Isomerization and reaction process of N₂O₄(H₂O)_n

Abstract

Liquid propellant N₂O₄ is prone to absorb H₂O to form an N₂O₄(H₂O)_n system during long-term storage, ultimately generating HNO₃, HNO₂, and other substances capable of corroding the storage tank, which will adversely affect the performance of weapons and equipment. In this work, the reaction process of the N₂O₄(H₂O)_n system is simulated using density functional theory, and the potential energy surface, the geometric configurations of the molecules, the charge distribution, and the bond parameters of the reaction course at n = 0–3 are analyzed. The results show that the potential energy of the system is lower and the structure is more stable when the H₂O in the N₂O₄(H₂O)_n system is distributed on the same side. When n = 1 or 2, the reaction profiles are similar, and the systems are partly ionic, although still mainly covalently bonded. When n = 3, the charge on the trans-ONONO₂ group and the ON–ONO₂ bond length change abruptly to −0.503 a.u. and 2.57 Å, respectively, at which point the system is dominated by ionic bonds. At n = 2, a proton-transfer phenomenon occurs in the reaction course, with partial reverse charge-transfer from NO₃⁻ to NO⁺, making the ON–ONO₂ bond less susceptible to cleavage, further verifying that N₂O₄(H₂O)_n tends to afford the products directly in one step as H₂O accumulates in the system.

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1 Introduction

Liquid-fuelled strategic missiles mainly use N₂O₄ and unsym-dimethylhydrazine (UDMH) as propellants, and during long-term storage, N₂O₄ as an oxidant will absorb moisture from the surrounding environment to produce an N₂O₄(H₂O)_n system, ultimately generating HNO₃, HNO₂, and other corrosive substances, accelerating corrosion of the receptacle and potentially allowing propellants to leak.¹ Traditional liquid-fuelled strategic missiles are constrained by this factor and can only be temporarily refilled with N₂O₄ before launch to shorten the contact time between N₂O₄ and the receptacle, but this process leads to long preparation cycles and slow operational response of such missiles, to the detriment of their operational performance.

N₂O₄ is a volatile, reddish-brown transparent liquid at room temperature. It is a highly toxic chemical, which hampers experimental studies. N₂O₄, as a dimer of NO₂, is an important intermediate (IM) in the hydrolysis of NO₂ and plays an important role in the formation of acid rain.² Due to its noxious nature, the use of quantum calculations to probe the evolution of the N₂O₄(H₂O)_n system is a trend of current research. Some studies have been carried out on the isomerization and self-ionization of N₂O₄ and the dimerization of NO₂, but the understanding of the chemical mechanism is still incomplete.^3–14 In particular, the effect of H₂O on the N₂O₄(H₂O)_n system needs to be explored more deeply. Pimentel et al.⁵ found that N₂O₄ isomerization and NO₂ dimerization in the presence of H₂O can directly form ONO–NO₂. Miller et al.⁴ simulated the interaction of H₂O with ONO–NO₂ at room temperature. For the N₂O₄(H₂O)_n system, the ionization rate is two orders of magnitude lower when n = 1 and 2 than when n > 2, indicating that, in the latter case, the reaction is transient and there is no IM. Medeiros et al.⁶ mentioned that local minima for the N₂O₄(H₂O)_n system can only be found when n is odd. Putikam et al.⁹ found a “roaming-like” transition state f formed in ONO–NO₂ during the collision with H₂O by the stretching of the N–N bond and the rotation of the –NO₂ group. Finlayson-Pitts et al.¹⁰ proposed a mechanism for the hydrolysis of N₂O₄:

2NO₂(g) ↔ N₂O₄(g) (1)

N₂O₄(g) ↔ N₂O₄(surface) (2)

N₂O₄(surface) → ONONO₂(surface) (3)

ONONO₂(surface) → NO⁺NO₃⁻(surface) (4)

NO⁺NO₃⁻(surface) + H₂O → HONO(g) + HNO₃(surface) (5)

N₂O₄ first forms sym-N₂O₄, which isomerizes to ONO–NO₂ and then reacts with H₂O to form HONO and HNO₃. The above hydrolysis mechanism reveals the complex diversity of species in the N₂O₄(H₂O)_n system and the high number of isomers of N₂O₄.³ The precise structures of the resulting HONO and HNO₃ after combining with H₂O remain uncertain.

