating the corrections for quantum tunneling and hindered internal rotors (HIR). The computed rate coefficients showed a strong curvature in the Arrhenius behavior, capturing the experimental literature data well at low temperatures. However, at T > 1500 K, the theory severely overpredicted the experimental data. The available theoretical studies did not align with the experiment at high temperatures, and the possible reasons for this discrepancy are discussed. At 300 K, the reaction of NH2 with C3H8 predominantly occurs at the secondary C-H site, which accounts for approximately 95% of the total reaction flux. However, the hydrogen abstraction reaction at the primary C-H site becomes the dominant reaction above 1700 K. A composite kinetic model was built, which incorporated the computed rate coefficients for NH2 + C3H8 reactions. The importance of NH2 + C3H8 reactions in predicting the combustion behavior of NH3/C3H8 blends was demonstrated by kinetic modeling.


Introduction
Ammonia has recently gained worldwide attention as a future energy carrier, with the potential to combat global warming by decarbonizing the energy sectors. However, the direct use of ammonia as an energy source has several limitations, such as low laminar flame speed, high auto-ignition temperature, high heat of vaporization, narrow flammability limits (16-25% by volume in air), and high NO x emissions [1]. Some researchers have explored the direct application of neat ammonia in internal combustion engines [2,3]. However, due to its poor combustion characteristics, a dual-fuel approach has been widely suggested to achieve the desired physical and chemical properties of ammonia for its use in combustion devices [4][5][6][7][8][9][10][11][12][13].
Over the past few years, we have been exploring the combustion behavior of ammonia blended with reactive oxygenated fuels like dimethyl ether (DME) [10], diethyl ether (DEE) [8,12], dimethoxymethane (DMM) [7], methanol (CH 3 OH), and ethanol (C 2 H 5 OH) [14]. It is well-known that co-firing NH 3 with these reactive fuels increases the system's complexity. The fundamental understanding of the interaction chemistry between the carbon and nitrogen families is still in its infancy. It makes the accurate modeling of the combustion behavior of NH 3 dual-fuel combustion far more complex. Recently, we studied the combustion behavior of the NH 3 /DEE blend over a wide range of experimental conditions [8,12]. Our findings revealed that the kinetic model can only accurately capture the low-temperature oxidation data by including cross-reactions between the carbon and nitrogen families. Our recent work on NH 3 /CH 3 OH/C 2 H 5 OH [14] led us to a similar conclusion. Therefore, the cross-chemistry between carbon and nitrogen chemistry is of utmost importance for accurately modeling NH 3 dual-fuel combustion. Unfortunately, there is limited availability of experimental and theoretical studies targeting the cross-reactions between nitrogen and carbon species.
Only a limited number of studies exploring the combustion behavior of NH 3 blended with higher hydrocarbons beyond methane exist in the literature. Liquefied petroleum gas (LPG) can also be a good candidate for enhancing the combustion behavior of ammonia. LPG is a mixture of hydrocarbon gases, specifically propane and butane, with a small quantity of olefins. Since propane (C 3 H 8 ) is a major component of LPG [15], it can serve as a suitable surrogate fuel for LPG. In a recent study, Wang et al. [16] measured the laminar flame speed characteristics of various NH 3 /C 3 H 8 /air blends at an equivalence ratio (φ) of 0.6-1.4, a pressure of 1-5 bar and a temperature of 298 K. They used NH 3 /C 3 H 8 blends with mole ratios of 20%, 50%, and 80% of C 3 H 8 . The authors observed a significant enhancement of the laminar flame speed of NH 3 by adding C 3 H 8 . Further, they also tested five different kinetic models from the literature to predict the laminar flame speeds of NH 3 /C 3 H 8 blends. They found significant differences in the performance of these kinetic models. In another study, Wang et al. [17] reached a similar conclusion after investigating the blending effects of C 1 -C 4 n-alkanes in promoting the combustion characteristics of ammonia.
Similarly, Chen et al. [18] performed an experimental and kinetic modeling study on various NH 3 /C 1 -C 3 alkanes/air flames. They investigated the effect of ozone addition on enhancing the laminar burning velocity of NH 3 and NH 3 /C 1 -C 3 alkane blends. They observed a significant increase in the laminar flame speed of NH 3 by the addition of the hydrocarbons flames; however, 5000 ppm of ozone addition in the oxidizer stream did not significantly enhance the flame speed compared to the NH 3 /C 1 -C 3 alkane blends. The kinetic models used by Wang et al. [16] and Chen et al. [18] to predict the laminar flame speed experimental trends omitted the cross-chemistry of the species derived from NH 3 and C 3 H 8 . These models are not tested at low temperatures due to a lack of experimental data; however, one expects these models to fail as they do not contain the nitrogen and carbon cross-chemistry. Such cross-chemistry can be crucial for accurately predicting the combustion behavior of NH 3 /hydrocarbon blends. Therefore, having accurate knowledge of NH 2 radicals reactions with C 3 H 8 is critical to understand the oxidation behavior of NH 3 /C 3 H 8 blends.
Several studies have been conducted in characterizing hydrogen abstraction reactions of C 3 H 8 by NH 2 radicals, experimentally [19][20][21][22] and theoretically [23][24][25]. The experimentally measured rate coefficients showed a strong curvature in the Arrhenius behavior. Such Arrhenius behavior is nicely captured by the theoretical predictions of Mebel and Lin [23] and Siddique et al. [25]. The theoretical predictions are within a factor of~2 of the experimental data below 1080 K. An earlier report of the theoretical rate coefficients work from Siddique et al. [24] showed more significant deviations from the experimental data. Lowering the G2M barrier heights of NH 2 + C 3 H 8 reactions by 0.5 kcal, Mebel and Lin [23] obtained a better match with the experimental data in the 300-520 K temperature range [k(theory) = (0.94 − 1.25) k (experiment)]. Their G2M barrier heights were significantly higher than those of Siddique et al. [25] at the CBS-QB3 level of theory (8.4 vs. 7.1 and 11.1 vs. 9.2 kcal/mol for secondary and primary C-H sites of C 3 H 8 , respectively). This clearly indicates that the energetics of the reaction of NH 2 with C 3 H 8 show quantum method dependence. Interestingly, the theoretical predictions of the rate coefficients by Mebel and Lin [23] and Siddique et al. [25] severely overpredict the only available high-temperature shock tube data by Hennig and Wagner [19]. In the worst-case scenario, the mismatch is as high as a factor of 4.2. This warrants high-level theoretical work to resolve the existing discrepancy of the NH 2 + C 3 H 8 reaction.
The objective of this work is several-fold: (i) map out the potential surface energy using a high-level quantum method, e.g., CCSD(T)/cc-pV(T, Q)//M06-2X/aug-cc-pVTZ level of theory; (ii) handle the kinetics of NH 2 radicals reactions with C 3 H 8 appropriately, ensuring accurate rate coefficients and aiming to resolve the existing discrepancy in the literature; (iii) build a composite kinetic model incorporating the crucial cross-reactions between the nitrogen and carbon families; (iv) validate the kinetic model using available experimental literature data for neat C 3 H 8 , neat NH 3 , and various blends of NH 3 /C 3 H 8 across a wide range of conditions; (v) as mentioned earlier, no literature data is available for the low-T oxidation kinetics of NH 3 /C 3 H 8 blends. Therefore, we will employ our kinetic model to predict the low-T combustion behavior of NH 3 /C 3 H 8 blends, such as ignition delay times. This will provide deeper insights into the role of cross-reactions between the nitrogen and carbon families, particularly their significance at low temperatures in influencing the fundamental combustion characteristics of NH 3 /hydrocarbon blends.

