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Reconciling the Debate on the Existence of Pentazole HN5 in the Pentazolate Salt of (N5)6(H3O)3(NH4)4Cl Huisheng Huang, jie zhong, Liang Ma, Liping Lv, Joseph S. Francisco, and Xiao Cheng Zeng J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/jacs.8b11335 • Publication Date (Web): 31 Jan 2019 Downloaded from http://pubs.acs.org on February 5, 2019
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Reconciling the Debate on the Existence of Pentazole HN5 in the Pentazolate Salt of (N5)6(H3O)3(NH4)4Cl Huisheng Huang,1,2,# Jie Zhong,2,# Liang Ma,2 Liping Lv,1 Joseph S. Francisco3,*, and Xiao Cheng Zeng2,* 1Chongqing
Key Laboratory of Inorganic Special Functional Materials, College of Chemistry and
Chemical Engineering, Yangtze Normal University, Chongqing 408100, China. 2Department
of Chemistry, University of Nebraska-Lincoln, Lincoln, NE, 68588, USA.
3Department
of Earth and Environmental Science and Department of Chemistry,
University of Pennsylvania, Philadelphia, PA, 19104, USA
ABSTRACT: The successful synthesis of the pentazolate salt (N5)6(H3O)3(NH4)4Cl has received considerable attention as it ends the long search for a method for the bulk preparation of cyclo-N5ˉ, a molecular ring with high energy density (Science 2017, 355, 374). A debate has recently arisen on the possible existence of a neutral HN5 species in the pentazolate salt (Science 2018, 359, eaao3672; Science 2018, 359, eaas8953). Herein, we show that the debate can be reconciled by the temperature effect on the proton transfer. At a low temperature (123 K), the proton transfer from H3O+ to cycloN5ˉ is energetically unfavourable; therefore, few neutral HN5 species exist in the pentazolate salt, which is consistent with the single-crystal X-ray diffraction measurements (Science 2017, 355, 374). As the temperature increases towards room temperature, endothermic proton transfer becomes increasingly feasible, promoting the formation of H2O∙∙∙HN5 via H2O-H-N5 as an intermediate species. In addition, the confusion over the apparent absence of a peak in the measured infrared spectrum corresponding to the out-of-plane bending of H3O+ can be resolved by the computationally established ultrafast interconversion among the neutral and anionic species under ambient conditions.
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INTRODUCTION Pentazolates have attracted substantial attention from researchers in the areas of energetic material1-8 and fundamental inorganic chemistry,9-10 since the pentazolate anion, cyclo-N5ˉ, is not only a prototype all-nitrogen high-energy species but also a carbon-free aromatic analogue of the cyclopentadienyl anion. There have been numerous attempts to produce cyclo-N5ˉ, but all have been unsuccessful until Östmark et al first reported the preparation of cyclo-N5ˉ in 2002.11 In the same year, Christe et al. detected the elusive pentazolate anion in the gas phase.12 Recently, cyclo-N5ˉ was prepared in a tetrahydrofuran solution and was found to be indefinitely stable below −40°C.13 In 2017, Hu et al. made a breakthrough and reported the first successful synthesis and characterization of the solid-state salt (N5)6(H3O)3(NH4)4Cl, which contains pentazolate anions that are stabilized via hydrogen-bonding interactions with the neighbouring H3O+ and NH4+ ions.14 Remarkably, the reported pentazolate salt was highly stable, and thermogravimetry experiments showed initial thermal decomposition temperatures as high as 117°C. Although the unique structural features of pentazolate salt (N5)6(H3O)3(NH4)4Cl were resolved by single-crystal X-ray diffraction analysis, a debate recently arose regarding the possible existence of neutral HN5 species in the same salt.15 Huang and Xu argued, based on their ab initio calculations of two isolated gas-phase complexes, H2O∙∙∙HN5 and H3O+∙∙∙cyclo-N5ˉ, that the neutral HN5 species should be favoured over the cyclo-N5ˉ species due to proton transfer.15 However, it remained unclear whether the gas-phase model can accurately describe the proton-transfer trends in the solid state. Indeed, Hu and co-workers countered that the gas-phase model employed by Huang and Xu does not reflect the realistic solid-state environment surrounding the cyclo-N5ˉ species and thus cannot mimic the proton-transfer process in the salt.16 Instead, Hu et al. proposed a phenomenological solid model to describe the proton-transfer process in the salt, and their preliminary calculations suggest that no neutral HN5 species are present in the salt. In addition to the debate presented above, an intriguing experimental phenomenon remains to be addressed. That is, an out-of-plane vibrational mode associated with the hydronium is not present in the experimental infrared (IR) spectrum. Does the absence of this expected peak in the IR spectrum reflect a certain dynamic process in (N5)6(H3O)3(NH4)4Cl that has not been reported? To address the debate and question above, a deeper understanding of the structure and protontransfer process in the solid-state (N5)6(H3O)3(NH4)4Cl is needed, which motivated us to conduct this 2
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comprehensive computational study. Towards this end, we employed density functional theory (DFT) calculations to simulate the thermal decomposition of the (N5)6(H3O)3(NH4)4Cl salt. An analysis of the kinetics, including the minimum-energy path, several transition states and the associated activation barriers, was conducted using the climbing image nudged elastic band (CI-NEB) method.17 Moreover, ab initio molecular dynamics (AIMD) simulations were performed to capture important dynamic features of the pentazolate salt at various temperatures.
