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. 2020 Sep 16;5(38):24946–24953. doi: 10.1021/acsomega.0c03835

Crystalline Structures and Energetic Properties of Lithium Pentazolate under Ambient Conditions

Wencai Yi †,*, Xingang Jiang †, Tao Yang ‡, Bingchao Yang †, Zhen Liu §,*, Xiaobing Liu †,*
PMCID: PMC7528499  PMID: 33015514

Abstract

graphic file with name ao0c03835_0009.jpg

Recently, it has been reported that high-pressure synthesized lithium pentazolates could be quenched down to ambient conditions. However, the crystalline structures of LiN5 under ambient conditions are still ambiguous. In this work, the structures of LiN5 compound were directly explored at atmospheric pressure by using a new constrain structure search method. By using this method, three new allotropes were confirmed, and they show lower energy than the previous reported LiN5 phases. Both their thermodynamic and dynamic stability were confirmed through formation enthalpies, phonon spectrum, and ab initio molecular dynamics simulations under ambient conditions. Moreover, these three allotropes show similar formation enthalpies and properties, which suggests that it is hard to obtain a single LiN5 phase, which is well consistent with the experimental phenomenon. Furthermore, because of their low formation energy, all of them possess low energy density when they directly decompose to Li3N and nitrogen (0.52 kJ/g). Instead, the decomposed energy could be further improved to 3.78 kJ/g when they decompose under an oxygen-rich environment.

1. Introduction

Pentazolate anion (cyclo-N5–) is receiving ever-increasing significant interest because of its potential application in high-energy density materials.1−9 Especially, since 2016, several breakthroughs have been witnessed in this field, including some metal-free pentazolate hydrates [such as (N5)6(H3O)3(NH4)4Cl salt] and metal salts {such as [Na(H2O)(N5)2]·2H2O, [Mn(H2O)4(N5)2]·4H2O and [Mg(H2O)6(N5)2]·4H2O} synthesized in experimentation under ambient conditions.10−21 However, the nonenergetic group (such as water and halogen) lowers the nitrogen concentration as well as energy density of these compounds.18,22 One important way to obtain nonenergetic group metal pentazolates (such as CsN5, NaN5) is by using high pressure and laser-heating, but few of them could be quenched down to ambient. In 2015, Peng et al. and Shen et al. independently predicted that LiN5 could be synthesized under high pressure (15–100 GPa) through theoretical prediction,23,24 and Laniel et al. successfully achieved this goal by the experiment method at 2018.25 Moreover, the synthesized compounds could remain stable when releasing pressure to ambient conditions. These reports are important for synthesizing and applying polynitrogen materials under atmospheric pressure. However, Laniel et al. could not obtain a single clean diffraction pattern containing solely the diffraction lines despite many attempts, and the crystalline structure of the LiN5 compound is still unclear.25

There are series of excellent reports that worked on predicting metal pentazolates, which usually can become thermodynamically stable under high pressure, such as CuN5, LiN5, NaN5, ZnN10, and AlN15.23,24,26−31 However, these predictions are hard to be directly applied to the ambient conditions, which require to directly search metastable structures. Notably, it is still a big challenge to directly find the most stable microstructures of metal pentazolate compounds by the pristine structure search algorithm because N2 molecules have much more selective advantages than the N5 ring in energy. Also, the structures were obtained from high-pressure search, and there is no guarantee that they have the lowest energy at atmospheric pressure and very often they do not.24,32 Recently, we have overcome this difficulty by proposing a constrained crystal structure search method to directly predict the most stable MgN10, AlN15, and CuN5 crystalline structure and property under ambient conditions.33−35 Although there are some theoretical reports on the structures of LiN5 compounds among 15–100 GPa, but the most stable phase structures still are not confirmed between 0 and 15 GPa. Hence, several basic questions are still in urgent need to be answered: (1) what is the most stable crystalline structure of LiN5 under atmospheric pressure? (2) How about their stability and energetic property? (3) Why can these compounds be stable under ambient conditions?

In this work, to answer the above questions, the constrained crystal structure search method was used to explore the crystalline structures between 0 and 15 GPa. Here, three possible new allotropes of LiN5 under the ambient condition were reported, and the structure phases between 0 and 15 GPa were confirmed in this work. Moreover, the stabilities of these structure phases were evaluated by formation enthalpies, phonon spectrum, and ab initio molecular dynamics (AIMD) simulations. These structures have a great possibility to coexist at a certain low pressure because they have very close formation enthalpy and similar properties, which could be used to explain that why Laniel et al. could not obtain solely the diffraction lines of the LiN5 compounds. Furthermore, these compounds show low energy density (about 0.53 kJ/g) when directly decompose to Li3N and N2. An alternative approach is to make LiN5 decomposing under an oxygen-rich environment, and the energy density would improve to 3.78 kJ/g.