Computational Methods
Similar to our earlier work on NH 2 + CH 3 OH/C 2 H 5 OH reactions [14], we optimized the geometry of all the stationary points for the NH 2 + C 3 H 8 reaction at the M06-2X//augcc-pVTZ level of theory. Our choice of the M06-2X level of theory is based on several earlier studies that reported the best suitability of the M06-2X//aug-cc-pVTZ level of theory for geometry optimizations, frequency calculations, and accurate energetics of many chemical systems [14,[26][27][28][29][30][31][32]. We characterized the identity of each stationary point in the potential energy surface (PES) of the NH 2 + C 3 H 8 reaction through normal model analysis. We used a scaling factor of 0.971 to correct the harmonic vibrational frequencies obtained at the M06-2X//aug-cc-pVTZ level of theory [33]. The correction factor compensates for the deviation between the experimental and theoretical values of the vibrational frequencies.
Scaled vibrational frequencies yielded zero-point corrected vibrational energies (ZPVE), eventually leading to zero-point corrected electronic energies. Additionally, at the same level of theory, we performed the IRC calculations [34,35] to map out the transition state, connecting the reactants and products appropriately. We used the lowest-lying conformers for the species involved to construct the potential energy surface and the subsequent kinetic analysis. We listed the optimized geometry and molecular parameters of all the stationary points in Tables S1 and S2 of the Supplementary Information (SI). For all the electronic structure calculations, we employed Gaussian09 Software [36].
For accurate energetic description, we utilized the computationally expensive coupledcluster method with single and double excitations, including the perturbative treatment of triple excitations, CCSD(T) [37][38][39]. Notably, the CCSD(T) method represents the gold standard in quantum chemistry. We performed CCSD(T) calculations using Dunning's correlation-consistent triple-ζ(cc-pVTZ) and quadruple-ζ(cc-pVQZ) basis sets and then extrapolated these energies to achieve CCSD(T) energies at the complete basis set (CBS) limit. We employed Halkier's scheme [40] of two-point extrapolation. Thus, we can refer to the extrapolated CCSD(T) energies as CCSD(T)/cc-pV(T, Q)//M06-2X/aug-cc-pVTZ level of theory. All the values of our T1 diagnostics are less than 0.02, indicating that the single reference electronic structure method employed here is adequate for an accurate energetic description of the reaction of NH 2 radicals with propane. As we will demonstrate later, the reactions of NH 2 radicals with C 3 H 8 involve simple hydrogen abstractions occurring through distinct transition states (TS). Therefore, with reasonable accuracy, one can calculate the rate coefficients for the hydrogen abstraction reaction of C 3 H 8 by NH 2 using conventional transition state theory (TST). We employed multi-species multi-channel (MSMC) code [41,42] to compute the high-pressure limiting rate coefficients (k ∞ (T)). We used one-dimensional (1D) asymmetrical potential for Eckart's tunneling treatment. For accurate partition functions, we treated the low vibrational modes of C 3 H 8, and the transition states as hindered internal rotors (HIR). Table S1 of Supplementary Information identifies these low vibrational modes as internal rotors in bold. Our previous work [43,44] describes the procedure of the HIR correction of the partition function. For HIR correction, we scanned the hindered rotor potential V(θ) as a function of the torsional angle (θ) along the single bonds (C-C bonds for C 3 H 8 and C-C and C-N bonds of the TSs) using the M06-2X/cc-pVDZ level of theory via a relaxed potential energy scan with a step size of 10 • in θ. We have compiled the hindered rotor potential V(θ) scans in Figure S1 of Supplementary Information.

Kinetic Modeling
Recently, we have developed a detailed kinetic model to accurately predict the oxidation kinetics of diethyl ether (DEE) and ammonia (NH 3 ) blends and their interaction with NO x chemistry [12]. Over the past five years, we have progressively built and validated this hierarchical kinetic model for C 1 -C 4 fuels, incorporating various experimental data across a wide range of conditions. Our kinetic model demonstrated satisfactory performance in capturing the oxidation behavior of C 1 -C 2 hydrocarbon/oxygenated fuels and their interaction with NO x . Note that our kinetic model embodied the detailed NO x chemistry from our previous works [45,46], which showed remarkable performance for NO x modeling during the oxidation of hydrocarbons/oxygenates and their blends with NH 3 . However, our previous model [12] did not contain C 3 hydrocarbons; particularly, propene (C 3 H 6 ) and propane (C 3 H 8 ) chemistry need to be included.
In this work, we have added the subset of C 3 hydrocarbon chemistry (i.e., C 3 H 6 and C 3 H 8 ), aiming to characterize the combustion behavior of NH 3 /C 3 H 8 blends reasonably. We adopted the subset of C 3 hydrocarbon chemistry from the experimental and modeling work of Burke et al. [47,48], who validated C 3 H 6 oxidation chemistry over a wide range of conditions. However, the authors did not test the predictive capabilities of their model for C 3 H 8 oxidation. In this study, we first validated the kinetic model for neat NH 3 and C 3 H 8 experimental data before validating against the NH 3 /C 3 H 8 blend. Our past experiences in modeling NH 3 -hydrocarbons/oxygenates duel-fuel combustion [7][8][9]12] indicated the importance of cross-reactions between the carbon and nitrogen families. Such interaction chemistry is critical to accurately model the combustion behavior of NH 3 and hydrocarbons or oxygenated fuel blends. Therefore, our current model incorporates the reactions of NH 2 radical with C 3 H 8 , which is one of the most critical reactions between the carbon and nitrogen families during the oxidation of NH 3 /C 3 H 8 blends. As discussed earlier, we employed CCSD(T)/cc-pV(T, Q)//M06-2X/aug-cc-pVTZ level of theory combined with the transition state theory to compute the temperature dependence of the reaction rate coefficients of reaction (1) and reaction (2).