COMPUTATION METHODS All DFT calculations were performed with using the Vienna Ab initio Simulation Package (VASP 5.4).18-19 The general gradient approximation (GGA) parametrized by Perdew, Burke and Ernzerhof (PBE)20 was used as the exchange-correlation functional, and the projected augmented wave (PAW) method21-22 was employed to describe the interaction between the valence electrons and the ion cores. The cutoff energy of plane wave basis was set to 520 eV. Grimme’s DFT-D2 correction23 was adopted to describe the weak van der Waals interaction. The primitive cell of (N5)6(H3O)3(NH4)4Cl containing 126 atoms was used for the computation, and the Brillouin zone integral was performed with a 2×2×2 k-point sampling. The quasi-Newton algorithm was used for the structural relaxation, and the criterion of convergence was set such that the residual force components were less than 0.05 eV/Å. The CINEB method17 incorporated in the VASP was employed to locate the transition states and minimumenergy path. Taking the lattice parameters and atomic coordinates from the single-crystal X-ray diffraction measurement as input, the theoretically optimized lattice constants and shape are in good agreement with the measurement (see Table S1),14 which validates our computation scheme. As suggested by Hu et al.,16 an approximation such that every hydrogen atom in H3O+ could be randomly assigned to one of two resonance states with the probability of 50% is undertaken. However, only one fixed occupancy site can be considered for the theoretical calculation. For the AIMD simulations, the fully optimized lattice cell of the pentazolate salt containing 504 atoms was used and the Brillouin zone was sampled only on the single Γ point. AIMD simulations were carried out in the canonical (NVT) ensemble with the temperature being controlled at 123 K (the same as the measured temperature in single-crystal X-ray diffraction experiment), or at 250 K (approaching the temperature of crystal growth), 313 K (the starting temperature of thermal analysis), 390 K (the purported onset decomposition temperature).14 We controlled the ionic temperature by 3
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using the Langevin thermostat. A velocity Verlet algorithm with a time-step of 1 fs was used to integrate equations of motion. For each simulation, the system was initially equilibrated for 10 ps, followed by additional 30 ps simulation to collect data for statistical analysis.
RESULTS AND DISCUSSION Mechanism and Kinetics of Proton Transfer. First, we find that when gas-phase models are used, conclusions regarding trends in proton transfer can be dependent on the initial structure set for the (N5)6(H3O)3(NH4)4Cl solid. As shown in Figure S1, a barrierless proton transfer is predicted with the N5ˉ∙∙∙H3O+ dimer as the model, whereas no proton transfer is predicted from the structural optimization starting from the tetramer of 3N5ˉ∙∙∙H3O+. These theoretical results indicate that the symmetry of the environment around the hydronium can have a marked effect on the proton-transfer behaviour. In other words, whether the anionic cyclo-N5ˉ species is truly protonated in bulk (N5)6(H3O)3(NH4)4Cl cannot be easily addressed based on the gas-phase models. Next, we employed a periodic system to model the bulk (N5)6(H3O)3(NH4)4Cl solid. We found that the solid-state model can provide clear evidence of the simultaneous formation of covalent Zundeltype complexes (H2O-H-N5) and hydrogen-bonded pairs of molecules (H2O∙∙∙HN5) (see Figure 1). Figure 1A shows the fully optimized primitive cell of the (N5)6(H3O)3(NH4)4Cl solid, which is in good agreement with the previously reported experimental structure (Table S1). This optimized structure is taken as the initial state (IS) for all reactions considered. Based on the decomposition products (neutral HN3, N2 and H2O) identified in the experiment, we initially consider a direct decomposition pathway starting from N5ˉ∙∙∙H3O+ in the pentazolate salt. The computed energy profile is shown in Figure 1B and Figure S2. A relatively high activation barrier (121.2 kJ/mol) must be overcome for the decomposition of the N5ˉ∙∙∙H3O+ ion pair, suggesting that an alternative pathway with a relatively low activation barrier might occur prior to the decomposition of cyclo-N5ˉ, especially for the pathway associated with the proton transfer. Our pathway search based on the NEB computation suggests that such a pathway should exist.
