Computational studies on nitramino derivatives of 1-amino-1,2-azaboriridine as high energetic material

Abstract

In this study, we have applied computational methods to determine the thermodynamic and explosive characteristics of nitramino derivatives of 1-amino-1,2-azaboriridine. Mono-, di- and tri-nitramino derivatives have been designed and considered for detailed study. Structure optimization and frequency calculation of the species have been performed at DFT-B3LYP/6-311++G(d,p) level of theory. The atomization method is employed to calculate the heat of formation (HOF), using electronic energy data calculated at G3 level. Utilizing the WFA program, crystal densities of designed compounds considered during the present study were predicted using the data obtained at B3PW91/6-31G(d,p) level. Results show that the number of nitramino groups influences the heat of formation of the title compounds. The calculated bond dissociation energies suggest that the N–NO₂ bond of the nitramino group is the weakest bond and may be treated as a trigger bond involved in the detonation process. The impact sensitivities (h₅₀) of all the compounds were evaluated and it was found that the designed compound 1-amino-2,3,3-trinitramino-1,2-azaboriridine is highly insensitive towards impact. Theoretical estimate of the condensed phase density of nitramino derivatives was found to be in the range of 1.60–1.80 g cm⁻³. Detonation velocity (D) and the detonation pressure (P) were found to be 8.0–9.0 km s⁻¹ and 26.2–35.2 GPa, respectively. The present investigation reveals that one of the designed compounds 1-amino-2,3,3-trinitramino-1,2-azaboriridine meets the criteria for high energy density materials.

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Introduction

The search for new high energy materials to be used as explosives and propellants have always drawn attention of research scientists.^1–5 The requisite properties for the materials to fall in the category of high energy materials include high density, high positive heat of formation, low sensitivity and good thermal stability. In the periodic table, the elements boron and nitrogen as a group “BN” give [3 + 5 = 8] valence electrons and this unit is isoelectronic with a “CC” unit. Thus, in a carbon containing moiety the CC unit can be formally replaced by a BN unit; hence, it is reasonable to expect the possibility of existence of a series of BN analogs with olefinic and aromatic character. Replacing carbons by nitrogens typically increases the crystal density of the compound and also its heat of formation. The greater density can be understood as a result of the N atom being smaller than C–H, while the increased heat of formation reflects the general weakness of N–N bonds in high N-content energy materials compared to C–N and C–C bonds, which make the molecule less stable.⁶ N-heterocycles and their derivatives have been widely used for developing energetic materials because of the relative stability of N₂ as a combustion product, releasing ∼946 kJ mol⁻¹ of energy during its formation from N-atoms.⁷ Furthermore, compounds containing boron would very likely form diboron trioxide (B₂O₃) during its combustion, which has an enthalpy of formation of −1273.5 kJ mol⁻¹, i.e. about 60 kJ of energy is given off per gram of boron combusted.⁷ Therefore, from the point of view of energy release during combustion, boron- and nitrogen-containing compounds seem to be a viable choice for developing high energy materials. Recently, Ball and his group^8,9 have performed significant computational studies on a series of B–N–C ring compounds and predicted the potentialities of boron–nitrogen–carbon compounds as high energy materials. In addition to the above, Koch and Klapötke¹⁰ also performed computational studies on cyclic and linear three- and four-membered B- and N-containing compounds and explored the possibility of using them as potential high energy density materials (HEDMs). Keeping this in mind, we have made an attempt to design azaboriridine systems and studied their thermochemical and explosive characteristics using computational methods. Azaboriridine is commercially available and synthetic routes to the preparation of various substituted B–N–C ring compounds have been documented by Miller¹¹ and Cernusac et al.¹² An amino group is attached to the nitrogen of the azaboriridine ring to increase the electron density of the BNC ring. The lone pair of electrons of N atoms may take part in the delocalization and ultimately increase the electron density of the ring resulting in an easier nitration. Moreover, this amino group has also been found to decrease the sensitivity of high energy materials towards external stimuli; thus, 1-amino-1,2-azaboriridine is taken as a moiety, as shown in Fig. 1, and its nitramino derivatives are designed.