In the propellant storage environment, N₂O₄ is distinct from that in the atmospheric environment and exists mainly in liquid form. The reaction profile of the N₂O₄(H₂O)_n system after absorbing H₂O from air and forming the N₂O₄(H₂O)_n system is unclear. Therefore, in this study, we have investigated the isomerization and reaction profile of the N₂O₄(H₂O)_n system based on density functional theory (DFT), focusing on the following issues:

(1) The effects on the N₂O₄(H₂O)_n system of n being an odd or even number.

(2) The route by which the N₂O₄(H₂O)_n system directly forms NO⁺ and NO₃⁻.

(3) The variations in the charges on the groups during the reaction course of the N₂O₄(H₂O)_n system when n = 0–3.

2 Calculation method

Based on the conclusions of Pimentel et al.,⁵ the DFT/B3LYP method was used to optimize N₂O₄ single-molecule isomerization at the 6-311++G (3df, 2p) basis group level, considering all species in the reaction of the N₂O₄(H₂O)_n system. The intrinsic reaction coordinates (IRC) were established through standard 6-311++G (3df, 2p) basis group calculations to confirm the connection of each transition state (TS) to the specified intermediate (IM). The resulting reactant, product, and IM frequencies were positive, with one and only one imaginary frequency for the TS. Single-point energies were re-determined at the B2PLYP/Def2-TZVP basis set level.¹⁵ To take into account the effect of the solvent medium, the self-consistent reaction field (SCRF) method and the implicit solvation model of the SMD model were used at n = 3, in conjunction with the conclusions of Miller⁴ and Putikam.⁹ All calculations were performed using the Gaussian 16 software package.¹⁶

3 Results and discussion

3.1 Isomerization of N₂O₄ (n = 0)

Experimental studies have shown that N₂O₄ has three main conformations; in addition to sym-N₂O₄, there are two asymmetric N₂O₄ isomers, namely trans-N₂O₄ and cis-N₂O₄.^17–19 Zhu et al.⁸ predicted the possible geometric conformations of N₂O₄ isomers based on ab initio molecular dynamics, and identified the most stable isomers as sym-N₂O₄ and trans-N₂O₄. Meanwhile, the spontaneous dissociation of N₂O₄ to NO₂ is less likely in the liquid propellant storage environment. Therefore, the work in this section mainly considers the mutual isomerization between sym-N₂O₄, cis-N₂O₄, and trans-N₂O₄. The potential energy surface (PES) and the geometric configurations and bond parameters of the conformers during the isomerization are shown in Fig. 1. The optimized sym-N₂O₄ has an N–N bond length of about 1.80 Å and N–O bond lengths of about 1.18 Å, in good agreement with reported values determined experimentally by electron diffraction analysis at 252 K.²⁰ When sym-N₂O₄ isomerizes to cis-N₂O₄, the N–N bond length in TS1 is 2.68 Å and the dihedral angle O4–N2–O6–N1 is 177°. The associated potential energy barrier is 166.91 kJ mol⁻¹, which further completes the isomerization process of NO₂ proposed by Liu et al.³ In contrast, the “roaming-like” TS structure proposed by Putikam et al.⁹ is more relaxed, with an N–N bond length of 3.70 Å, a dihedral angle O4–N2–O6–N1 of 76°, and a potential energy barrier of 34.31 kJ mol⁻¹, significantly different from the values calculated here. For the isomerization of sym-N₂O₄ to trans-N₂O₄ via TS3, the two –NO₂ groups of the reactants and products are coplanar, but the structure of TS3 is vertical, the N–N bond length is only 2.08 Å, and the associated potential energy barrier is about 175.94 kJ mol⁻¹. In contrast, in the TS structure reported in the literature, the N–N bond length reaches 3.57 Å, the two –NO₂ groups are almost dissociated, and the electron density between the interacting groups is reduced, so the TS potential energy barrier (53.56 kJ mol⁻¹) is much lower than that calculated here.⁹ The course of the isomerization of cis-N₂O₄ to trans-N₂O₄ is similar to that calculated in the literature.²¹

Fig. 1 Potential energy surface of N₂O₄ isomerization and the geometries and bond parameters of the conformers (key length unit: Å, key angle unit: °).

3.2 Isomerization and reaction processes of N₂O₄(H₂O) and N₂O₄(H₂O)₂ (n = 1, 2)

From Section 3.1, it is clear that the relative energy of trans-N₂O₄ is lower than that of cis-N₂O₄, indicating that the former is more stable in the course of the isomerization. Hence, only trans-N₂O₄ is considered in the following calculations. Fig. 2 shows the PES and the geometric configurations of the molecules with bond parameters for the isomerization and reaction course of N₂O₄(H₂O). When N₂O₄ absorbs H₂O, a complex such as IM1 is produced due to van der Waals forces. At this point, two pathways are available for IM1 for the next reaction step.