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The hydrogen abstraction reactions of C 3 H 8 by NO 2 can also yield NC 3 H 7 and IC 3 H 7 radicals (Reactions (3)-(6)). The rate constants for these reactions are adopted from the theoretical work of Chai and Goldsmith [49].  (6) NO is abundant under the combustion environment of NH 3 and its blend with other fuels, verified by our previous study [12]. The reaction of NO with the peroxyl radicals (RO 2 ) can significantly alter the low-temperature combustion behavior of the fuel [46]. Therefore, the reactions of NO with the peroxy radicals pertinent to NC 3 H 7 O 2 and IC 3 H 7 O play a critical role in accurately predicting the low-T oxidation kinetics of NH 3 /C 3 H 8 blends. Unfortunately, no experimental and/or theoretical data for these reactions are available in the literature. Consequently, we took CH 3 O 2 + NO [50] as a reaction analogy to estimate the rate coefficients for Reactions (7) and (8) Figure 1 illustrates the potential energy surface (PES) of the reaction of NH 2 radicals with C 3 H 8 . The reaction energetics were obtained using the CCSD(T)/cc-pV(T, Q)//M06-2X/aug-cc-pVTZ level of theory. As shown, the energy barrier (∆E 0 = ) for the hydrogen abstraction reaction at the primary carbon site (-CH 3 ), reaction (1), was 10.5 kcal/mol, which was 2.2 kcal/mol higher than that at the secondary carbon site (-CH 2 ), i.e., reaction (2). The barrier heights for the reactions of NH 2 radicals at the primary and secondary carbon sites of C 3 H 8 nicely correlate with the reaction enthalpies (∆ rxn, 0K H • ) and bond dissociation energies according to the Evans-Polanyi principle. It is evident that reaction (1) was less exothermic than reaction (2) and occurred via a tighter transition state (∆E 0 = of TS1 = 10.5 kcal/mol and imaginary frequency (ν i ) = 1701 cm − Figure 1). Interestingly, we located the product complexes PC1 and PC2 for reaction (1) and reaction (2), respectively. However, these reaction complexes exhibited little binding energy (<1 kcal/mol), indicating their energy proximity to the corresponding products. Previous theoretical studies by Siddique et al. [24] and Mebel and Lin [23] did not indicate the existence of such complexes for the NH 2 + n-alkanes/branched alkanes reactions. The reported values of the barrier heights in these works depict a significant discrepancy for both reactions, indicating the energetics of NH 2 + C 3 H 8 reactions exhibit strong dependence on the ab initio methods. For example, Mebel and Lin [23] reported barrier heights ranging from 11.1-11.6 kcal/mol and 13.3-15.5 kcal/mol for reaction (1) at the G2M and CCSD(T) based approaches, respectively. For reaction (2), the barrier heights ranged from 8.4-8.6 kcal/mol (G2M-based approaches) and 9.7-12.9 kcal/mol (CCSD(T) method). Based on the G2M Energies 2023, 16, 5943 6 of 19 energetics, their computed values of the rate coefficients showed a reasonable agreement with the experimental values below 1100 K. However, at high temperatures (T > 1500 K), the theoretical rate coefficients significantly overestimated (by a factor of 2.6-4.1) the experimental rate coefficients. By adjusting the G2M barrier height by 0.5 kcal/mol, the authors found a better agreement at low temperatures while worsening the scenarios at high temperatures. Siddique et al. [24] reported significantly lower barrier heights, e.g., 9.2 and 7.1 kcal/mol, for Reactions (1) and (2) in the CBS-QB3 composite method, respectively. One can observe a similar trend for higher alkanes + NH 2 reactions. Siddique et al. [24] reported an overall mean unsigned deviation (MUD) of 2.3 kcal/mol for the barrier heights of NH 2 + selected alkanes (C 1 -C 4 ) reactions. Our values of the barrier heights at the CCSD(T)/cc-pV(T, Q)Z//M06-2X/aug-cc-pVTZ compare very well with those reported by Mebel and Lin [23] for the G2M methods within chemical accuracy (~1 kcal/mol). However, a larger deviation (~2 kcal/mol) was observed for the heat of reactions. Interestingly, we located the product complexes PC1 and PC2 for reaction (1) and reaction (2), respectively. However, these reaction complexes exhibited little binding energy (<1 kcal/mol), indicating their energy proximity to the corresponding products. Previous theoretical studies by Siddique et al. [24] and Mebel and Lin [23] did not indicate the existence of such complexes for the NH2 + n-alkanes/branched alkanes reactions. The reported values of the barrier heights in these works depict a significant discrepancy for both reactions, indicating the energetics of NH2 + C3H8 reactions exhibit strong dependence on the ab initio methods. For example, Mebel and Lin [23] reported barrier heights ranging from 11.1-11.6 kcal/mol and 13.3-15.5 kcal/mol for reaction (1) at the G2M and CCSD(T) based approaches, respectively. For reaction (2), the barrier heights ranged from 8.4-8.6 kcal/mol (G2M-based approaches) and 9.7-12.9 kcal/mol (CCSD(T) method). Based on the G2M energetics, their computed values of the rate coefficients showed a reasonable agreement with the experimental values below 1100 K. However, at high temperatures (T > 1500 K), the theoretical rate coefficients significantly overestimated (by a factor of 2.6-4.1) the experimental rate coefficients. By adjusting the G2M barrier height by 0.5 kcal/mol, the authors found a better agreement at low temperatures while worsening the scenarios at high temperatures. Siddique et al. [24] reported significantly lower barrier heights, e.g., 9.2 and 7.1 kcal/mol, for Reactions (1) and (2) in the CBS-QB3 composite method, respectively. One can observe a similar trend for higher alkanes + NH2 reactions. Siddique et al. [24] reported an overall mean unsigned deviation (MUD) of 2.3 kcal/mol for the barrier heights of NH2 + selected alkanes (C1-C4) reactions. Our values of the barrier

