Energyefficient nitrogencontaining atomic systems and nanomaterials based on them for the new generation energy sources
This webpage contains the main results of computer simulation of pure nitrogen and nitrogencontaining highenergydensity materials obtained in the framework of the scientific project “Energyefficient nitrogencontaining atomic systems and nanomaterials based on them for the new generation energy sources” that is supported by the Russian Foundation for Basic Research (RFBR) (Grant No. 183220139 mol_a_ved).
Why is nitrogen the fuel of the future?
A significant amount of energy can be released in the decomposition of metastable nitrogencontaining atomic clusters due to the formation of the N2 molecules. So for the pure nitrogen clusters energyrelease exceeds 2 eV/atom (energy of the system is reduced greatly due to the rupture of single covalent N–N bonds and the formation of triple N–N bonds). For this reason, nitrogencontaining atomic clusters are regarded as the functional units of highenergy materials and nextgeneration fuels of highdensity energy stored (HEDM – highenergydensity materials).
What is needed to be done to accelerate the dissemination of nitrogen as fuel?
Despite the intensive research stimulated by the successful synthesis of polymeric nitrogen and the number of small charged nitrogen clusters and nanomaterials based on them in early 2000s, until now the pure nitrogen structures, which are stable at atmospheric pressure and room temperature are not obtained. At the same time, some highenergy organic clusters containing in addition to nitrogen carbon, oxygen and hydrogen atoms (e.g., CL20, polynitrocubane, etc.) exhibit high thermal stability. Therefore, proper nitrogen stabilization is the key to its dissemination as a fuel. Stabilization can be carried out in different ways: a) the boundary/surface doping (passivation), b) the formation of endohedral complexes (the introduction of pure nitrogen clusters inside the carbon cage), and c) the creation of the combined carbon/siliconnitrogen framework. Examples are shown in Figure 1.
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Figure 1 – Examples of nitrogen stabilization: nitrogen nanotube edge doping with hydrogen atoms (a), N_{8}@C_{60} endohedral complex (b), carbonnitrogen CL20 framework (c). 
Structural features indicating the stability of nitrogen cages
After the traditional carbon fullerenes were discovered, the isolatedpentagon rule (IPR) was proposed. This rule can be formulated as follows: the most stable carbon fullerenes are those in which no two pentagons share an edge, that is, each pentagon is completely surrounded by hexagons. Unfortunately, for nitrogen fullerenes, this rule turned out to be inapplicable. We were able to note a number of topological features that may indicate the stability of nitrogen cages or quasifullerenes. So, stable structures are those in which sixmembered nitrogen rings (hexagons) are absent or maximally distant from each other and/or nitrogen atoms in adjacent hexagons do not lie in the same plane, forming (due to concavity) the socalled “nitrogen boats”. The first case includes N_{20} or N_{24} fullerenes, and the last case includes the extended nitrogen nanotubes, see Figure 2.
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Figure 2 – Stable nitrogen fullerenes N_{20} (left) and N_{24} (right) (a) and capped nanotube (b) with characteristic structural features indicating the stability. 
Stable nitrogen quasifullerens are presented in Figure 3.
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Figure 3 – Stable nitrogen quasifullerenes: N_{6} (a), N_{8} (b), N_{8} (c), N_{10} (d), N_{10} (e), N_{12} (f), N_{12} (g), N_{14} (h), and N_{16} (i). 
Nitrogen nanotubes
We apply the density functional theory to investigate structural, energetic, and electronic properties and stability of extended armchair and zigzag nitrogen nanotubes with a length of ≈ 3 nm. The capping effect, as well as the passivation of nanotubes’ ends by hydrogen atoms and hydroxyl groups on their stability, are studied. According to our calculations, pristine nitrogen nanotubes are unstable. Both capping and passivation of the nanotube end provide thermodynamic stability only for (3,0) and (4,0) zigzag nitrogen nanotubes (see Figure 4). Moreover, the calculated frequency spectra of considered systems confirm their dynamic stability. The calculated HOMOLUMO gaps for these stable extended systems are of the order of 4 eV, so they can be assigned to the class of insulators. It is shown that nitrogen nanotubes are able to store a large amount of energy and can be used as a basis for new highenergydensity materials.
Figure 4 – Atomic structures of the capped nitrogen nanotubes (a) (3,0)NNT(N_{102}), (b) (3,0)NNT(N_{98}), (c) (4,0)NNT(N136). Topside view and bottomtop view. Symbols l_{} and l_{┴} correspond to the interlayer and intralayer NN bonds in the distance of the capped ends, respectively. 
Table 1 presents the values of HOMOLUMO gaps ΔHL and binding energies E_{b}.