2. Calculational Methods

The structure predictions were through a global minimization of potential energy surfaces based on the particle swarm optimization methodology as implemented in the CALYPSO code.36−38 The stoichiometric (LiN5)x (x = 2–6) up to 3000 structures was directly searched in our simulations under 1 atm. The cyclo-N5– was constrained as a group unit to produce initial structures, and all the structures were optimized by the local density functional theory (DFT) soft package until converged. Also, then, structures were ranked according to their enthalpy, and the top 50 structures were further optimized with finer convergence criteria and used for further stability analysis.

The local structural relaxations and electronic properties calculations were performed in the framework of DFT as implemented in the Vienna Ab initio Simulation Package (VASP).39,40 The one-electron wave function was expanded using a plane-wave basis set with an energy cutoff of 750 eV. The projector augmented wave method41 was used to describe the interactions between the ion and electron. Also, electron correlation was treated with the generalized gradient approximation with the Perdew–Burke–Ernzerhof (PBE) functional,42 in which 1s22s1 and 2s22p3 are treated as valence electrons for Li and N atoms, respectively. The atomic positions and lattice constants were optimized using the conjugate gradient scheme until the residual Hellmann–Feynman forces on each atom were less than 0.01 eV/Å, and the self-consistent field calculations were stopped until energy change was smaller than 1 × 10–5 eV/atom. Brillouin zone (BZ) integrations are performed using a Monkhorst–Pack43k-point mesh with a resolution of 2π × 0.03 Å–1. The phonon spectrum was calculated by the density functional perturbation theory method with a supercell containing about 100 atoms for different phases, as implemented in Phonopy.44 The AIMD simulations were implemented using an NVT ensemble with a large supercell containing about 100 atoms for different phases to evaluate their thermal stability. The Raman spectrum was calculated by CASTEP code, and the Raman peak (1331 cm–1) of diamond was used for peak position corrections.45 The convergence test results are shown in Figure S1, which prove that our computational parameters are reliable. The formation enthalpy (Hf) was calculated by using the following formula (refers to the reaction of 2·Li + 5·N2 → 2LiN5)

2. 1

in which enthalpy H is obtained for the thermodynamically stable structures of certain compositions at each given pressure. For pure N2, Pa3-phase, P42/mnm-phase, and P21/c-phase nitrogen crystal were considered.46 For pure Li, the bcc-phase, fcc-phase, cI16-phase, and Aba2-40-phase were considered.47 The decomposed energy (Ed) of LiN5 compounds was evaluated by directly decomposing with the reaction of 3·LiN5 → Li3N + 7·N2 by using the following formula

2. 2

in which energy H is obtained for the thermodynamically stable structures of certain compositions at 1 atm, and MLiN5 is the relative atomic mass of LiN5. Also, under an oxygen-rich environment, with the reaction of 4·LiN5 + O2 → 2·Li2O + 10·N2 was used to calculate the Ed by using the following formula

2. 3

All the calculations were assisted by qvasp.48

3. Results and Discussion

3.1. Formation Enthalpy and Energy Density

After thousands of times calculations and data screening, we get three new LiN5 allotropes, whose formation enthalpies are both negative at 1 atm. Their space groups are P6122, P212121, and Pnan, so they were named P6122-LiN5, P212121-LiN5, and Pnan-LiN5, respectively. As shown in Figure 1a, we listed the formation enthalpies of these seven LiN5 allotropes, including three new phases and four have already reported phases (obtained from high pressure) (named P21-LiN5, P21/m-LiN5P21/c-LiN5, and C2c-LiN5)23,24 in the pressure range of 0–15 GPa. Notably, the four allotropes, including P6122-LiN5, P212121-LiN5, Pnan-LiN5, and P21/c-LiN5, are more stable than the others because they have negative formation enthalpy at 1 atm (shown in Table 1). If ignoring the kinetic barrier, they show great possibility to be formed when their high-pressure-synthesized compounds were released pressure to ambient conditions. In particular, the formation enthalpy curve of P6122-LiN5 decreases very slowly when compared to other allotropes, which indicate that P6122-LiN5 is harder to directly form under high pressure. Furthermore, the formation enthalpy curve of P212121-LiN5 and P21/c-LiN5 is very close at 0–15 GPa (small than 0.07 eV/atom), and these two phases are with great possibility to coexist at low pressure that might be used to explain why Laniel et al. could not obtain solely the diffraction lines of the LiN5 compounds.25

Figure 1.