High-Pressure Limiting Rate Coefficients k ∞ (T)
The computed PES revealed that the reaction of NH 2 radicals with C 3 H 8 is a simple type of hydrogen abstraction reaction (see Figure 1). The post-reaction complexes (PCs) had no kinetic relevance due to the shallow nature of the well. Their energies were very close to those of the dissociated fragments, i.e., final products. One can expect that their pressure stabilization was extremely difficult, even at very high pressures. Therefore, we handled the kinetics of the NH 2 + C 3 H 8 reaction using the conventional transition state rate theory (TST) with explicit corrections of quantum tunneling and hindered internal rotors. Figure 2 displays our computed values for the temperature dependence of the high-pressure limiting rate coefficients (k ∞ (T)), whereas Figure 3a,b provide the individual rate coefficients for reactions (1) and (2), respectively. Table 1 further compiles the three-Arrhenius parameters obtained by fitting the computed rate coefficients over the 300-2000 K temperature range (see Table S3 for k ∞ (T)). Table 1. Fitted Arrhenius parameters, as given by k(T) = AT n exp(−E/T) over T = 300-2000 K. Arrhenius parameters (A and E) are in units of cm 3 molecule −1 s −1 and K, respectively. The fitting error is less than 2%. theory (TST) with explicit corrections of quantum tunneling and hindered internal rotors. Figure 2 displays our computed values for the temperature dependence of the highpressure limiting rate coefficients (k ∞ (T)), whereas Figure 3a,b provide the individual rate coefficients for reactions (1) and (2), respectively. Table 1 further compiles the three-Arrhenius parameters obtained by fitting the computed rate coefficients over the 300-2000 K temperature range (see Table S3 for k ∞ (T)).  ("Expt.", "Est." and "Calc." stand for "experimental", "estimated" and "calculated" studies, respectively). Figure 2 compares our computed rate coefficients with the available literature data. Our theory excellently captures the experimental trends of the temperature dependence of the rate coefficients, with the exception of the high-temperature experimental data reported by Hennig and Wagner [19]. At high temperatures, our theoretical predictions of the rate coefficients are ~2.6-4.5 higher than the measurements of Hennig and Wagner [19]. Mebel  ("Expt.", "Est." and "Calc." stand for "experimental", "estimated" and "calculated" studies, respectively). Figure 2 compares our computed rate coefficients with the available literature data. Our theory excellently captures the experimental trends of the temperature dependence of the rate coefficients, with the exception of the high-temperature experimental data reported by Hennig and Wagner [19]. At high temperatures, our theoretical predictions of the rate coefficients are~2.6-4.5 higher than the measurements of Hennig and Wagner [19]. Mebel and Lin [23] made a similar observation. As stated earlier, their theoretical predictions were 2.6-4.1 higher than the experimental values over the temperature range of 1500-1900 K. Along the same line, the theoretical rate coefficients reported by Siddique et al. [24,25] are significantly higher than the experimental data (see Figure 2). Noteworthy, our theoretical predictions of k ∞ (T) excellently agree with the recent theoretical works of Mebel and Lin [23] and Siddique et al. [25]. However, Siddique et al. [24] earlier reports of the rate coefficients (derived using the CBS-QB3 and TST methods) showed a more significant deviation from the experimental literature data (see Figure 2). For example, their reported values lie within a factor of 0.17-0.69 of the experimental value over the temperature range of 300-500 K, whereas their values are higher by a factor of 3.8-4.4 in the intermediate temperatures (T = 500 − 1000 K). In their subsequent work, Siddique et al. [25] recalculated the rate coefficients based on the CBS-QB3 energies from their earlier work, which showed an excellent agreement with our work, including the one from Mebel and Lin [23] (see Figure 2). Not only for the total rate coefficients but also the individual rate coefficients for Reactions (1) and (2), we observed an excellent agreement with the earlier theoretical reports from Mebel and Lin [23] and Siddique et al. [25] (see illustration in Figure 3a,b). Note that the green lines in Figures 2 and 3 represent the rate coefficients calculated by Mebel and Lin [23] with the adjustment of G2M barrier heights by 0.5 kcal/mole lower for both reactions, including Eckart tunneling correction. tions were 2.6-4.1 higher than the experimental values over the temperature range of 1500-1900 K. Along the same line, the theoretical rate coefficients reported by Siddique et al. [24,25] are significantly higher than the experimental data (see Figure 2). Noteworthy, our theoretical predictions of k ∞ (T) excellently agree with the recent theoretical works of Mebel and Lin [23] and Siddique et al. [25]. However, Siddique et al. [24] earlier reports of the rate coefficients (derived using the CBS-QB3 and TST methods) showed a more significant deviation from the experimental literature data (see Figure 2). For example, their reported values lie within a factor of 0.17-0.69 of the experimental value over the temperature range of 300-500 K, whereas their values are higher by a factor of 3.8-4.4 in the intermediate temperatures (T = 500 − 1000 K). In their subsequent work, Siddique et al. [25] recalculated the rate coefficients based on the CBS-QB3 energies from their earlier work, which showed an excellent agreement with our work, including the one from Mebel and Lin [23] (see Figure 2). Not only for the total rate coefficients but also the individual rate coefficients for Reactions (1) and (2), we observed an excellent agreement with the earlier theoretical reports from Mebel and Lin [23] and Siddique et al. [25] (see illustration in Figure 3a,b). Note that the green lines in Figures 2 and 3 represent the rate coefficients calculated by Mebel and Lin [23] with the adjustment of G2M barrier heights by 0.5 kcal/mole lower for both reactions, including Eckart tunneling correction. As shown in Figure 2, our theory remarkably predicts the experimental values of the rate coefficients reported by Demissy et al. [22] and Lesclaux et al. [21] at low temperatures (T = 300-520 K). For example, at 300 K, our value of the theoretical rate coefficient of 2.89 × 10 −17 cm 3 /molecule/s excellently matches the experimental value of 2.7 × 10 −17 cm 3 /molecule/s reported by Demissy et al. [22] and Lesclaux et al. [21]. This shows that quantum tunneling is important for predicting reliable rate coefficients at low temperatures. This is particularly true for the type of reactions being dealt with here. For such reactions, the light hydrogen atom between the two heavy moieties can easily penetrate the classically forbidden potential energy barrier, increasing the rate coefficients significantly at low temperatures. Therefore, tunneling is a quantum mechanical effect, and its correction depends upon several factors, e.g., potential barrier height, shape of the barrier, reduced mass of the system, and imaginary frequency of the transition state. Vandeputte et al. [52] theoretically studied the effect of hindered internal rotation and quantum tunneling on the rate coefficients of 21 hydrogen abstraction reactions by methyl radicals. The authors have nicely demonstrated the effect of quantum tunneling on the activation energy (E a and pre-exponential factor (A). Quantum tunneling has a pronounced effect on E a ; its effect on E a decreases with increasing temperature. At low temperatures, the tunneling correction has a significant impact on logA. As temperature increases, the effect of quantum tunneling on logA diminishes rapidly. At 300 K, we find that quantum tunneling increased the rate coefficients by 36.8 and 18.5 fold for Reactions (1) and (2), respectively. At 500 K, the quantum tunneling factor is ca. 3 for both reactions. Our calculations show large imaginary frequencies υ ‡ (TS1) = 1700.9 cm −1 and υ ‡ (TS2) = 1603 cm −1 corresponding to Reactions (1) and (2), respectively. The large imaginary frequency hints to a small barrier width of a reaction, resulting in pronounced quantum tunneling. Our observation of the large quantum tunneling correction is not surprising. Above 1500 K, the contribution of quantum tunneling to the predicted rate coefficients was insignificant (see Table S4). Quantum tunneling has a more pronounced effect on the rate coefficients than the hindered internal rotor (HIR) corrections at low temperatures. We find that HIR corrections had a subtle effect on the rate coefficients at low temperatures (see Figure S2 and Table S5 of Supplementary Information). For example, HIR correction increased the rate coefficients by a factor of~1.6 at 300 K. Above 1000 K, the rate coefficients could be reliably obtained with rigid rotor-harmonic oscillator (RRHO) approximation; i.e., RRHO and HIR treatment yields no difference in the calculated values of rate coefficient at high temperatures. Vandeputte et al. [52] illustrated how HIR treatment influences both E a and A factors. They showed that the change in A due to HIR treatment is more significant than that of E a . At low temperatures, our values of rate coefficients compare with the experimental data better than those of Mebel and Lin [23] (see Figure 2). Here, differences in the theoretical rate coefficients appeared to be originated from RRHO and HIR treatment of the low-frequency modes. Noteworthily, we appropriately treated some low-frequency modes as HIRs to calculate the partition functions accurately.