Fig. 1 1-Amino-1,2-azaboriridine.

The superiority of the nitramino (–NHNO₂) group substituted systems has been envisaged in view of the fact that it increases the nitrogen content, which in turn could lead to high crystal density and high heats of formation.¹³ The latter are desired properties for increasing the detonation characteristics of energetic materials. Thus, as shown in Fig. 2, mono-, di- and tri-nitramino derivatives have been designed and undertaken for detailed study.

Fig. 2 Schematic representation of the title compounds.

During the present study, we attempted to look into the factors that are useful to design new energetic compounds with reduced sensitivity. One of the key factors in assessing the potentialities of an energetic material is the energy that is produced in the decomposition or combustion processes. Ordinarily, this can be estimated if the heat of formation (Δ_fH) of the compound is known. The energy released during the detonation process is also related to the sensitivity towards detonation. In order to make a reliable estimate of Δ_fH of the designed compounds, we utilized the atomization procedure, which has been shown to yield reliable values.^14–16 The density and thermodynamic properties of a compound are preferred to be in the condensed phase in order to assess the potential of an energetic material. Thus, condensed phase densities and heats of formation of the designed compounds were calculated using the procedure developed by Politzer et al.¹⁷ and Byrd and Rice.¹⁸ Other explosive characteristics, such as oxygen balance (OB₁₀₀), detonation velocity (D) and detonation pressure (P), have also been calculated to assess the potentialities of the designed compounds.

Computational details

Electronic structure calculations were performed using the Gaussian 09 software package.¹⁹ Structures of all the designed compounds were optimized using the Becke three-parameter (B3) functional with Lee–Yang–Parr correlation functional with 6-311++G(d,p) basis set and the B3LYP hybrid density functional with 6-311++G(d,p) basis set. DFT-B3LYP has been shown to accurately predict the structural parameters and frequency calculations of many organic compounds and nitro-substituted polyaromatic compounds.^20–22 The extended basis set with diffused and polarized functions were used to take into account the highly delocalized electrons of the designed molecules considered during the present investigation. Each optimized structure was subjected to vibrational frequency calculation to ensure that all the calculated frequencies were real and positive, and the structures belonged to true minima on their potential energy surface. Based on the optimized structures, the other properties of the designed compounds considered during the present study, such as heat of formation, density, electrostatic potential, detonation pressure and detonation velocity, were also determined. The procedure involved in calculating these properties is briefly discussed here as follows.

Heat of formation

The enthalpies of formation of title compounds are needed for the evaluation of the detonation properties of HEDMs. Computational studies have been widely applied to this purpose, and the atomization method has been the chosen approach in several studies.^14–16 The energy and the enthalpy data needed during the calculation were obtained at G3 level composite method,²³ which has been shown to accurately predict the heat of formation of a variety of compounds within an accuracy of ±1 kcal.²⁴ In the case of B–N–C compounds considered during the present study, the procedure followed to calculate it is schematically shown in Fig. 3.

Fig. 3 Thermodynamic cycle for the determination of heat of formation using an atomization procedure.

In the above figure, the energy involved in step 1 is called the atomization energy, which is defined as the energy needed to atomize the species to its constituent atoms in their most stable state. This value is calculated at 0 K; therefore, the energy (E) and the enthalpy (H) values are the same. Thus,

Δ_aH (0 K) = [aE_C(³P) + bE_H(²S) + cE_N(⁴S) + dE_O(³P) + eE_B(²P)] − E (G3, 0 K)[C_aH_bN_cO_dB_e] (1)

where E's for the atoms are the total electronic energies at 0 K calculated at G3 level of calculation and a, b, c, d and e are their stoichiometric coefficient present in the molecule. The second term in eqn (1) is the zero-point corrected total energy for the designed molecules considered during the present study, also evaluated at G3 level. The second step (step 2) is the sum of the gas-phase heats of formation of the elements in their most stable state multiplied by their stoichiometric coefficients. Applying the Hess's law, the heat of formation of the molecular species C_aH_bN_cO_dB_e at 0 K can thus be written as follows:

Δ_fH (0 K)[C_aH_bN_cO_dB_e] = [aΔ_fH (0 K, C) + bΔ_fH (0 K, H) + cΔ_fH (0 K, N) + dΔ_fH (0 K, O) + eΔ_fH (0 K, B)] − Δ_aH (0 K)[C_aH_bN_cO_dB_e] (2)

where Δ_fH's of constituent atoms C, H, N, O and B are the experimental heats of formation at 0 K, and these are taken from the NIST Web book⁷ as 711.19, 216.04, 470.82, 246.79 and 559.91 kJ mol⁻¹, respectively.

For most applications, it is advantageous to have the heat of formation of the molecule at 298 K; therefore, the heats of formation of the desired molecules calculated at 0 K must be changed to 298 K. This is accomplished by adding the increase in enthalpy of the molecule when going from 0 to 298 K and subtracting the corresponding increase for the elements in their standard state. Thus, Δ_fH (298 K) is determined from the value of the Δ_fH (0 K) using the following expression:

Δ_fH (298 K)[C_aH_bN_cO_dB_e] = Δ_fH (0 K)[C_aH_bN_cO_dB_e] + ΔΔH[C_aH_bN_cO_dB_e] − [aΔΔH C(graphite) + b/2ΔΔH H₂ (g) + c/2ΔΔH N₂ (g) + d/2ΔΔH O₂ (g) + eΔΔH B (s)] (3)

where ΔΔH's are the enthalpy increases of the respective species when going from 0 to 298 K. These values for C (graphite), H₂ (g), N₂ (g), O₂ (g) and B (s) are taken from the NIST Database⁷ as 1.050, 8.468, 8.670, 8.680 and 1.213 kJ mol⁻¹, respectively, whereas the same values for the designed molecules considered during the present study are taken as the difference of the G3 enthalpies obtained at 298 and 0 K.

As shown in reactions (4a–c), combustion enthalpies (ΔH_comb) of the designed molecules considered during the present study were calculated using the following stoichiometric combustion reactions, and the principle of maximum exothermic principle, in which we assumed that carbon, hydrogen and boron formed their oxides and nitrogen atoms producing N₂ gas in the combustion of the he species concerned.

CH₅BN₄O₂ + 2O₂ (g) → CO₂ (g) + 0.5B₂O₃ (s) + 2.5H₂O (l) + 2N₂ (g) (4a)

CH₅BN₆O₄ + O₂ (g) → CO₂ (g) + 0.5B₂O₃ (s) + 2.5H₂O (l) + 3N₂ (g) (4b)

CH₅BN₈O₆ → CO₂ (g) + 0.5B₂O₃ (s) + 2.5H₂O (l) + 4N₂ (g) (4c)

The enthalpies of formation of water, carbon dioxide and diboron trioxide (B₂O₃) used in above reactions were taken from the NIST database.⁷

Density

Density (ρ) plays an important role in determining the explosive properties of high-energy density materials (HEDM) because it strongly influences their detonation. It can be represented in its simplest form as follows:

ρ = M/V_m(0.001) (5)

where M is the molecular mass in g per molecule, and V_m(0.001) is the molecular volume of an isolated gas phase molecule in cm³ per molecule, determined at 0.001 electron per bohr³ density space by performing 100 single point calculation by the Monte Carlo integration method on the optimized structures of the molecules. Thus, the average volume determined was used for the calculation of the density using eqn (5). However, the most important missing part when using the Monte Carlo integration method is that no allowance was made to take into account the specific intermolecular interaction taking place in the crystal lattice. Politzer et al.¹⁷ developed an improved method for determining the crystal density by considering the role played by intermolecular forces in the crystal lattice and provided an expression to determine the crystal density of the designed energetic molecules using ab initio data, as shown in eqn (6).