Table 1. Binding energies (E_{b}) and HOMOLUMO gaps (Δ_{HL}) for the stable nitrogen nanotubes. 
To estimate the stored energy in our stable nitrogen nanotubes, we determine the reaction energy for one atom
is equal to 1.88 eV/atom. This value is comparable with the calculated energy difference ΔE[N_{4}→2N_{2}]=2 eV/atom for experimentally synthesized N_{4}, which demonstrates the prospects of using these systems as the highenergydensity materials (Figure 5).
Figure 5 – Schematic illustration of energy release during the nitrogen nanotube decomposition into the molecular nitrogen. 
So, only (3,0) and (4,0) zigzag nitrogen nanotubes with extremely small diameters can be stable under ambient conditions. Their stability can be achieved via the capping or passivation of their ends by the hydrogen atoms or hydroxyl groups. Among all the systems considered, the most energetically feasible is the (3,0) nitrogen nanotube with passivated by hydrogen atoms ends. It can release a large amount of energy during the decomposition to the isolated nitrogen molecules.
Nitrogen astralenes
Nitrogen astralenes is a new class of purely nitrogen systems. Nitrogen astralenes are the complex molecular covalent forms built from the fragments of nitrogen nanotubes and nitrogen fullerenes. Examples of nitrogen astralenes are presented in Figure 6.
Figure 6 – Examples of elementary nitrogen astralenes. 
On the basis of nitrogen astralenes, the formation of a wide variety of covalent highenergy crystals is possible through the direct covalent bonding of isolated astralenes (see Figure 7).
Figure 7 – Fragments of nitrogen covalent crystals based on the nitrogen astralenes. 
Cubane inside the fullerene
Within the framework of this project, we analyze how the C_{60} shell affects the stability of the nitrogen cubane system N_{8} placed inside. Cubic N_{8} system is the allnitrogen analogous of wellknown hydrocarbon cubane C_{8}H_{8}, which is the basis of the broad family of the already synthesized highenergydensity materials. The N_{8} effective size is a reasonable compromise between rather small highly strained systems (N_{4}, N_{6}) and too large clusters (N_{10}, N_{12}), which is quite difficult to place inside the C_{60}. The cubic structure of N_{8} was found to be stable: its lowest vibrational frequency by some estimates was about 530 cm^{1}. Because of its strained structure, N_{8} cage possesses higher total energy than the other nine possible N_{8} isomers. On the other hand, the relative energies of different competitive isomers can change under the action of spatial constraints. Cubic system N_{8} has the smallest effective diameter among all N_{8} isomers, and its shape and size are very suitable for the encapsulation inside the nearly spherical C_{60}.
Using the original method of finding the saddle configuration implemented in the NTBM program (ntbm.info), we are able to determine the decomposition scheme of the isolated cubane N_{8} and cubane N_{8} inside the C_{60} cage, as well as to calculate the minimum energy barrier U preventing the caged cubane decomposition. Figure 8 presents the isolated N_{8} decomposition path, and Figure 9 shows the N_{8} decomposition path inside the fullerene cage.
Figure 8 – The mechanism of the isolated cubane N_{8} decomposition. I_{s0} is the initial configuration corresponded to the energy minimum, TS is the transition state or saddle point, and I_{s1} is the decomposition product represented by the nitrogen molecules. 
Figure 9 – The mechanism of cubane N_{8} decomposition inside the fullerene C_{60}. I_{s0} corresponds to the undistorted configuration cubane@C_{60}, TS is the transition state or saddle point, and I_{s1} is the decomposition product represented by the nitrogen molecules attached to the inner surface of the fullerene cage. 
The kinetic stability of the system is determined by the height of the minimum energy barrier separating I_{s0} from I_{s1}. The detailed analysis shows that the lowest energy path of both isolated and caged cubane N_{8} rearrangement leads to the molecular nitrogen through the single saddle configuration (see Figures 8 and 9). However, in the case of caged N_{8}, the nitrogen molecules N_{2} can be covalently bound with the inner surface of the fullerene cage (Figure 9). According to our calculations, the value of U equals 0.11 eV for the isolated cubane molecule and 0.20 eV for the caged one. It should be noted that the energy barrier U for the encapsulated cubane is twice as large as the corresponding value for the isolated one. Thus, the fullerene cage significantly increases the stability of the N_{8} cube.
To analyze the kinetic stability of N_{8} inside the fullerene cage in detail and follow the decay process in realtime, we perform the molecular dynamics simulation for the N_{8}@C_{60} complex at different temperatures. The activation energy E_{a} of cubane decomposition is determined by analyzing the temperature dependence of its lifetime τ using the Arrhenius equation. Approximating the inverse temperature dependence of ln(τ) by a straight line, we can determine activation energy E_{a} and frequency factor A by the slope angle of this line and its yintercept, respectively. These values and their standard deviations are found to be E_{a}=0.18±0.01 eV and A=10^{15.23±0.37} s^{1}.