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Figure 1. (A) The fully relaxed primitive cell of the (N5)6(H3O)3(NH4)4Cl solid. (B) A pathway for the direct decomposition of an ion pair of N5ˉ∙∙∙H3O+ into HN3, N2 and H2O, in the pentazolate salt. Such a pathway is unlikely to occur due to existence of alternative pathway with lower energy barriers. (C) Computed energy profiles that involve multiple transition states (TS1 – TS5 and TSˊ) and intermediate states (IM1 – IM5) for a specific proton transfer at 0 K, i.e., from H3O+ to cyclo-N5ˉ in the (N5)6(H3O)3(NH4)4Cl solid. (D) The fully optimized crystal structure of IM5 containing a Zundel-type complex and an HN5 molecule. O1 involves a large deviation from linearity in their hydrogen bond angles, whereas O2 involves a small deviation.14 All energies are given in kJ/mol.
Figure 1C shows the computed proton-transfer reaction pathway for the solid-state (N5)6(H3O)3(NH4)4Cl at 0 K. The geometries of the corresponding initial state (IS), multiple transition states (TS1 – TS5 and TSˊ), and intermediate states (IM1 – IM5) are displayed in Figure S3. As shown in Figure 1C, both pre-reaction paths, from IS → TS1 → IM1 and from IM1 → TS2 → IM2, are endothermic and the associated reaction enthalpies are very small (0.2 and 2.0 kJ/mol, respectively). The associated reaction barriers are fairly low as well (only 1.4 and 4.7 kJ/mol, respectively). In the 5
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IS, IM1 and IM2 states, the bond lengths of O1i-H1i are always the longest among all the O-H bonds, and their lengths were 1.082, 1.112 and 1.088 Å, respectively (Figure S3). Notably, the H3O+ (O1ii) group undergoes a distinct distortion in the IM2 state of the pre-reaction (Figure S3), and the changes in the bond lengths of O1ii-H1ii and O1i-H1i are clearly seen. Interestingly, when the O-H bond length increases, the corresponding N∙∙∙H bond shortens, and vice versa. To examine whether a proton-transfer event could occur, we investigated the bonding nature of the N5ˉ∙∙∙H3O+ ion pair in the pentazolate salt by computing the electron localization function (ELF). Note that the ELF represents the relative degree of electron localization in the periodic structures. For example, regions such as lone pairs, covalent bonds and cores tend to have higher ELF values.24 Figure 2 shows the interatomic distances associated with the proton-transfer events and the computed ELF contours drawn in the plane containing the relevant N, H and O atoms. The first proton-transfer reaction (from IM2 → TS3 → IM3) is energetically unfavorable since the IM3 state is 30.9 kJ/mol higher in energy than the IM2 state. The corresponding activation barrier of 31.0 kJ/mol is also quite high (Figure 1C). As depicted in Figure 2, this proton-transfer process gives rise to a Zundel-type complex (in IM3 state), in which proton H1i is shared between a cyclo-N5ˉ ion and a H2O molecule, and the bond lengths of N1i-H1i and O1i-H1i are 1.303 and 1.191 Å, respectively. The high ELF regions (red) near the N1i, H1i and O1i atoms demonstrate the formation of covalent bonds between N1i-H1i and O1i-H1i. The low ELF region (green) between the N1ii and H1ii atoms indicates that no covalent bond formed between the two atoms, and H1ii does not actually transfer from O1ii to N1ii in the IM3 state. Next, the reaction proceeds over the TS4 which has a relatively high energy barrier of 34.9 kJ/mol, whereas the corresponding formation energy is substantially reduced to 2.7 kJ/mol (Figure 1C). Compared to the IM3 state, the bond length and ELF of N1i-H1i and O1i-H1i in the IM4 state are quite similar, while those of N1ii-H1ii and O1ii-H1ii are noticeably changed. In the IM4 state, the ELF value between N1ii and H1ii is relatively high (yellow); thus, a partial N1ii-H1ii bond is formed, while the O1ii-H1ii bond is slightly weakened with concomitant generation of the corresponding Zundel-type complex. As a result, the IM4 state exhibits two H2O-H-N5 complexes with both H1i and H1ii partially transferring from the hydronium to the pentazolate anion.