Crystal density (ρ) = α (M/V_m(0.001)) + β (νσ_total²) + γ (6)

where α, β, and γ are empirical parameters and ν and σ_total² are the balance parameter and total variance which are related to electrostatics potentials due to positive and negative charges as follows:

σ_total² = σ₊² + σ₋² (8)

Politzer et al.¹⁷ determined the values of empirical parameters α, β, γ by performing calculations at B3PW91/6-31G(d,p) for a set of “trainee molecules.” They fitted the experimental and calculated densities using eqn (6) and listed them as 0.9183, 0.0028, and 0.0443, respectively. In order to use the values of parametric constants, i.e. α, β, and γ, as listed by Politzer et al.,¹⁷ we also optimized the structures of the designed molecules at B3PW91/6-31G(d,p) and used these optimized structures to evaluate the value of V_m(.001). These structures were also used in the calculation of ν and σ_total² utilizing the electrostatic potential (ESP) method with WFA-SAS code,²⁵ which are used to evaluate the crystal density using eqn (6).

Detonation properties

For known explosives, the energy released during detonation (Q) and the density (ρ) can be determined experimentally, and thus their performance parameters, the detonation velocity (D) and the detonation pressure (P) can be calculated using Kamlet–Jacobs equations,²⁶ given by the following expressions:

D = 1.01 (NM^1/2Q^1/2)^1/2 (1 + 1.30ρ) (9)

P = 1.558ρ²NM^1/2Q^1/2 (10)

where D is expressed in km s⁻¹, P is expressed in GPa, N is the number of moles of gaseous detonation product formed per gram of explosive, M is the average molecular weight of the gaseous products (g mol⁻¹) and Q is the heat of detonation, representing the chemical energy of detonation reaction in (cal g⁻¹) of explosive. The heat of detonation (Q) can be determined as follows:

N, M and Q are determined from the stoichiometric reactions developed for maximum exothermic principle, using arbitrary H₂O–CO₂–N₂–B₂O₃ decomposition assumption. However, in the case of oxygen deficient molecules, the formation of BN was also taken into account. Due to the sensitivity and explosive nature of the high energy materials, the experimental determination of their Q and ρ are not very frequent, and theoretical approaches have been found to be a viable option. The condensed-phase HOF (ΔH_f(c)) can be obtained from the gas-phase HOF (ΔH_f,g), and the heat of sublimation (ΔH_sub) can be obtained by applying the Hess's law, and it can be written as follows:

ΔH_f(c) = ΔH_f(g) − ΔH_sub (12)

In order to determine the heat of sublimation we applied the method developed by Byrd and Rice,¹⁸ which is given by the following expression:

ΔH_sub = aA² + b(νσ_total²)^0.5 + c (13)

where A is the surface area of the 0.001 electrons per bohr³ isosurface of the electronic density of the molecule, ν describes the degree of balance between positive and negative potentials on the isosurface, and σ_total² is a measure of the variability of the electrostatic potential on the molecular surface. The latter two quantities have been shown by Politzer et al.¹⁷ to be important in relating macroscopic properties that are dependent on non-covalent electrostatic interactions. The coefficients a, b, and c were determined by Byrd and Rice¹⁸ through a least square fit of eqn (13) between the known (experimental values) and their theoretically evaluated values by performing the calculations at the optimized structures of a set of “trainee molecules” at B3LYP/6-31G(d) level. These coefficients are reported as 0.000267, 1.650087 and 2.966078, respectively. In the present study, the descriptors A, ν and σ_total² are calculated by the computational procedure proposed by Bulat et al.²⁵ In order to use the parametric constants evaluated Byrd and Rice,¹⁸ we also performed the calculation on the structures optimized at the same level of theory.