The molecular dynamics data obtained allowed us to find the temperature dependence of the caged N_{8} lifetime and to determine the activation energy and the frequency factor for its decay. These data are confirmed by the transition state search and further calculation of the minimum energy barrier preventing the decay. It is confirmed that the C_{60} significantly increases the stability of the N_{8} cube.
CL20 frameworks
A CL20 based cages in which carbon/oxygen atoms are replaced by silicon/fluorine ones (Figure 10) are studied using the ab initio molecular dynamics, density functional theory, and timedependent density functional theory. In contrast to the pristine CL20, the first step of the pyrolysis of these cages is the migration of oxygen/fluorine atoms to silicon. Molecules containing fluorine are unstable at room temperature. The highenergy siliconcontaining molecule (CSi_{5}H_{6}N_{12}O_{12}) is approximately as stable as pristine CL20. The energy barrier preventing its decomposition is about 200 kJ/mol. Energies of the frontier orbitals and reactivity descriptors of CSi_{5}H_{6}N_{12}O_{12} are very close to the corresponding values of pure CL20. All studied cages can form covalent dimers via the methylene molecular bridges. It is found that the reactions of dimerization are exothermic. Dimers’ isomers in which silicon atoms are located closer to the methylene bridges possess lower internal energies. It is found that the mechanisms of dimers’ thermal decomposition are similar to the analog mechanisms of corresponding monomers. The dimerization of the cages results in the redshifts of their ultraviolet spectra.
Figure 10 – Atomic structures of C_{6}H_{6}N_{12}O_{12} (CL20, 1) (a) and its substituted derivatives CSi_{5}H_{6}N_{12}O_{12} 2 (b) and C_{4}Si_{2}H_{6}N_{12}F_{12} 3 (c). Grey, blue, red, white, brown, and green circles correspond to carbon, nitrogen, oxygen, hydrogen, silicon, and fluorine atoms, respectively. 
CL20 is a highly strained metastable compound and, therefore, it decomposes at high temperatures with heat releasing. According to the previous studies, decomposition of CL20 starts with the fission of the nitro group that induces a skeleton destabilization and further decomposition. So, the NO_{2} fission determines the overall activation barrier. The N–NO_{2} bond dissociation is a barrierless process, and the corresponding bond dissociation energy needed for the NO_{2} fission is about 200 kJ/mol. It was proposed a natural assumption that the same mechanism (NO_{2} or NF_{2} fission) was also relevant to the CL20 derivatives. However, this assumption was not confirmed by our ab initio molecular dynamics simulations. Observing the evolution of heated CL20 derivatives, we found two competitive mechanisms of the initial decomposition step. The first mechanism is the NO_{2} or NF_{2} fission, and the second one is a migration of O or F atom with the formation of Si–O or Si–F covalent bond. Migration is possible for the Sicontaining CL20 derivatives because silicon possesses a larger covalent radius (1.11 Å) than the carbon (0.76 Å). Corresponding energetic diagrams are presented in Figure 11.
Figure 11 – Two competitive mechanisms of 2 (a) and 3 (b) decomposition: NO_{2}/NF_{2} fission versus O/F migration to Si. Black and red lines correspond to the internal energies and Gibbs energies at T = 3000 K, respectively. 
For the 2 system, the barrier for the NO_{2} fission is somewhat lower than that for the O migration. Therefore, the NO_{2} fission mechanism prevails at room temperature. However, at higher temperatures, one should consider thermal corrections. For example, at T = 3000 K (it is about the half of CL20 explosive temperature) O migration mechanism becomes more feasible with regard to the lower Gibbs energy, as it is presented in Figure 11a. Anyway, the energy barrier for the CSi_{5}H_{6}N_{12}O_{12} decomposition is about 200 kJ/mol. This value is close to the corresponding value for the pristine CL20. Therefore, it can be said that 2 is as kinetically stable as pristine CL20. In contrast to oxygen, fluorine is able to easily migrate to the silicon atom and to destabilize the 3 cage, see Figure 11b. So, the 3 system is much less stable. To evaluate its lifetime t before the decomposition, we adopt the Arrhenius formula. In our evaluation, we assume the activation energy is equal to the energy barrier (0.18 eV, see Figure 11b). Frequency factor w can be defined from the Vineyard formula. So, we obtain E_{a} = 0.18 eV and w = 1.93·1015 1/s. In accordance with the Arrhenius formula, t ~ 0.5 ps at T = 300 K. So, 3 cage is unstable at room temperature and is barely suitable for practical applications.