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Figure 2. Variations in the interatomic distances (Å) associated with the proton-transfer events and the computed ELF contours illustrated in the plane containing the corresponding N, H and O atoms in the IM3, IM4 and IM5 state, respectively.
It is important to know whether HN5 can be formed in the pentazolate salt via full proton transfer. As shown in Figure 2, the ELF value between O1ii and H1ii in the IM5 state is relatively low (green), whereas that between N1ii and H1ii in the IM5 state is quite high (red), implying that the O1ii-H1ii bond is fully broken, while the N1ii-H1ii bond is formed. Hence, HN5 and H2O are formed at the same time. Note that H1i in the IM5 state is still nearly equally shared between cyclo-N5ˉ and H2O. As shown in Figure 1C, HN5 is ultimately produced in the reaction path from IM4 → TS5 → IM5. Because the formation energy continues to rise, HN5 is energetically less stable than the cyclo-N5ˉ in the pentazolate salt. However, the IM3 state can go through the transition state TS′ to reach the IM5 state, even though the barrier increases to 37.4 kJ/mol, which is much higher than those associated with other protontransfer processes discussed above. Hence, we conclude that the protons can undergo either partial or full transfer in the pentazolate salt. Figure 1D depicts the fully relaxed crystal structure corresponding to the IM5 state, and a covalent Zundel-type complex (H2O-H-N5) and a hydrogen-bonded molecular pair (H2O∙∙∙HN5) can be seen. Both species are generated via proton transfer from H3O+ (O1i and O1ii) to cyclo-N5ˉ. In addition, the H3O+ (O1iv) is significantly distorted such that the hydrogen-bonding interaction between the H3O+ 7
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(O1iv) ion and the surrounding cyclo-N5ˉ ions changes considerably. These observations suggest that cooperative hydrogen-bonding relaxation occurs during proton transfer. Moreover, H3O+ (O2) (see Figure 1A) is located in a more symmetric environment than H3O+ (O1),14 and thus it is less prone to proton transfer. This finding is consistent with the results based on the geometry optimization in the gas phase.
Temperature Effect on Dynamical Behavior of Proton Transfer. Although the proton-transfer between H3O+ and N5ˉ at 0 K was confirmed by the CI-NEB calculations, occurrence of multiple proton-transfer pathways and symmetry broken of pentazolate salt cannot be accounted for in the CINEB calculations. Hence, the barriers depicted in Figure 1C should be viewed as the upper limit. To describe the population and lifetime of various N5ˉ∙∙∙H3O+ complexes more quantitatively at finite temperatures and to elucidate the dynamic behaviors of proton-transfer in pentazolate salt with considering the thermal effects, AIMD simulations were performed at four different temperatures (123, 250, 313 and 390 K). Figure 3 presents the radial distribution functions (RDFs) for the O and H atoms of H3O+, the N atom of N5ˉ and the H atom of H3O+, and the N and H atoms of NH4+ at the four temperatures. Here, two prominent peaks at 1.05 and 1.45 Å are easily observed for the RDF of O (H3O+)-H (H3O+), and its counterpart, namely, the RDF of N (N5ˉ)-H (H3O+), also exhibits two corresponding peaks at 1.65 and 1.15 Å, suggesting that the proton of the hydronium ion can be transferred to the cyclo-N5ˉ ion (see Movies S1-S4). However, the RDF of N (NH4+)-H (NH4+) only exhibits one peak at 1.05 Å, indicating that the proton of the ammonium ion cannot be transferred to the cyclo-N5ˉ ion in the (N5)6(H3O)3(NH4)4Cl solid (Movies S1-S4), which is because NH3 generally has a stronger proton affinity than H2O.25 Moreover, as shown in Figure 3 A and B, the intensity of the peak varies with temperature. Thus, the proton-transfer process is significantly dependent on temperature.