Fig. 2 Potential energy surface of N₂O₄(H₂O) isomerization and reaction process, and the geometries and bond parameters of molecules (key length unit: Å, key angle unit: °).

(1) IM1 may be directly converted to HNO₃ + trans-HONO via TS4, as shown in Fig. 2. TS4 is a compact five-membered-ring structure with an associated potential barrier of 138.62 kJ mol⁻¹. This value is similar to that reported by Chou et al.²² Upon further conversion of TS4, H8 in H₂O gradually detaches and combines with one of the –NO₂ groups to produce trans-HONO. The remaining –OH of H₂O combines with the other –NO₂ group to produce HNO₃.

(2) IM1 may be converted to TS5 to generate trans-ONONO₂. In this case, the structure of TS5 is more similar to TS3. In the course of isomerization of sym-N₂O₄ to trans-N₂O₄, one of the –NO₂ groups rotates about the N–N bond, thus causing a shift of H₂O, and the distance between N1 and O7 reaches 4.02 Å. When structurally stable trans-ONONO₂ is generated, the distance between N1 and O7 is 2.85 Å. As the reaction continues, trans-ONONO₂ produces HNO₃ + trans-HONO and HNO₃ + cis-HONO through two six-membered-ring transition states, TS6 and TS7, respectively. In TS6, H8 of H₂O is transferred to O5 in –NO₃, eventually forming HNO₃, while the remaining –OH of H₂O combines with –NO. The structure of TS7 is similar to that of TS6, except that H₂O is rotated by a certain angle. It follows a similar reaction course to finally form HNO₃ + cis-HONO, the reaction potential of which is 2.41 kJ mol⁻¹ higher than that of HNO₃ + trans-HONO.

In Fig. 2, it can be seen that the energy of trans-HONO is lower than that of cis-HONO, indicating that the former is more stable and the reaction pathway is more likely to occur. Therefore, the reaction course of cis-HONO is not considered in the following calculations. When the content of H₂O is further increased, N₂O₄ combines with more H₂O in the vicinity to produce N₂O₄(H₂O)₂. The PES and geometric configurations of the molecules with bond parameters for the isomerization and reaction course are shown in Fig. 3.

Fig. 3 (a) PES of N₂O₄(H₂O)₂ isomerization and reaction course. (b) Molecular geometrical configurations and bond parameters for N₂O₄–(H₂O)₂ isomerization and reaction course (bond lengths in Å, bond angles in °).

Similar to IM1 in Fig. 2, when N₂O₄ is combined with 2 H₂O, two N₂O₄(H₂O)₂ complexes, IM2 and IM3, are produced, as shown in Fig. 3(b), in which the 2 H₂O molecules are located on the same or opposite sides of N₂O₄, respectively. Therefore, its reaction course will follow two main pathways.

3.2.1 IM2 reaction process. ① IM2 is directly converted to TS12, from which HNO₃ + trans-HONO + H₂O are formed. TS12 has a five-membered-ring structure, similar to TS4, with only one H₂O molecule involved in the reaction. Meanwhile, O10 of the other H₂O molecule interacts with H8 and O7 in the five-membered-ring structure to form an O–H–O hydrogen bond.

② IM2 first passes through TS8 to form trans-N₂O₄–2H₂O. Both H₂O molecules are involved in the reaction course, and the product trans-N₂O₄–2H₂O has an eight-membered-ring structure. Upon further reaction of trans-N₂O₄–2H₂O, the final product is formed through TS10. During this process, both H₂O molecules engage in proton-transfer phenomena, i.e., O7 and H10 of one H₂O molecule combine with NO to form trans-HONO, while H12 of the other H₂O molecule combines with NO₃⁻ to form HNO₃. The remaining H8 and O10 of the two H₂O molecules recombine with H11 to form a new H₂O molecule.

3.2.2 IM3 reaction process. ① IM3 undergoes a direct reaction via TS13 to form HNO₃ + trans-HONO + H₂O. The two H₂O molecules of IM3 in the steady state are symmetrically distributed on the upper and lower sides of N₂O₄, forming four N–O bonds, which are longer than the N–O bonds in IM2. Hence, IM3 is higher in energy than IM2. Upon isomerization of IM3, the H₂O molecule on one side resides closer to N₂O₄ after rotating through a certain angle about the N–N bond, and can participate in the reaction. At this point, TS13 also adopts a five-membered-ring structure. Compared with TS12, only the atoms connected to H₂O (O7), which is free from the five-membered-ring structure, are different. H9 of H₂O (O7) in TS13 is connected to O6 of one of the –NO₂ groups, forming a stable TS structure.