Figure 1

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(a) Formation enthalpies of LiN5 compounds under the pressure range of 0–15 GPa; (b) calculated thermodynamically stable ranges for LiN5 compounds under the pressure range of 0–100 GPa.

Table 1. Formation Enthalpy at 1 atm and Decomposing Energy Density with and without Oxidant.

name P6122 P212121 Pnan P21/c P21 P21/m C2c
formation enthalpy at 1 atm (eV/unit) –0.13 –0.05 –0.05 –0.06 0.38 0.57 0.51
decomposed energy without oxidant (kJ/g) 0.52 0.61 0.61 0.61 1.15 1.38 1.31
decomposed energy with oxidant (kJ/g) 3.68 3.78 3.78 3.78 4.31 4.55 4.48
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Also, the formation enthalpies at higher pressure of up to 100 GPa of these seven allotropes are listed in Figure S2, and as shown in Figure 1a, we add structural phase information at an unknown range of 0–15 GPa. Furthermore, as shown in Figure 1b, we confirmed that the P6122-LiN5 has lower formation enthalpy at 0–1 GPa, P212121-LiN5 occupied at 2–14 GPa, P21/c-LiN5 occupied in 14–15 GPa, P21/m-LiN5 occupied in 15–62 GPa, and C2/c-LiN5 at 62–100 GPa. Then, we list the decomposed energy of LiN5 with and without oxidant, as shown in Table 1. We can directly see the remarkable contradiction between high energy density and high stability, and the P6122-LiN5 shows the lowest energy density because of low formation enthalpy. All the LiN5 allotropes show low energy density (0.52–1.38 kJ/g) when directly decomposed under an oxygen-free environment. Also, the energy density improved to 3.68–4.55 kJ/g when directly decomposed under an oxygen-rich environment, which is higher than TNT. Considering the explosion pressure obtained from large amounts of gas N2 molecules released from an oxidizing reaction, the compounds of LiN5 are still great potential application in propellant and explosives.

3.2. Structure Features

As discussed above, here, we focus on the structures of LiN5 compounds with negative formation enthalpy, which include P6122-LiN5, P212121-LiN5, Pnan-LiN5, and P21/c-LiN5, because they have great possibility to maintain stability at ambient conditions. The lattice constant and Wyckoff positions of them are shown in Table S1. As shown in Figure 2a, P6122-LiN5 presents a hexagonal symmetry, each Li forms five bonds with the η5-N5 ring, and a half octahedral configuration around the Li atom is presented in the structure. The bond lengths of N–N are both about 1.32–1.33 Å, which is close to the typical N–N bond length of cyclo-N5– in [Mn(H2O)4(N5)2]·4H2O, and the nearly equal bond length indicates the good aromatic properties of cyclo-N5– in P6122-LiN5. Also, there are three type Li–N bonds, including the length of 2.31, 2.10, and 2.14 Å (Figure 2a), which is a bit larger than the average bond length (2.11 Å) of Li–N in P63/mmc-Li3N.

Figure 2.

Figure 2

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Unit cell of the (a) P6122-LiN5, (b) P212121-LiN5, (c) P21/c-LiN5, and (d) Pnan-LiN5 at 1 atm. Half octahedral and tetrahedral Li coordination units are composed of the compounds.

For P212121-LiN5, P21/c-LiN5, and Pnan-LiN5, they are all composed of the tetrahedral Li configuration unit, and each Li forms four bonds with the η4-N5 ring. Also, they just show different space groups. As shown in Figure 2b–d, the P212121-LiN5 and Pnan-LiN5 present a rectangular block lattice, and P21/c-LiN5 shows a monoclinic lattice. The bond lengths of N–N in P212121-LiN5, P21/c-LiN5, and Pnan-LiN5 compounds are all about 1.32–1.33 Å, which are close to the P6122-LiN5 phase, indicating good aromaticity in cyclo-N5–. The bond length of Li–N in P212121-LiN5, P21/c-LiN5, and Pnan-LiN5 phase is all about 2.10 Å, which is a bit smaller than the P6122-LiN5 phase. Hence, the similar coordination unit and bond length could result in very close formation enthalpy between these three phases at ambient conditions. Suffering from less coordination number, these three phases have a bit higher formation enthalpy (0.072 eV/atom) than P6122-LiN5, and these three phases show more homogeneous bonding features, which increases their possibility of coexisting at ambient conditions.