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Figure 3. Computed radial distribution functions (RDFs) for (A) O (H3O+)-H (H3O+), (B) N (N5ˉ)-H (H3O+), and (C) N (NH4+)-H (NH4+).
Next, we computed the percentages of the ion pair (N5ˉ∙∙∙H3O+), the Zundel-type complex (H2OH-N5), and the molecular pair (H2O∙∙∙HN5) in the (N5)6(H3O)3(NH4)4Cl crystal at 123, 250, 313, and 390 K (Figure 4A). Note that our previous discussion above shows that N1ii∙∙∙H1ii∙∙∙O1ii successfully transfers the proton from H3O+ to N5ˉ when it proceeds from the IM4 to IM5 state (Figure 2). Thus, the H1ii-O1ii distance in the IM4 state and the N1ii-H1ii distance in the IM5 state, with distances of 1.138 Å and 1.192 Å, respectively, can be considered the corresponding bonding cutoffs. As depicted in Figure 4A, at 123 K (the measured temperature in the experiment), the average percentages of N5ˉ∙∙∙H3O+, H2O-H-N5, and H2O∙∙∙HN5 in the simulated structure are 79.5%, 10.4%, and 10.2%, respectively. This result indicates that the ion pair N5ˉ∙∙∙H3O+ is the majority species at very low temperatures. Moreover, we found that the fluctuation in the percentage of the complex during the simulation is relatively small, as shown by the narrow distributions of percentages, namely, 73%~87% for N5ˉ∙∙∙H3O+, 2.4~17% for H2O-H-N5, and 5.4~15% for H2O∙∙∙HN5 (see the full width at half maximum in Figure S4). This result suggests that equilibrium of the interconversion between complexes is easily reached at low temperatures (123 K). As the temperature increases, the percentage of N5ˉ∙∙∙H3O+ decreases dramatically, whereas those of H2O-H-N5 and H2O∙∙∙HN5 increase substantially. This result is consistent with the CI-NEB results of the proton-transfer reaction being endothermic, and the equilibrium shifts towards the endothermic direction with increasing temperature. In addition, a large fluctuation in the percentage of the complex (see Figure S4) indicates relatively strong interconversion between complexes at high temperatures. As shown in Figure 4B, the probabilities of proton transfer from H3O+ (O1) are much greater than those from H3O+ (O2) at all simulated temperatures, which is consistent with the CI-NEB results that 9
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only H3O+ (O1) undergoes full proton transfer to cyclo-N5ˉ at 0 K. This result can be attributed to the differences in the environments of the two hydronium ions, i.e., increasing asymmetry in the force on the H3O+ leads to easier proton transfer from the H3O+ to cyclo-N5ˉ. As the temperature increases, the symmetry of the structure is distorted, and H3O+ (O2) can transfer its proton. Meanwhile, the disappearance of the symmetry can explain the strong synergistic effect observed in the proton-transfer reaction, especially at high temperatures where many proton-transfer processes in the (N5)6(H3O)3(NH4)4Cl salt can occur simultaneously (see Figure S5).
Figure 4. (A) Computed proportions of the ion pair N5ˉ∙∙∙H3O+, Zundel-type complex H2O-H-N5, and the molecular pair H2O∙∙∙HN5 in the (N5)6(H3O)3(NH4)4Cl crystal at four different temperatures. (B) Computed probabilities of proton transfer from H3O+ (O1) and from H3O+ (O2).