Bond dissociation energy

Bond dissociation energy is one of the important parameters of the molecule that has been found to have a profound impact on the detonation characteristics of the energetic molecules, especially impacting the sensitivity and the thermal stability of the compounds.^27–29 BDE is defined as the enthalpy change involved in a chemical bond dissociation process. In the case of a neutral molecule A–B dissociating homolytically into two radicals A˙ (g) and B˙ (g) as follows:

A–B (g) → A˙ (g) + B˙ (g), (14)

the bond dissociation enthalpy DH(A–B) would correspond to the enthalpy of reaction given by the following expression:

Δ_rxnH₂₉₈ = Δ_fH (A˙) + Δ_fH (B˙) − Δ_fH (A–B) (15)

where Δ_fH's are the heats of formation of the corresponding species at 298 K and 1 atm pressure. For most organic molecules, the terms “bond dissociation energy” (BDE) and “bond dissociation enthalpy” often appear interchangeably.³⁰ Therefore, at 0 K, the homolytic bond dissociation energy BDE₀(A–B) can be written as follows:

BDE₀(A–B) = E₀(A˙) + E₀(B˙) − E₀(A–B) (16)

where E₀'s are the total electronic energies of the species calculated at B3LYP/6-311++G(d,p) level of theory. Note that DFT/B3LYP method has been found to predict reasonably accurate BDEs.^31,32 Using the zero-point corrected total energies of reactant and products, BDE(A–B) can be determined as follows:

BDE(A–B)_ZPE = BDE₀(A–B) + ΔZPE (17)

where ΔZPE is the difference in ZPE's between products and reactants during the bond dissociation process.

Impact sensitivity

The term “sensitivity” refers to an ease with which the initiation of reaction is achieved, leading to a self-decomposition process that produces high temperature and pressure. In more specific terms, it refers to the vulnerability of the energetic compound when the latter is subjected to external stimuli such as impact, shock, heat, friction, and spark. Impact sensitivity is commonly measured by the height, from which a mass m dropped on to the compound to produce detonation 50% of the time (h₅₀).³³ The sensitivity is then expressed as either the drop height, h₅₀ (usually in cm) or as impact energy mgh₅₀. The larger the value of h₅₀, the lower is the sensitivity. For a 2.5 kg mass, the impact energy for a h₅₀ of 100 cm would correspond to 24.5 J. For known explosives, experimental tools are available and a statistical value of h₅₀ (cm) can be determined. However, for designed molecules, which are yet to be synthesized, computational approach has been devised. Pospíšil et al.³⁴ have correlated the explosive characteristics of an energetic material to the electrostatic potential of the molecule, and they have proposed an empirical formula relating h₅₀ to the electrostatic potential of the molecule, as given by the following expression:

h₅₀ = ασ₊² + βν + γ (18)

where σ₊ is the electrostatic potential for the positive charge and ν is the degree of balance between the positive and negative potentials on an isosurface determined at 0.002 electron per bohr³ of the energetic molecule, which is defined by eqn (7). The coefficients α, β and γ are the regression coefficients determined to be −0.0064, 241.42 and −3.43 respectively.³⁴

Oxygen balance

Oxygen balance, represented as OB₁₀₀, is defined as the ratio of the oxygen content of the compound to the total oxygen required for the complete combustion of all the constituents present in the molecule. It is represented in terms of the percentage of oxygen required for complete conversion of carbon to carbon dioxide, hydrogen to water, nitrogen to N₂, and any metal to its oxide. It is calculated as follows:where X, Y, Z, and M are the number of C, H, O, and B atoms present in the molecular formula of the compound.