② IM3 can also go through TS9 to first form H₂O–trans-N₂O₄–H₂O, and then O7 of H₂O, which is closer to N1, binds to N1 to form the six-membered-ring structure TS11. The latter is lower in energy and more stable than the eight-membered-ring structure of TS10. Of the H₂O (O7) molecule involved in the reaction, H8 combines with NO₃ to form HNO₃, while O7 and H9 combine with NO to form trans-HONO.

3.3 Isomerization and reaction profile of N₂O₄(H₂O)₃ (n = 3)

In N₂O₄(H₂O)₃, there are two possible distributions of H₂O molecules, i.e., all three H₂O molecules residing on one side of N₂O₄, or two H₂O molecules on one side and the third on the other side. Our calculations reveal that N₂O₄–3H₂O is lower in energy than 2H₂O–N₂O₄–H₂O. Combined with the results in Section 3.2, 2H₂O–N₂O₄–H₂O can be studied with reference to the isomerization and reaction profiles of IM2 and IM3, and so this section focuses on the isomerization and reaction profiles of N₂O₄–3H₂O, for which the PES and the geometric configurations and bond parameters of the molecules are shown in Fig. 4.

Fig. 4 Potential energy surface of N₂O₄(H₂O)₃ isomerization and reaction process, and the geometries and bond parameters of molecules (key length unit: Å, key angle unit: °).

(1) IM4 may directly generate HNO₃ + trans-HONO + 2H₂O via TS16. In IM4, the three H₂O molecules are connected sequentially to form a ring structure with one of the –NO₂ groups, while O10 of the H₂O molecule located above N₂O₄ forms a stable triangular structure with both N atoms. The two N–O bonds are almost equal in length. Although only one H₂O molecule is involved in the reaction, H₂O (O10), in TS16 it forms both an eight-membered-ring structure with the remaining two H₂O molecules and a five-membered-ring structure with N₂O₄.

(2) IM4 first forms trans-N₂O₄–3H₂O via TS14, and the three H₂O molecules also break from the ring structure into a single chain and then rejoin with O3 to form a ring. The trans-N₂O₄–3H₂O then undergoes proton transfer, with H₂O (O7) providing –OH and H₂O (O10) providing H to form IM5. IM5 already has the structure of the products, but the molecules are still connected to each other and only form the products after bond-breaking.

N₂O₄(H₂O)_n has one and only one stable structure during the isomerization and reaction course when n < 2. When n ≥ 2, the distribution of H₂O affects the stable structure of N₂O₄(H₂O)_n, resulting in different energies. If H₂O is distributed on the same side of N₂O₄, with fewer interconnected chemical bonds and shorter bond lengths, the energy is lower and the structure is more stable, as in IM2 and IM3 in Fig. 3(b). Irrespective of whether n is odd or even, multiple pathways are available for N₂O₄(H₂O)_n to undergo isomerization reactions. To verify the speculation of Miller et al.,⁴ the potential energy barriers associated with different pathways of N₂O₄(H₂O)_n isomerization for different values of n and pertaining to the most stable conformation are plotted in Fig. 5.

Fig. 5 Potential energy barriers associated with different reaction paths for N₂O₄(H₂O)_n isomerization reactions.

The energy of 166.01 kJ mol⁻¹ for n = 0, i.e., the direct ionization of N₂O₄ to form NO + NO₃, and combining TS4, TS12, and TS16 as the reaction potential for the direct reaction of N₂O₄(H₂O)_n to form the product pathway; the first step of isomerization process of N₂O₄(H₂O)_n through multiple steps to generate products as the reaction potential of its multi-step reaction pathway, i.e., N₂O₄(H₂O)_n → trans-N₂O₄–(H₂O)_n: TS3, TS5, TS8, and TS14. From Fig. 5, it can be seen that the potential energy barrier of N₂O₄(H₂O)_n gradually decreases as n is increased and more H₂O is involved in the reaction. When n = 0–2, the differences in the potential energy barriers associated with the direct and multi-step reaction paths are small, such that N₂O₄(H₂O)_n may follow both reaction paths at the same time. When n = 3, however, the difference in potential energy barriers associated with the two paths reaches 28.4 kJ mol⁻¹, indicating that N₂O₄(H₂O)₃ will preferentially pass through TS16 to afford the products directly. Combined with the finding in Fig. 4 that TS15 is lower in energy than the reaction potential of the products when N₂O₄(H₂O)₃ undergoes a multi-step reaction path, it is clear that the multi-step reaction path of N₂O₄–(H₂O)₃ is difficult to reach. On the basis of thermodynamics, Mulliken charge analysis was performed on the intermediate product trans-ONONO₂–(H₂O)_n, and the results in terms of charge on the trans-ONONO₂ group and ON–ONO₂ bond length are shown in Table 1.

