Towards understanding the stability of the N₅⁺-containing salts: the role of counterions

Abstract

The thermal stabilities of the N₅⁺M⁻ species (M = Sb(OH)₆, Sb(OH)₄F₂, AlF₆, AlF₄, BF₄, B(CF₃)₄, PF₆, AsF₆ and SbF₆) have been studied by means of density functional theory. The present calculations indicate that their thermal stabilities (represented by activation enthalpy, ΔH^≠ in kcal mol⁻¹) decrease in the order N₅⁺ (47.2) > N₅B(CF₃)₄ (34.1) ≈ N₅SbF₆ (31.6) ≈ N₅AsF₆ (31.5) > N₅PF₆ (30.5) > N₅AlF₄ (27.1) ≈ N₅BF₄ (27.1) > N₅AlF₆ (8.5). Only N₅SbF₆ has a small positive reaction enthalpy, Δ_rH. The thermal stability of the N₅⁺ salt depends on the amount of electron transfer from the counterion to N₅⁺ in the reaction. The high electronegativite atoms or groups in the counterion are essential. Another crucial factor is bond strength between the central ion and the ligand. Studies of the N₅Sb(OH)₄F₂ isomers indicate that the OH rather than the fluorine ions in the axial coordination positions could stabilize the decomposition transition structure through partial dissociation of the Sb–OH bond, which is used to explain the reason why there is an obvious difference in the decomposition activation enthalpies of the three isomers.

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Introduction

Polynitrogen compounds have received great attention as high energy density materials (HEDMs) for propulsion or explosive applications.^1–7 Although a wealth of theoretical calculations have indicated that N_n (n = 4, 6, 8, 11) systems may exist in acyclic forms or linear structures,^8–14 no such compounds have yet been successfully synthesized^15,16 because of their extreme instability. Inspiringly, N₅AsF₆ was successfully synthesized in 1999 (ref. 17) by Christe, which caused an instant sensation and shocked the world. Indeed, N₅AsF₆ was considered as only the third known compound containing a stable homoleptic polynitrogen moiety, after N₂ isolated in 1772 by Rutherford and N₃⁻ first synthesized in 1890 by Curtius.¹⁸ However, this white solid was only marginally stable at 22 °C and the damage it caused during low temperature Raman analysis revealed its instability. In 2001, N₅SbF₆ (ref. 19) was successfully obtained and proved to be more stable, decomposing only at above 70 °C.

To date, a total of 12 N₅⁺-containing salts have been synthesized,^17,20,21 among which N₅SbF₆ is the most stable. In more than a decade, no further novel N₅⁺-containing salts with better thermal stability have been synthesized. Most published papers on N₅⁺-containing salts focused on their synthesis and properties, whereas there seems to have been limited research on the mechanism of their thermodynamic stability.^22,23 Questions arise, such as why N₅SbF₆ has quite high thermal stability. In order to gain insight into the role of the central Sb atom as well as of the ligand F atoms in SbF₆⁻, other N₅⁺M⁻ salts (M = Sb(OH)₆, SbF₂(OH)₄, BF₄, B(CF₃)₄, AlF₄, AlF₆, AsF₆, and PF₆) (Scheme 1) have been selected for a comparative study.

Scheme 1 The strategy employed to study the root of the thermal stability of N₅SbF₆.

Computational details

All calculations were performed using the Gaussian 09 package.²⁴ Geometry optimizations of the starting structures were carried out at the M06-2X (ref. 25) level with the 6-311+G(d) basis set for B, C, N, F, Al and P atoms and SDD for other heavy metal atoms.²² Each optimized structure was confirmed as local energy minima on the potential-energy surface without imaginary frequencies. Note that M06-2X functional is very suitable to multi-nitrogen or pure nitrogen molecules according to previous studies.²⁶

Thermal stability is a key factor in evaluating the synthetic possibilities, and is closely related to the activation enthalpy of thermal dissociation (ΔH^≠), which is determined by the transition state (TS). Calculations were performed to obtain the barrier heights in order to further discuss the relative stability of the relevant compounds. Activation enthalpy (ΔH^≠) was calculated according to eqn (1):

ΔH^≠ = ΔH_TS − ΔH_R (1)

where ΔH_TS and ΔH_R represent the enthalpies of the transition state and the reactant, respectively.