Moreover, the lifetimes of the N5ˉ∙∙∙H3O+ ion pair, Zundel-type complex H2O-H-N5, and molecular pair H2O∙∙∙HN5 can be computed. As shown in Table 1, both the average and maximum lifetimes (see Supporting Information for definitions) become shorter with increasing temperature. Clearly, the lifetime of H2O-H-N5 is much shorter than those of N5ˉ∙∙∙H3O+ and H2O∙∙∙HN5 since the proton in the Zundel-type complex can shuttle back and forth via a hydrogen bond to form the ion pair and molecular pair, while the protons in N5ˉ∙∙∙H3O+ and H2O∙∙∙HN5 can only shift in one direction to generate H2O-H-N5. Interestingly, by examining the structure, the proton-transfer process, and the lifetime, we find that the two interconversions, (N5ˉ∙∙∙H3O+)-(H2O-H-N5) and (H2O∙∙∙HN5)-(H2O-HN5), are analogous to the Eigen-Zundel [(H2O∙∙∙H3O+)-(H2O∙∙∙H+∙∙∙H2O)] interconversion.26-27 The latter exists in water with excess protons and gives sub-100-fs experimental exchange times28-29 and an average theoretical lifetime of 165 fs.30 An earlier experimental study of the excess protons in liquid 10
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water showed that the Eigen and Zundel complexes and their ultrafast exchange can lead to broad overlapping spectral characteristics in the linear infrared spectrum,31 making classification of the Eigen and Zundel structures challenging. Likewise, the absence of the expected peak corresponding to the out-of-plane bending mode of the hydronium in the infrared spectrum of (N5)6(H3O)3(NH4)4Cl salt is understandable because the N5ˉ∙∙∙H3O+ ion pair also undergoes rapid evolution through various hydrogen-bonding configurations in the pentazolate salt.
Table 1. Computed average and maximum lifetimes for N5ˉ∙∙∙H3O+, H2O-H-N5, and H2O∙∙∙HN5 in the pentazolate salt at four different temperatures. Temperatur e
Average lifetime (fs)
Maximum lifetime (fs)
(K)
N5ˉ∙∙∙H3O+
H2O-H-N5
H2O∙∙∙HN5
N5ˉ∙∙∙H3O+
H2O-H-N5
H2O∙∙∙HN5
123
340
12
214
6069
208
2275
250
51
9
52
682
111
798
313
32
8
69
341
88
1001
390
20
8
53
239
114
785
CONCLUSION In
summary,
the
proton-transfer
mechanism
and
dynamics
behaviour
of
crystalline
(N5)6(H3O)3(NH4)4Cl have been studied using DFT (CI-NEB) calculations and AIMD simulations. The results show that the proton-transfer reaction is endothermic and occurs prior to the decomposition of cyclo-N5ˉ (i.e., without releasing any gas species). Hence, the thermal stability of the pentazolate salt cannot be assessed based on the thermogravimetry measurement alone because the thermogravimetry data may suggest a falsely high thermal stability. The asymmetric force on the H3O+ can effectively promote proton transfer, while there is a strong cooperative hydrogen-bonding effect involved in the proton-transfer reaction. As the temperature increases, the probability of proton transfer substantially increases. Because of the ultrafast interconversion between different hydrogen-bonding configurations, the peak corresponding to the out-of-plane bending mode of H3O+ may be masked by the broad features in the infrared spectrum of the pentazolate salt, resulting in its apparent absence from the experimental spectrum. These findings not only can resolve the recent debate on the possible 11
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existence of neutral HN5 species in the pentazolate salt but also provide conceptual guidance for the synthesis of compounds with pure cyclo-N5ˉ or HN5 species by tuning the intermolecular interactions associated with H3O+ and/or H2O.
ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website. Table S1 gives the calculated and experimental lattice parameters of the primitive cell of pentazolate salt. Figure S1 shows the gas-phase geometry optimization. Figures S2-S3 give the structures of the associated transition and intermediate states for decomposing an ion pair N5ˉ∙∙∙H3O+ into HN3, N2 and H2O, and the proton-transfer reactions in the pentazolate salt, respectively. Figures S4 gives the probabilities of different percentage of group of N5ˉ∙∙∙H3O+, H2O-H-N5, and H2O∙∙∙HN5 at 123 K, 250 K, 313 K and 390 K, respectively. Figures S5 displays the snapshots that several protons transfer simultaneously to form HN5 molecules from the actual simulation at various temperatures. Movies S1-S4 show the trajectories of the AIMD simulations at 123 K, 250 K, 313 K and 390 K, respectively.
AUTHOR INFORMATION # Authors contribute equally. Corresponding Authors *Email:
[email protected] *Email:
[email protected] ACKNOWLEDGMENTS This work is supported by the Scientific and Technological Research Program of Chongqing Municipal Education Commission (KJ15012002), and the Young Talented Researcher Plan of Yangtze Normal University (2014QNRC03). We thank computation support of UNL Holland Computing Center.
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