3.3. Stability Evaluations

Furthermore, the stabilities of these allotropes were evaluated by dynamic and thermodynamic analysis. All of these four structures were examined by calculating the phonon spectrum and density of states (DOS) and are shown in Figure 3a–d. No imaginary phonon frequency is found in the whole BZ, indicating that all of these allotropes are dynamically stable at 1 atm. We can see from phonon-projected DOS (PDOS) of all LiN5 allotropes that the high-frequency modes (>22 THz) are contributed by N–N vibrations modes, which suggest that the N–N bonds are very strong. Also, the phonon PDOS overlaps between Li+ cation and cyclo-N5– anion at about 8–12 THz, suggesting that the interactions between Li+ cation and cyclo-N5– anion are quietly strong. Also, the weak phonon modes have been resulted from the translational motion of LiN5 lattice.

Figure 3.

Figure 3

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Phonon dispersion curves for (a) P6122-LiN5, (b) P212121-LiN5, (c) P21/c-LiN5, and (d) Pnan-LiN5 at 1 atm.

Furthermore, we used AIMD simulations to evaluate the thermodynamic stability of these allotropes. As shown in Figure 4a–d, the total energies of these allotropes both fluctuate around a certain energy level, the fluctuations are quite small, and the images of the geometry structure at the end of simulations clearly reveal that the structural skeleton did not suffer a large shape change up to 600 K. When temperature increases to 800 K, as shown in Figure S3a–d, the total energies experience violent vibration around the reference energy line, and the structures at the end of simulations clearly revealed that the cyclo-N5– maintains its structural skeleton, except for clear change for Li tetrahedron. When temperature continues to increase to 1000 K, cyclo-N5– decomposed to N2 molecules. The simulation results were consistent with our previous reports33 that the N–N bonds are harder to be decomposed than the metal–N bonds, suggest that it is much easier to isolate cyclo-N5– from metal pentazolate compound than phenylentazoles.49

Figure 4.

Figure 4

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Images for the equilibrium structures at the end of 10 ps AIMD simulations and fluctuations of the total energies of (a) P6122-LiN5, (b) P212121-LiN5, (c) P21/c-LiN5, and (d) Pnan-LiN5 at 600 K.

3.4. Bonding Analysis

Electron localization function (ELF) is a measurement of the possibility to detect an electron at a given spatial point. In Figure 5a–d, the red area is close to 1.0 probability to detect electrons while the blue area is 0 possibility to find electrons. ELF was used to evaluate the bond property and strength of Li–N bond, and Figure 5a–d clearly shows that the localized electrons are between N and N atoms and between Li and N atoms in all LiN5 allotropes, indicating that there might form a strong covalent bond between N and N atom in cyclo-N5–, and Li atoms form coordinate bonds with the lone pair electrons of N atoms.

Figure 5.

Figure 5

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Sectional view of ELF along the cyclo-N5– plane of (a) P6122-LiN5, (b) P212121-LiN5, (c) P21/c-LiN5, and (d) Pnan-LiN5 at 1 atm. The Bader charge of each atom is marked in the structures of (e) P6122-LiN5, (f) P212121-LiN5, (g) P21/c-LiN5, and (h) Pnan-LiN5 at 1 atm. The integrated crystal orbital Hamilton populations (−ICOHPs) between Li and N atoms and between N and N atoms are marked in the structures of (i) P6122-LiN5, (j) P212121-LiN5, (k) P21/c-LiN5, and (l) Pnan-LiN5 at 1 atm.

The charge information on each atom was further calculated by Bader’s quantum theory of atoms in molecules50,51 and is shown in Figure 5e–h, and we can see that the Li atoms play a role of the electron-donating unit, and each Li atom loses about 0.86 electrons to cyclo-N5– and shows +1 valence state. The charge distribution on cyclo-N5– is more homogeneous (0.10–0.20) than many known pentazolates (Figure S4), which reveals good aromaticity in these compounds. Especially in P6122-LiN5, each Li atom has five coordination number, every N atom in cyclo-N5– is coordinated with the Li atom, and the electrons on the N atom in cyclo-N5– are roughly equal, which caused better aromatic property and lower formation enthalpy than other allotropes.