Results and discussion

Geometries of N₅⁺M⁻

The structure of N₅SbF₆ (see structure 2 in Fig. 1) was in good agreement with the reported data,²³ which proved that our employed method was reliable. The obtained structures of N₅⁺-containing salts 1 to 11 are depicted in Fig. 1 and 2, in which compounds 3, 4, 10, and 11a–11c are the novel designed complexes indicated in Scheme 1. Selected bond lengths are listed in the figures.

Fig. 1 Geometrical structures of the N₅⁺ complexes in which the central atom Sb was substituted by Al, P, B, As and Sn with selected bond length shown in the structures.

Fig. 2 Geometrical structures of the N₅⁺ complexes in which the ligand F was substituted by OH and CF₃ in N₅SbF₆ and N₅BF₄ with selected bond length shown in the structures.

The structural difference between the compounds 3, 4 and 5–8 in Fig. 1 is that they have the same ligand F but different central atoms, P, Al, As and Sn, respectively. The four compounds 2, 11a, 11b, and 11c in Fig. 2 have the same central atom Sb, but four or six of the fluorine atoms in N₅SbF₆ are substituted by OH. Compounds 11a, 11b, and 11c are structural isomers with the same C₂ point group. They differ in the positions of the two fluorine atoms of the counter-ion. From the bond length shown in Fig. 1 and 2, it is noteworthy that the bond lengths in the isolated N₅⁺ unit are slightly longer than those in the other N₅⁺ salts, except in the case of structure 3 (N₅AlF₆), in which the N(1)–N(3) bond length (1.311 Å) is longer than that in the isolated N₅⁺ unit (1.300 Å). These data showed that the central Al ion is strongly bonded with only four fluorine anions, while the other two fluorine ions are clearly away from the central Al ion through observation of the Al–F bond lengths of 1.784–1.961 Å in 3 (N₅AlF₆) and 1.664–1.727 Å in 4 (N₅⁺AlF₄⁻). These indicate the stronger Al–F bonds in the latter. Additionally, the Sb(6)–F(7) and Sb(6)–F(8) bond lengths (1.959 Å) in N₅SbF₆ are clearly shorter than the corresponding Sb–F bond lengths (2.002 Å) in 11a. The similar cases are also observed through comparison of the bond lengths between Sb(6)–F(9) in 2 and Sb(6)–F(7) in 11b, Sb(6)–F(10) in 2 and Sb(6)–F(7) in 11c. Combined with N₅⁺SbF₆⁻ results, N₅⁺ with a high oxidation potential influences the Sb–F bond length. Moreover, the numbers of fluorine in counterion clearly influence the electronegativity, which results in the difference of Sb–F bond length. These structural differences could reflect the variation of stability of the Sb-containing N₅⁺ salts.

Decomposition mechanism of N₅⁺M⁻

For the thermal decomposition of isolated N₅⁺, the activation enthalpy was estimated to be 47.2 kcal mol⁻¹, indicating that N₅⁺ has a good thermal stability. In addition, we explored the electronic spin reverse, i.e. the photodissociation and coupling of thermal cracking events that may occur during the thermal dissociation of the N₅⁺ cation. The energy curves for both the triplet and singlet states of N₅⁺ are shown in Fig. 3. As the reaction coordinate changes, there is a crossover point between the two states of N₅⁺. The actual thermal dissociation process should initiate from the reactant to the crossover point; thereafter, this process continues along the triplet potential energy surface of N₅⁺ to the products, the linear triplet N₃⁺ and N₂, as suggested by Nguyen.⁵ The energy difference between the crossover point and the reactant was estimated to be ca. 35.6 kcal mol⁻¹. The above analysis indicates that the N₅⁺ is thermally stable in the gas phase.

Fig. 3 The energy curves for both the triplet and singlet states of N₅⁺ during its dissociation process.

When N₅⁺ is combined with M⁻, the decomposition mechanism of N₅⁺ should be similar to that in its isolated case. Table 1 showed NPA charge plus of all nitrogen atoms of N₅⁺ salts in the reactant and their decomposition transition states.