Table 1 Variations in charge on the trans-ONONO₂ group and ON–ONO₂ bond length in trans-ONONO₂–(H₂O)_n

n	0	1	2	3
Electric charge/a.u.	0	−0.019	−0.025	−0.503
Key length/Å	1.62	1.76	1.79	2.57

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As can be seen from Table 1, the charge on the trans-ONONO₂ group gradually becomes more negative as the H₂O content in trans-ONONO₂–(H₂O)_n is increased, indicating increased polarity. Concomitantly, the bond length of ON–ONO₂ also increases, and –ON gradually dissociates and from the trans-ONONO₂ group. It can be seen that the differences in charge on the trans-ONONO₂ group and ON–ONO₂ bond length are not large when n = 1 and 2. However, when n = 3, the charge on the trans-ONONO₂ group and the ON–ONO₂ bond length change abruptly, reaching −0.503 a.u. and 2.57 Å, respectively. These results support the conjecture of Miller et al.;⁴ when n = 1 or 2, trans-ONONO₂-(H₂O)_n is partly ionically bonded, but still mainly covalently bonded. When n = 3, however, ionic bonding becomes dominant. Meanwhile, combined with the reaction rate results of Miller et al.⁴ and analyzed by the potential energy surfaces in Fig. 2–4, the reaction rate constant increases by two orders of magnitude when n = 3 compared with n < 3. In Section 3.2.1, trans-N₂O₄–2H₂O was seen to undergo a proton-transfer phenomenon as the reaction proceeds. Luo et al.¹⁴ confirmed that the formation of hydrogen bonds and a polar environment are prerequisites for intermolecular proton transfer. Proton-transfer due to trans-ONONO₂ dominates in the production of –OH, which is also supported by experimental results,²³ leading to a shorter lifetime of trans-ONONO₂ with the increase of H₂O. All charge-transfer steps result in partial reverse charge-transfer from NO₃⁻ to NO⁺, making the ON–ONO₂ bond less susceptible to cleavage, further verifying that when n = 3, the N₂O₄(H₂O)₃ system is dominated by ionic bonds between molecules. Due to the short-lived existence of trans-ONONO₂ and the difficulty of breaking the ON–ONO₂ bond, the reaction can be considered as being completed instantaneously.²⁴ That is to say, IM4 mainly passes through TS16 to directly generate the final products HNO₃ + trans-HONO + 2H₂O.

4 Conclusions

(1) N₂O₄(H₂O)_n system structure reaction course of the local minimum is not related to the parity of the n value. When H₂O molecules are distributed on the same side, the potential energy of the system is lower, and the structure is more stable. When n = 1 or 2, the two reaction pathways are similar in energy. The systems are partly ionically bonded, but mainly still covalently bonded.

(2) When n = 3, the charge on the trans-ONONO₂ group and the ON–ONO₂ bond length change abruptly, reaching −0.503 a.u. and 2.57 Å, respectively, and the system is then dominated by ionic bonds.

(3) When n = 2, the reaction course shows the phenomenon of proton-transfer, with partial reverse charge-transfer from NO₃⁻ to NO⁺, making cleavage of the ON–ONO₂ bond more difficult. Combining the change of potential energy surface, the charge on the ONONO₂ group, and the molecular bond parameters during the course of the reaction, it is again verified that N₂O₄(H₂O)_n tends to afford the products directly in one step with increasing H₂O content in the system.

Author contributions

Y. Guo: conceptualization, investigation, methodology, writing – original draft. Z. Y. Huang: data curation, formal analysis. G. Tian: project administration, validation. W. Wu: resources, supervision. J. Lin: software, validation. X. L. Chang: funding acquisition, writing – review & editing.

Conflicts of interest

We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work.

Acknowledgements

This research was funded by the National Natural Science Foundation of China (No. 52272446) and Natural Science Foundation of Shaanxi Province (No. 2021JM-250).

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