Reaction TS
There are a few important points to consider. First, the reaction of NH 2 radicals with C 3 H 8 shows a strong curvature in the Arrhenius behavior. Several factors cause such Arrhenius behavior: (i) strong quantum tunneling and HIR effects at low temperatures, as discussed above; (ii) the temperature dependence of the pre-exponential factor; (iii) the channel switching of the competing reactions, (1) and (2). The reaction of NH 2 radicals with C 3 H 8 goes exclusively via reaction (2) below ambient temperature (branching ratio of~95% at 300 K). In contrast, both reactions contributed equally at 1700 K. Beyond 1700 K, Reaction (1) took over (see Figure 4). Our predictions of the branching ratios nicely resonate with the theoretical predictions from Mebel and Lin [23] (see Figure 4) and Siddique et al. [25] (not shown in Figure 4). Second, our theoretical predictions of the rate coefficients, are like those of Mebel and Lin [23] (see Figure 4) and Siddique et al. [25], which nicely follow the experimental trends of the rate coefficients reported by Ehbrecht et al. [20] in the intermediate T-range (550 ≤ T/K ≤ 1073). The theory overpredicts the experimental kinetic data of Ehbrecht et al. [20] by a factor of~2 only at the high-temperature end. Third, as seen in Figure 2, all theories severely overpredict the only available high-T experimental data of Hennig and Wagner [19]. The rate coefficient estimates from Rozenberg and Voronkov [51] are far too low. The observed differences between the theoretical and Hennig and Wagner's experimental rate coefficients [19] at high temperatures urge a closer look.
Energies 2023, 16, x FOR PEER REVIEW 10 of 20 mental kinetic data of Ehbrecht et al. [20] by a factor of ~2 only at the high-temperature end. Third, as seen in Figure 2, all theories severely overpredict the only available high-T experimental data of Hennig and Wagner [19]. The rate coefficient estimates from Rozenberg and Voronkov [51] are far too low. The observed differences between the theoretical and Hennig and Wagner's experimental rate coefficients [19] at high temperatures urge a closer look. Surprisingly, and not only in the NH2 + C3H8 reaction, the theoretical and high-T shock tube data from Henning and Wagner [19] also show a large difference to NH2 + CH4/C2H6 reactions (see Mebel and Lin [23]). The theory significantly overpredicts experimentally measured rate coefficients by Henning and Wagner [19] for high temperatures of NH2 + C1-C3 alkane reactions. However, the theoretical predictions agree quite nicely with the experimental data of Wagner and co-workers in the intermediate T-range (T = 400-1080 K). This warrants a closer look into the high-T kinetic measurements of Hennig and Wagner [19]. The authors investigated the reactions of NH2 radicals with C1-C3 alkanes in the temperature range of 1500 K to 2100 K. Using a narrow line laser-absorption technique, and the authors monitored NH2 radicals at 597.375 nm behind incident shock waves. In their experiments, the authors observed an overwhelmingly large concentration of hydrocarbons (0.2-2.1%) compared to 15-80 ppm of N2H4 (NH2 radical precursor) so that the decay of NH2 radicals follows the first-order kinetics. They extracted the rate coefficients of the reactions of NH2 with alkanes from the pseudo-first-order approximation of NH2(t) decay profiles, assuming that the secondary chemistry is unimportant. We believe the secondary chemistry severely compromised their extracted rate coefficients. One can expect a significant loss of the hydrocarbon reactant in their experimental time scale of a few tens of microseconds. For example, we obtained a 1/e decay period (τ1/e) of ≈ 3 μs for the unimolecular decomposition of C3H8 at 1600 K (k(C3H8 → CH3 + C2H5) = 3.2 × 10 5 s −1 [53]). In such cases, one should obtain the rate coefficients through detailed kinetic modeling of the measured NH2(t) profiles. In addition, one can also argue that the measured NH2(t) profiles at 597.375 nm may have been obscured spectroscopically by interfering intermediate/product species resulting in the slowdown of NH2(t) decay profiles. However, we cannot confirm this claim of any other species interfering with the absorption of NH2 radicals at 597.37 nm. We believe additional experimental studies targeting the reactions of NH2 radicals with alkanes at high-T will help resolve the existing discrepancy. Surprisingly, and not only in the NH 2 + C 3 H 8 reaction, the theoretical and high-T shock tube data from Henning and Wagner [19] also show a large difference to NH 2 + CH 4 /C 2 H 6 reactions (see Mebel and Lin [23]). The theory significantly overpredicts experimentally measured rate coefficients by Henning and Wagner [19] for high temperatures of NH 2 + C 1 -C 3 alkane reactions. However, the theoretical predictions agree quite nicely with the experimental data of Wagner and co-workers in the intermediate T-range (T = 400-1080 K). This warrants a closer look into the high-T kinetic measurements of Hennig and Wagner [19]. The authors investigated the reactions of NH 2 radicals with C 1 -C 3 alkanes in the temperature range of 1500 K to 2100 K. Using a narrow line laser-absorption technique, and the authors monitored NH 2 radicals at 597.375 nm behind incident shock waves. In their experiments, the authors observed an overwhelmingly large concentration of hydrocarbons (0.2-2.1%) compared to 15-80 ppm of N 2 H 4 (NH 2 radical precursor) so that the decay of NH 2 radicals follows the first-order kinetics. They extracted the rate coefficients of the reactions of NH 2 with alkanes from the pseudo-first-order approximation of NH 2 (t) decay profiles, assuming that the secondary chemistry is unimportant. We believe the secondary chemistry severely compromised their extracted rate coefficients. One can expect a significant loss of the hydrocarbon reactant in their experimental time scale of a few tens of microseconds. For example, we obtained a 1/e decay period (τ 1/e ) of ≈ 3 µs for the unimolecular decomposition of C 3 H 8 at 1600 K (k(C 3 H 8 → CH 3 + C 2 H 5 ) = 3.2 × 10 5 s −1 [53]).
In such cases, one should obtain the rate coefficients through detailed kinetic modeling of the measured NH 2 (t) profiles. In addition, one can also argue that the measured NH 2 (t) profiles at 597.375 nm may have been obscured spectroscopically by interfering intermediate/product species resulting in the slowdown of NH 2 (t) decay profiles. However, we cannot confirm this claim of any other species interfering with the absorption of NH 2 radicals at 597.37 nm. We believe additional experimental studies targeting the reactions of NH 2 radicals with alkanes at high-T will help resolve the existing discrepancy.