Table 1 NPA charge plus of all nitrogen atoms of N₅⁺ salts and their decomposition transition states^a

a qN (a) represents the NPA charge plus of all nitrogen atoms of each salt in the reactant state. qN (b) represents the NPA charge plus of all nitrogen atoms of each salt in the decomposition transition state.
Compound	N5AlF4	N5AlF6	N5AsF6	N5SbF6
qN (a)	0.958	0.756	0.961	0.964
qN (b)	0.783	0.386	0.786	0.785
Compound	N5BF4	N5B(CF3)4	N5PF6	N5Sb(OH)6
qN (a)	0.952	0.970	0.959	0.941
qN (b)	0.744	0.789	0.778	0.624
Compound	11a	11b	11c
qN (a)	0.940	0.952	0.942
qN (b)	0.664	0.718	0.645

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From Table 1 we can find the partially negative charges (ca. 0.03–0.05e) transfer from the counterion to N₅⁺ of the salt in the reactant states. N₅AlF₆ has the most amount of charge transfer. These results discover the intermolecular essentially electrostatic interaction between M⁻ and N₅⁺. Moreover, this interaction can further induce N₅⁺ decomposition into N₂ and more oxidative N₃⁺, which results in more negative charge transfer from the counterion to the N₂⋯N₃⁺ complex, seen in Table 1. Ultimately, N₃⁺ can capture one F anion of the counterion to form N₃F product (seen in ESI†). Thus, the stronger the ability of M⁻ to retain electrons in the decomposition reaction, the more stable the N₅⁺M⁻ species is.

The role of the central atom in stabilizing N₅⁺M⁻

To study the role of the central atom in stabilizing N₅⁺, we replaced Sb in N₅SbF₆ with Al, B, P and As. Table 2 lists the thermal decomposition activation enthalpy (ΔH^≠) and reaction enthalpy (Δ_rH) of the N₅⁺-containing salts. Calculations show that the thermal stability is in the order N₅B(CF₃)₄ ≈ N₅SbF₆ ≈ N₅AsF₆ > N₅PF₆ > N₅AlF₄ ≈ N₅BF₄ > N₅AlF₆. On one hand, the larger volume of the counterion favors improvement of the thermal stability of the salt. On the other hand, the present reactivity order is clearly explained through the amount of the negative charge transfer from the counterion to N₅⁺ during the reaction procedure, seen Table 1. An interesting case is found for N₅AlF₆, where the two fluorine ions in the equatorial positions are obviously separated from the central Al ion. The partially dissociated Al–F bond suggests that the two F ions could be not strongly bound by the central Al ion so that F ion tends to shift to N₅⁺, which could promote decomposition of the N₅⁺ cation. The shorter Al–F bond in N₅AlF₄ indicates stronger interaction between Al and F, which is relatively more difficult to be broken in the decomposition reaction. This is why AlF₄⁻ should be preferred over AlF₆⁻ to stabilize N₅⁺. Both activation and reaction enthalpies calculations indicated that N₅AlF₄ is more stable than N₅AlF₆, which is consistent with the conclusion that the bond strength between the central atom and the ligand is significant for N₅⁺ stability. The more strongly bound F anion in SbF₆⁻ and AsF₆⁻ has a relatively less chance for dissociation of F anion so as to approach N₅⁺, which leads to their higher thermal stability. Moreover, comparison of thermodynamics between N₅BF₄ and N₅B(CF₃)₄ salts shows that group B(CF₃)₄⁻ with higher electronegativity should be preferred to stabilize N₅⁺. Note that the reaction enthalpy of N₅SbF₆ is only small positive among the salts, which shows that the salt has not only dynamic stability but thermodynamic one. Though N₅PF₆ has the barrier height close to N₅SbF₆, more exothermic decomposition reaction of N₅PF₆ could be one of the reasons why the salt is not stable enough in room temperature.