We also stress the fact that the kinetic stability of any cage compound is determined by the energy barrier preventing its decomposition rather than the strain energy enclosed in its framework. For example, methylcubanes demonstrate an inverse relationship between their strain energies and kinetic stabilities. Moreover, initial processes leading to the CL20 decomposition do not necessarily involve any framework transformation. For these reasons, cage strain energy is not a suitable measure of the stability of the CL20 derivatives. Although the CL20 derivatives containing silicon possess higher strain energies, they are not necessarily kinetically unstable.
Within the framework of this project, we consider pyrolysis mechanisms, stability, and reactivity of two promising silicon CL20 derivatives as well as their dimers. We obtain that the presence of silicon atoms in the cage changes the mechanisms of initial pyrolysis step, but does not significantly reduce the stability of the cage. In addition, Sicontaining cages are more prone to dimerization. On the other hand, the simultaneous presence of silicon and fluorine atoms results in the compound instability. With regard to the presented results, the 2 compound seems to be the most attractive structure. It demonstrates higher crystalline densities, decomposition reaction heats, detonation velocities, detonation pressures, and explosion temperatures than the pristine CL20. At the same time, according to the presented results, its kinetic stability, frontier orbitals, and chemical reactivity are very similar to the CL20 characteristics.
Various nitrogen crystals
Within the framework of this project, several nitrogen crystalline phases with the following symmetries I2_{13}, I43m, Pba2, and P2_{1}2_{1}2_{1} were examined. The unit cells of these crystals are shown in Figure 12.
Figure 12 – Unit cells of various nitrogen crystalline phases: I2_{13} (A), I43m (B), Pba2 (C), and P2_{1}2_{1}2_{1} (D). 
Figure 13 shows the pressure dependence of enthalpy per atom of a unit cell of the nitrogen crystalline phases considered in the range of 25–400 GPa. For clarity, in this Figure, the enthalpy of the I2_{13} phase is taken as zero for every pressure value.
Figure 13 – Dependence of the enthalpy of various crystalline nitrogen phases, measured from the enthalpy of phase I2_{13}, on pressure. 
It can be seen that the nitrogen phase with I2_{13} symmetry is energetically preferable among the nonmolecular nitrogen phases at pressures lower than ≈175 GPa. At pressure equals 25 GPa, the phase P2_{1}2_{1}2_{1} transforms to I2_{13}; therefore, the enthalpy values at this pressure coincide for these phases. In the range from ≈175250 GPa, the phase with Pba2 symmetry is energetically favorable, and at higher pressures, the I43m phase is preferable. Phase I2_{13} is dynamically stable in the pressure range considered, as evidenced by the absence of imaginary frequencies in its phonon spectra (see Figure 14 at P = 25 GPa, Figure 15 at P = 175 GPa).
Figure 14 – Phonon spectrum and phonon density of states for the crystalline phase of nitrogen with I2_{13} symmetry at a pressure of 25 GPa. 
Figure 15 – Phonon spectrum and phonon density of states for the crystalline phase of nitrogen with I2_{13} symmetry at a pressure of 175 GPa. 
Using the VCNEB (variable cell NEB) technique, a transition barrier of the nitrogen phase with I2_{13} symmetry to the molecular phase was determined at a pressure of 50 GPa. The value of this barrier turns out to be quite high and equals to 1.2 eV, which indicates the possibility of experimental synthesis of this metastable crystalline form of nitrogen.
Publications
For detailed information, see the following publications:
1. Katin K.P., Grishakov K.S., Podlivaev A.I., Maslov M.M. Molecular hyperdynamics coupled with the nonorthogonal tightbinding approach: Implementation and validation // arXiv: https://arxiv.org/abs/1910.09990
2. Katin K.P., Javan M.B., Kochaev A.I., Soltani A., Maslov M.M. Kinetic Stability and Reactivity of Silicon and FluorineContaining CL20 Derivatives // ChemistrySelect. 2019. V. 4. P. 96599665. DOI: 10.1002/slct.201902583
3. Grishakov K.S., Katin K.P., Gimaldinova M.A., Maslov M.M. Stability and energy characteristics of extended nitrogen nanotubes: Density functional theory study // Letters on Materials. 2019. V. 9. P. 366369. DOI: 10.22226/2410353520193366369
Acknowledgments
The presented study was performed with the financial support of the Russian Foundation for Basic Research (RFBR) (Grant No. 183220139 mol_a_ved). We are grateful to DSEPYRI for the organizational support and computational resources provision.