Kinetic Modeling Implications
As discussed in Section 3, we have developed a composite kinetic model comprising C 3 hydrocarbons and NH 3 subset chemistry. The developed model has also accommodated essential cross-chemistry between nitrogen and carbon families. In particular, our model has incorporated new rate data for the critical cross-reactions between NH 2 radicals and C 3 H 8 obtained in this work using a high level of theory (see discussion above). By incorporating these critical updates of the reaction rate parameters, we will demonstrate the performance of our kinetic model against various experimental targets below. Figure 5 illustrates the predictive capability of our kinetic model against the available literature laminar flame speed (LFS) data for various NH 3 /C 3 H 8 /air blends at 1 bar and 298 K. In Figure 5, the symbols represent the experimental literature data from the recent works of Wang et al. [16] and Chen et al. [18]. The solid and dashed lines correspond to the model predictions from this work. The solid lines depict the modeling results of the complete kinetic mechanism, which includes the cross-reactions between C 3 H 8, and nitrogen chemistry discussed in Section 3. The dashed lines represent the modeling results without considering the cross-reactions between the nitrogen and carbon families. The solid and dashed lines overlap, revealing that the cross-chemistry between the nitrogen and carbon families has minimal influence on accurately predicting the LFS. These results indicate that cross-reactions do not govern the oxidation kinetics of NH 3 /hydrocarbon blends at high temperatures.

Ignition Delay Time (IDT)
To the best of our knowledge, there are no existing reports in the literature regarding the experimental data for ignition delay times (IDTs) of NH3/C3H8 blends. Therefore, our initial validation process involved confirming the accuracy of our kinetic model by comparing it with IDTs obtained for neat C3H8 and NH3. Validation of the kinetic model  [18] and Wang et al. [16], whereas the lines are the model predictions from this work, In Figure 5a, we demonstrate a remarkable performance of our kinetic model capturing the φ-dependence of the experimental LFS data for different NH 3 /C 3 H 8 blends. However, for neat C 3 H 8, we observed a little discrepancy. Our model slightly underpredicts the Chen et al. [18] LFS data for the equivalent ratios (φ) between 0.9 and 1. We further compared our model predictions against a large pool of the experimental literature data (see Figure S3 of Supplementary Information). The experimental data showed a large scatter around the stoichiometric C 3 H 8 /air mixtures. Overall, our model performed well, capturing the observed trends of the φ-dependence of most LFS experimental literature data for C 3 H 8 /air mixtures. Similarly, Figure 5b plots the LFS data as a function of C 3 H 8 content from 0-100% in the NH 3 /C 3 H 8 blend. We can observe that with an increase in the C 3 H 8 in a blend, LFS increases. For instance, LFS increased by a factor of 2 and 3, respectively, for 10% and 20% of C 3 H 8 compared to neat NH 3 at φ = 1.0 and 298 K. For 30% and 40% of C 3 H 8 , in the blends, the LFS increased only by a factor of 3.46 and 3.87, respectively. The blend had a steeper gradient of up to 20% of C 3 H 8 . The trend was somewhat linear beyond 20% of C 3 H 8 in the mixture. Such a trend indicates that the LFS shows high sensitivity at a low C 3 H 8 mole fraction compared to high C 3 H 8 content in the NH 3 /C 3 H 8 blends. The model-predicted adiabatic flame temperature and the maximum mole fraction of the key radicals (OH, H, and O) further justify the observed trends of the LFS data (see Figure S4 in Supplementary Information). With an increase in C 3 H 8 content, one can observe a more significant discrepancy between the experimental data of Chen et al. [18] and Wang et al. [16]. Our model shows a better agreement with the measurements of Wang et al. [16] for all NH 3 /C 3 H 8 blends (χ C3H8 = 0-100%, χ C3H8 = Further model validations are shown in Figures S5 and S6 for different conditions.