Table 2 Activation enthalpy (ΔH^≠) and reaction enthalpy (Δ_rH) of N₅⁺ complexes (in kcal mol⁻¹)

Compound	N5AlF4	N5AlF6	N5AsF6	N5SbF6
ΔH^≠	27.1	8.5	31.5	31.6
ΔrH	−4.7	−56.9	−2.5	+1.2
Compound	N5BF4	N5B(CF3)4	N5PF6
ΔH^≠	27.1	34.1	30.5
ΔrH	−17.5	−0.2	−10.9

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The role of fluorine atoms in stabilizing N₅⁺M⁻

All known stable N₅⁺-containing salts have F atoms in their counterions. To better study the role of fluorine ion in stabilizing N₅⁺M⁻, the OH group was selected to substitute F because OH and F are isoelectronic and moreover, oxygen and fluorine have the closest electronegativities among all single atoms. The calculated activation energy of N₅Sb(OH)₆ is 19.1 kcal mol⁻¹, which is much lower than that of N₅SbF₆ (30.3 kcal mol⁻¹).

This large thermal stability difference between N₅Sb(OH)₆ and N₅SbF₆ should originate from the different electronegativity of fluorine and OH. Fluorine has higher electronegativity than OH, and for the same central atom Sb, the bond strength of Sb–F is greater than that of Sb–OH. Thus, electrons are more favorably bound in SbF₆⁻ and less charge is transferred to N₅⁺ to accelerate its dissociation, compared with the case in N₅Sb(OH)₆. Considering that fluorine has the highest electronegativity of any single atom, we may reasonably infer that fluorine is indispensable in stabilizing N₅⁺-containing salts if the ligand is a single atom. Additionally, seeking other potential functional groups with high electronegativity contained in the counterion might be helpful to improve the stability of the N₅⁺ salts.

There are six fluorine ions in SbF₆⁻, and a further question that arises is which of these plays a major role in stabilizing N₅⁺. In order to ascertain the position of the functional fluorine ions, we studied the N₅Sb(OH)₄F₂ isomers – 11a, 11b, and 11c. Calculations show that the relative enthalpy of the above isomers is 0.0 (11a), 0.8 (11b), and 0.3 (11c) kcal mol⁻¹ in their reactant states. However, the relative enthalpy is 0.0 (11a), 7.7 (11b), and −0.6 (11c) kcal mol⁻¹ in their transition states. The order of their activation barriers is 11b (28.6) > 11a (21.7) > 11c (20.8). These data clearly show that the stability variation among the isomers should be attributed to the difference of their total energies in the transition states. NBO calculations show that in the decomposition transition structure of 11b, there are the smallest charge amounts transferred from the counterion to N₅⁺ decomposition structure, which corresponds to the highest reaction barrier height among the decomposition reactions of the three isomers. Actually, the two fluorine atoms in the axial coordination positions of 11b are relatively not favorable to stabilize the transition structure. Comparison of the transition structures of the three isomers discovers that the two OH ions in the axial coordination positions of 11a and 11c should be better selection to stabilize the transition structures with respect to lower barrier heights. The case should be attributed to the stronger Sb–F than Sb–OH bonds so that the former is relatively more difficult to be ruptured to form F ion. Thus, the bound F has no enough negative charge on itself to stabilize the formed N₃⁺ fragment in the transition structure. In 11a and 11c, one of the axial coordination OH anions could stabilize the N₃⁺ fragment in the transition structure through Sb–OH partial bond dissociation. The remaining two fluorine ions should also contribute to stabilize N₅⁺, whether they are close to or far away from the formed N₅⁺ fragment. This is consistent with the conclusion of 11a and 11c having almost the same barrier heights.

Conclusions

Density functional theory studies have indicated that the interaction between M⁻ ion and the N₅⁺ cation causes thermal instability in the latter. Strong bonding between the central atom and the ligand atom in the counter anion is significant for holding ligand anion in M⁻ so as to favour N₅⁺ stability. Among the simple single-atom ligands, fluorine is the best choice due to its highest electronegativity. In addition, fluorine atoms in specific positions show greater contributions to control the N₅⁺ decomposition. We hope that our theoretical work could provide a useful contribution for future synthesis of the novel and more complex anions to stabilize N₅⁺.

Acknowledgements

The authors gratefully acknowledge the support of the Foundation of NSAF (No. 11176004).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c5ra16304h

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