We employ crystal orbital Hamilton population (COHP) to analyze the bond strength quantitively. COHP is an energy-weighted DOS, which describes bonding and antibonding state arrangements in the band energy scale. Moreover, −ICOHP was used to estimate the overlap strength of N–N bonds and Li–N bonds, which was calculated by using the LOBSTER program.52 The larger positive value means stronger bonding between two atoms. As shown in Figure 5i, the −ICOHP is 0.58–0.72 for Li–N bonds and 13.89–13.93 for N–N bonds in P6122-LiN5, which again revealed that there formed a strong chemical bond between Li–N and N–N, and N–N bonds are much stronger than Li–N bonds, and the Li–N bonds would be broken first in AIMD simulations. For other LiN5 allotropes (Figure 5h–l), the −ICOHP is 0.69–0.85 for Li–N bonds and 13.84–14.45 of N–N bonds, and the bond strength of Li–N is a bit stronger than P6122-LiN5, but the homogeneity of N–N bond is a bit weaker than P6122-LiN5.

The calculated electronic band structure of LiN5 allotropes is shown in Figure 6a–d. The results reveal that these two LiN5 compounds are both semiconductors with a large band gap (both than 5 eV) at the PBE level at 1 atm. Considering density functional calculations usually lead to a considerable underestimation of the energy gap, and the actual band gaps are expected to be larger than the calculated results, thus the LiN5 compounds would present the transparent crystal at ambient conditions because large optical band gap will induce weak visible light absorption.34 The band gap as a function of pressure is shown in Figure S5 from the range of 0–15 and 0–100 GPa. The band gap of all LiN5 allotropes decreases with the increase of pressure, and they still show a big band gap at high pressure except P6122-LiN5, which is consistent with the experimental phenomenon that microphotographs appear translucent at 52.0 GPa.25

Figure 6.

Figure 6

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Electronic structure of (a) P6122-LiN5, (b) P212121-LiN5, (c) P21/c-LiN5, and (d) Pnan-LiN5 at 1 atm (calculated at the PBE level).

The Raman spectrum of experimental data and all the LiN5 allotropes under ambient conditions is shown in Figure 7, and more detailed low-intensity Raman peaks are shown in Figure S6. The calculated results reveal that the breathing and stretching cycle-N5– Raman modes could still be measured at peaks around 1200, 1130, and 1035 cm–1 in all LiN5 allotropes. The faint low-frequency peak (364 cm–1) is observed in P212121-LiN5, P21/c-LiN5, and Pnan-LiN5 (both 374 cm–1), and these results are well consistent with the experimental.25 Moreover, many newly observed low-intensity peaks are marked in Figure 7, and except P6122-LiN5, all other allotropes are possible to exist or coexist in experimental synthetic samples, which could be used to make clear that why Laniel et al. cannot get solely the diffraction lines of the LiN5 compounds despite many attempts.

Figure 7.

Figure 7

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Raman spectrum of the experimental data and the LiN5 allotropes at 1 atm. The experimental data were obtained by WebPlotDigitizer from ref (25) as a comparison.

4. Conclusions

In summary, here, we reported three new LiN5 compounds with negative formation enthalpy and supplemented the structure phases between 0 and 15 GPa. The stability of them is both confirmed by the phonon simulations, AIMD simulations, and bonding analysis. The calculated results reveal that the N–N bonds are harder to decompose than Li–N bonds, and the cyclo-N5– can be maintained at least to 600 K, which is enough to be as a metastable explosive material at ambient conditions. The electronic calculations suggest that these allotropes are transparent crystals. Also, the similar formation enthalpy, coordination features, electronic structure, and Raman spectrum indicate that these allotropes show great possibility of coexisting at atmospheric pressure, which could be used to explain that why Laniel et al. could not obtain solely the diffraction lines of the LiN5 compounds despite many attempts. Moreover, our calculated results also reveal that LiN5 could be applied under a strong oxidant environment (energy density is up to 3.78 kJ/g).

Acknowledgments

We sincerely thank Prof Maosheng Miao for his helps and discussions. This work was supported by the National Natural Science Foundation of China (grant nos. 21905159, 11974207 and 11974208), Natural Science Foundation of Shandong Province (grant nos. ZR2019BA010, ZR2019MA054, and 2019KJJ020), and the Project of Introduction and Cultivation for Young Innovative Talents in Colleges and Universities of Shandong Province. Calculations were performed at the High-Performance Computing Center (HPCC) of Qufu Normal University.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.0c03835.

  • Crystal detail; formation enthalpies under 0–100 GPa; AIMD simulations results at 800 K; band gap change with pressure; Bader charge of known pentazolates; and Raman spectrum with low-intensity peaks (PDF)

The authors declare no competing financial interest.

Supplementary Material

ao0c03835_si_001.pdf (931.7KB, pdf)

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