Ignition Delay Time (IDT)
To the best of our knowledge, there are no existing reports in the literature regarding the experimental data for ignition delay times (IDTs) of NH 3 /C 3 H 8 blends. Therefore, our initial validation process involved confirming the accuracy of our kinetic model by comparing it with IDTs obtained for neat C 3 H 8 and NH 3 . Validation of the kinetic model against the neat fuels is the only reliable approach in the absence of experimental data for the NH 3 /C 3 H 8 fuel blend. Subsequently, we conducted a numerical investigation to explore the IDT behavior of NH 3 /C 3 H 8 blends. Figure 6 displays the predictive capabilities of our kinetic model. The symbols represent experimental IDT data from Lam et al. [54] for C 3 H 8 /O 2 /Ar at φ = 0.5 and 6-60 atm ( Figure 6a) and NH 3 /O 2 /Ar at φ = 0.5 and 40 bar from He et al. [55] (Figure 6b). The lines are the model predictions from this work. As seen in Figure 6a, our model remarkably captured IDT's pressure and temperature dependence for neat C 3 H 8 . Likewise, our model effectively predicted the experimental IDT trend of pure NH 3 (see Figure 6b). We refer readers to our earlier works [10,12] for further model validations of neat ammonia at other conditions. Overall, our model performed remarkably well in capturing the IDT behavior of neat ammonia. However, it tended to overpredict the IDT of pure NH 3 at temperatures higher than 1100 K. At present, we do not want to optimize the kinetic model further to improve its predictive capabilities at high temperatures. However, our model remarkably captured the experimental literature data for the laminar flame speed ( Figures S5 and S6 in Supplementary Materials and Figure 5) of various NH 3 /C 3 H 8 blends. Note that laminar flame speed is driven by high-temperature chemistry. Figure 7 illustrates the effect of NH 2 + C 3 H 8 reactions in predicting the IDT behavior of NH 3 /C 3 H 8 /air blends. It shows a case example for 95%NH 3 /5%C 3 H 8 (Figure 7a,b) and 90%NH 3 /10%C 3 H 8 (Figure 7c) blends at 40 bar, φ = 1.0 and 0.5. In Figure 7a-c, solid black lines represent the model-predicted IDT for neat NH 3 . In contrast, the red solid and dashed lines show the IDT predictions, including and excluding NH 2 + C 3 H 8 reactions, respectively, in our kinetic model. Unlike the case in the laminar flame speed (see Figure 5), the low-temperature oxidation kinetics of NH 3 /C 3 H 8 blends were significantly affected by the cross-reaction of NH 2 with C 3 H 8 . This reaction largely influenced the model prediction by yielding shorter IDTs below 1250 K. Above 1250 K, the NH 2 + C 3 H 8 reactions had no significant influence on the model prediction. This observation aligns very well with the model predictions for the laminar flame speed (see Figure 5). The cross-reaction between the nitrogen and carbon families is critical in accurately predicting the combustion behavior of NH 3 /C 3 H 8 blends at low temperatures.  Figure 7 illustrates the effect of NH2 + C3H8 reactions in predicting the IDT behavior of NH3/C3H8/air blends. It shows a case example for 95%NH3/5%C3H8 (Figure 7a,b) and 90%NH3/10%C3H8 (Figure 7c) blends at 40 bar, ϕ = 1.0 and 0.5. In Figure 7a-c, solid black lines represent the model-predicted IDT for neat NH3. In contrast, the red solid and dashed lines show the IDT predictions, including and excluding NH2 + C3H8 reactions, respectively, in our kinetic model. Unlike the case in the laminar flame speed (see Figure  5), the low-temperature oxidation kinetics of NH3/C3H8 blends were significantly affected by the cross-reaction of NH2 with C3H8. This reaction largely influenced the model prediction by yielding shorter IDTs below 1250 K. Above 1250 K, the NH2 + C3H8 reactions had no significant influence on the model prediction. This observation aligns very well with the model predictions for the laminar flame speed (see Figure 5). The crossreaction between the nitrogen and carbon families is critical in accurately predicting the combustion behavior of NH3/C3H8 blends at low temperatures.
The IDT predictions for 95%NH3/5%C3H8 were three times shorter (~516 ms vs. 167 ms) with the inclusion of the NH2 + C3H8 reaction at ϕ = 1.0 and 800 K (see Figure 7a). At ϕ = 1.0 and around 1000 K, the IDTs were ~2.8 times shorter, which was about the same as that of the 95%NH3/5%C3H8 blend at ϕ = 0.5 and 800 K (see Figure 7b; the IDTs were shorter by a factor of 2.5 with the inclusion of the NH2 + C3H8 reaction). However, for the 90% NH3/10% C3H8 blend at ϕ = 1.0 and 800 K (see Figure 7c), including the NH2 + C3H8 reaction shortened the IDTs by only a factor of ~2. This indicates that the NH2 + C3H8 reaction significantly impacted the model predictions at low concentrations of C3H8 in the blend, and the sensitivity decreased with the increase of C3H8. This can be partly explained by the fact that with increasing C3H8 concentration, NH2 radicals become less available for reaction. Furthermore, the impact was less pronounced for lean conditions than stoichiometric conditions. Figure 8 displays the 16 top most sensitive reactions towards IDT at ϕ = 1.0, 800 K, and 40 bar. Positive sensitivity indicates that the reaction enhanced the system reactivity, while negative sensitivity implies the opposite. It is evident that the NH2 + C3H8 reactions were the second and fourth most sensitive reactions influencing the IDTs of model predictions. Interestingly, reaction (1) (NH2 + C3H8 = NC3H7 + NH3) enhanced the system reactivity by shortening the IDTs, whereas reaction (2) (NH2 + C3H8 = IC3H7 + NH3) inhibited it by prolonging the IDT behavior of NH3/C3H8 blends. The reactions of OH radicals with C3H8 exhibited similar behavior.
To obtain further insight into the kinetics, we performed the reaction flux analysis at 800 K, 40 bar and ϕ = 1.0 for 95% NH3/5%C3H8/air blend. Figure 9 shows the results for the major paths only. The reaction pathways indicated by the blue color highlight the interaction between nitrogen and carbon chemistry. As seen, C3H8 was mainly consumed The IDT predictions for 95%NH 3 /5%C 3 H 8 were three times shorter (~516 ms vs. 167 ms) with the inclusion of the NH 2 + C 3 H 8 reaction at φ = 1.0 and 800 K (see Figure 7a). At φ = 1.0 and around 1000 K, the IDTs were~2.8 times shorter, which was about the same as that of the 95%NH 3 /5%C 3 H 8 blend at φ = 0.5 and 800 K (see Figure 7b; the IDTs were shorter by a factor of 2.5 with the inclusion of the NH 2 + C 3 H 8 reaction). However, for the 90% NH 3 /10% C 3 H 8 blend at φ = 1.0 and 800 K (see Figure 7c), including the NH 2 + C 3 H 8 reaction shortened the IDTs by only a factor of~2. This indicates that the NH 2 + C 3 H 8 reaction significantly impacted the model predictions at low concentrations of C 3 H 8 in the blend, and the sensitivity decreased with the increase of C 3 H 8 . This can be partly explained by the fact that with increasing C 3 H 8 concentration, NH 2 radicals become less available for reaction. Furthermore, the impact was less pronounced for lean conditions than stoichiometric conditions. Figure 8 displays the 16 top most sensitive reactions towards IDT at φ = 1.0, 800 K, and 40 bar. Positive sensitivity indicates that the reaction enhanced the system reactivity, while negative sensitivity implies the opposite. It is evident that the NH 2 + C 3 H 8 reactions were the second and fourth most sensitive reactions influencing the IDTs of model predictions. Interestingly, reaction (1) (NH 2 + C 3 H 8 = NC 3 H 7 + NH 3 ) enhanced the system reactivity by shortening the IDTs, whereas reaction (2) (NH 2 + C 3 H 8 = IC 3 H 7 + NH 3 ) inhibited it by prolonging the IDT behavior of NH 3 /C 3 H 8 blends. The reactions of OH radicals with C 3 H 8 exhibited similar behavior.
To obtain further insight into the kinetics, we performed the reaction flux analysis at 800 K, 40 bar and φ = 1.0 for 95% NH 3 /5%C 3 H 8 /air blend. Figure 9 shows the results for the major paths only. The reaction pathways indicated by the blue color highlight the interaction between nitrogen and carbon chemistry. As seen, C 3 H 8 was mainly consumed by NH 2 Figure 10 plots the mole fraction time histories of some important species. These plots further reinforce the importance of cross-reactions influencing the reactivity of NH 3 -propane blend. As seen, the fuels (NH 3 (Figure 10a) and C 3 H 8 (Figure 10e)) were consumed earlier with the inclusion of cross-reactions. Both the OH (Figure 10b) and HO 2 (Figure 10f) radicals appeared early in the reaction system when cross-reactions were included. Interesting to note here is the evolution of NO (Figure 10d) and NO 2 (Figure 10h) species. NO 2 started to evolve at early reaction time, while NO did not appear until 160 ms. At~160 ms, NO 2 was readily consumed, forming NO. The NO↔NO 2 looping was mainly governed by the reactions indicated above.

Conclusions
We conducted a theoretical investigation of the reactions between NH2 radicals and C3H8 using a high-level ab initio method (CCSD(T)/cc-pV(T, Q)Z//M06-2X/aug-cc-pVTZ level of theory) as well as conventional transition state theory (TST) methods. We demonstrated the kinetic implications of the NH2 + C3H8 reaction in the combustion of NH3-C3H8 dual-fuel blends. Some of the key points are summarized below.
1. The energetics of the NH2 + C3H8 reaction show strong quantum method dependence.
Our quantum approach at the CCSD(T)/cc-pV(T, Q)Z//M06-2X/aug-cc-pVTZ level of theory yielded barrier heights of 10.5 and 8.3 kcal/mol for Reactions (1) and (2), respectively. These barrier height values closely match those of the G2M approaches reported by Mebel and Lin [23]. 2. Our theory nicely captured the severely curved Arrhenius behavior shown by the experimental literature data. Quantum tunneling and hindered internal rotors corrections are crucial in capturing the experimental rate coefficients at low temperatures. 3. Our theoretical predictions of the rate coefficients excellently matched with those of earlier theoretical studies from Mebel and Lin [23] and Siddique et al. [25]. However, all theories severely overpredict the experimental data of Hennig and Wagner [19] at high temperatures. It appears that the reported high-T kinetic data by Hennig and Wagner [19] are affected by the significant loss of the hydrocarbon reactants such that a simple first-order analysis to extract the rate coefficient is not applicable in their case. 4. Over the temperature range of 300-2000 K, our theoretical rate coefficients can be given by the following Arrhenius expressions in units of cm 3 /molecule/s: We developed a composite kinetic model consisting of NH3 and C3H8 subset chemistries. We incorporated the cross-reactions between the nitrogen and carbon families. Additionally, we updated the rate parameters for the reactions of NH2 radicals with At high temperatures, our model suggests that C 3 H 8 mainly reacted with NH 2 to yield IC 3 H 7 and NC 3 H 7 with a minor contribution from the abstraction reactions by OH and H species (not shown here). In contrast to reactions at low temperatures, the reactions of IC 3 H 7 and NC 3 H 7 with O 2 were unimportant at high temperatures. Needless to say, the reactions of NO with peroxy radicals (IC 3 H 7 O 2 /NC 3 H 7 O 2 ) did not occur at high temperatures. Therefore, NO↔NO 2 looping reactions were suppressed (see species profile shown in the Figure S7 of the Supplementary Materials). As seen, NH 3 consumption occurred at the same time for both cases (with and without nitrogen and carbon crosschemistry). Figure S8 displays the heat release rate at 800 K and 1400 K. These results again demonstrate the importance of cross-reactions for blends, which is particularly true at low temperature. Therefore, we conclude that the reactions of NH 2 radicals with C 3 H 8 are inevitable in accurately modeling the low-temperature oxidation of NH 3 /C 3 H 8 fuel blends. Our previous studies also observed similar effects with other fuel blends [10,12,14]. Considering these facts, the observations made here for NH 3 -propane blends are not too surprising. Again, we note that the importance of cross-reactions between carbon and nitrogen families has not been reported in earlier studies for NH 3 /C 3 H 8 blends. This is the first study to recognize the importance of the title reactions for modeling NH 3 /C 3 H 8 blends.

Conclusions
We conducted a theoretical investigation of the reactions between NH 2 radicals and C 3 H 8 using a high-level ab initio method (CCSD(T)/cc-pV(T, Q)Z//M06-2X/aug-cc-pVTZ level of theory) as well as conventional transition state theory (TST) methods. We demonstrated the kinetic implications of the NH 2 + C 3 H 8 reaction in the combustion of NH 3 -C 3 H 8 dual-fuel blends. Some of the key points are summarized below.

1.
The energetics of the NH 2 + C 3 H 8 reaction show strong quantum method dependence.
Our quantum approach at the CCSD(T)/cc-pV(T, Q)Z//M06-2X/aug-cc-pVTZ level of theory yielded barrier heights of 10.5 and 8.3 kcal/mol for Reactions (1) and (2), respectively. These barrier height values closely match those of the G2M approaches reported by Mebel and Lin [23].

2.
Our theory nicely captured the severely curved Arrhenius behavior shown by the experimental literature data. Quantum tunneling and hindered internal rotors corrections are crucial in capturing the experimental rate coefficients at low temperatures.

3.
Our theoretical predictions of the rate coefficients excellently matched with those of earlier theoretical studies from Mebel and Lin [23] and Siddique et al. [25]. However, all theories severely overpredict the experimental data of Hennig and Wagner [19] at high temperatures. It appears that the reported high-T kinetic data by Hennig and Wagner [19] are affected by the significant loss of the hydrocarbon reactants such that a simple first-order analysis to extract the rate coefficient is not applicable in their case.

4.
Over the temperature range of 300-2000 K, our theoretical rate coefficients can be given by the following Arrhenius expressions in units of cm 3 /molecule/s:

5.
We developed a composite kinetic model consisting of NH 3 and C 3 H 8 subset chemistries. We incorporated the cross-reactions between the nitrogen and carbon families. Additionally, we updated the rate parameters for the reactions of NH 2 radicals with C 3 H 8 , as determined in this study. To validate our kinetic model, we compared it against available literature data for the oxidation kinetics of neat C 3 H 8 , NH 3 , and NH 3 /C 3 H 8 blends across various conditions. Our kinetics model remarkably captured the observed trends of the low-and high-temperature experimental literature data. 6.
The reactions of NH 2 radicals with C 3 H 8 significantly affected the low-temperature oxidation behavior of NH 3 /C 3 H 8 blends. We found that the predicted ignition delay times were shortened considerably by including the NH 2 + C 3 H 8 reaction. For instance, at φ = 1.0 and 800 K for the 95%NH 3 /5%C 3 H 8 blend, the model predicted ignition delay time was~three times shorter with NH 2 + C 3 H 8 reactions compared to when these reactions were excluded. Furthermore, we found that the NH 2 + C 3 H 8 reactions did not impact the high-temperature chemistry, as observed for the laminar flame speed of NH 3 /C 3 H 8 blends.