Results and discussion

Electronic structure and thermal stability

The optimized structures of the titled compounds determined at B3LYP/6-311++G(d,p) level are shown in Fig. 4. A detailed analysis of the structures performed with the Gaussview visualization program³⁵ reveals that the structural features of the BNC ring remain intact. To elucidate the pyrolysis mechanism of title compounds, the dissociation energy of various possible bond dissociation processes have been determined, and the bond associated with the lowest energy has been identified. The latter is designated as the “trigger bond.” This bond is presumed to be responsible for the initiation of the detonation process.^36,37 Mainly three different types of bonds, namely, Ring-NH₂, Ring-NHNO₂ and NH–NO₂, have been taken into consideration. In earlier studies, bond order has been used as a measure of the bonding capacity between two atoms, and as a measure of the overall bond strength.^3,11 Bond dissociation energy of a few selected bonds along with its bond order determined by natural bond analysis (NBO)^38,39 are also listed on the optimized structures shown in Fig. 4. Results show that the weakest bond is the N–NO₂ bond associated with the NHNO₂ group, which is designated as P_NH–NO2. The bond dissociation energy corresponding to P_NH–NO2 and the respective bond order are recorded in Table 1. In order to compare our data, we also calculated the above two parameters for two well-known explosives: RDX and HMX. Results show that the trigger bond designated in the designed molecules possesses considerably higher bond dissociation energy and bond order than that of RDX and HMX, showing thereby that the designed molecules may be thermally more stable. In earlier studies,⁴⁰ it has been pointed out that the HOMO–LUMO energy gap can be utilized to predict the chemical stability of the compound. Table 2 lists the ΔE_HOMO–LUMO for the designed molecules considered during the present study determined at B3LYP/6-311++G(d,p) level. The results show that the energy gap of all the designed compounds are higher than RDX and very close to HMX, showing thereby that the stability of the compounds will be comparable to HMX, which is known to be a powerful and stable explosive compound.

Fig. 4 Optimized structures of title compounds at B3LYP/6-311++G(d,p). Values represent BDE (without parentheses) and bond order (within parentheses).

Table 1 Calculated bond dissociation energies (BDE) and the bond order of the trigger bond in designed and reference molecules

Compound	Trigger bond	Bond order	BDE^0 (kJ mol^−1)	BDEZPE (kJ mol^−1)
1-Amino-3-nitramino-1,2-azaboriridine	PNH–NO2	1.0583	187.89	167.30
1-Amino-3,3-dinitramino-1,2-azaboriridine	PNH–NO2	1.0399	179.87	159.43
1-Amino-2,2,3-trinitramino-1,2-azaboriridine	PNH–NO2	1.0338	197.16	176.92
RDX (1,3,5-trinitro-1,3,5-triazinane)	Ring-NO2	1.0187	157.14	137.06
HMX (1,3,5,7-tetranitro-1,3,5,7-tetrazocine)	Ring-NO2	0.9898	174.74	154.85

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Table 2 HOMO, LUMO energies and ΔE_LUMO–HOMO of title compounds calculated at B3LYP/6-311++G(d,p) level. Values are in a.u

Compound	EHOMO	ELUMO	ΔELUMO−HOMO
a Values for these molecules are calculated during the present study.
1-Amino-3-nitramino-1,2-azaboriridine	−0.24438	−0.04714	0.19724
1-Amino-3,3-dinitramino-1,2-azaboriridine	−0.26385	−0.07030	0.19355
1-Amino-2,2,3-trinitramino-1,2-azaboriridine	−0.26714	−0.08681	0.18033
RDX^a	−0.31361	−0.08820	0.15618
HMX^a	−0.30542	−0.09996	0.20546

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Heats of formation

In general, the heat of formation reflects the energy content of an energetic material. The enthalpy data of the designed compounds are listed in Table 3. The parameters needed for the evaluation of the heats of sublimation of the compounds using the method of Byrd and Rice¹⁸ are also listed in Table 3. In order to use the values of the empirically determined parameters a, b and c of eqn (13), we used the optimized structures of species concerned at B3LYP/6-31G(d) level, which had been used by Byrd and Rice.¹⁸ This was performed to use the same level of parameterization, and the results show that the heat of sublimation of the titled compounds increased along with the number of nitramino groups. In the case of the mononitramino derivative, the heat of sublimation was 89 kJ mol⁻¹, which increased to 109 kJ mol⁻¹ in the case of the trinitramino derivative. This increase in ΔH_sub shows that the presence of nitroamino group increases the stability of the designed molecule. This is also supported by the heat of formation data which also decreased from 194.7 kJ mol⁻¹ to 143.4 kJ mol⁻¹, except in the case of the dinitroamino compound. A close look at the optimized structure with Gaussview reveals that in the case of a compound containing two nitramino groups, both groups are attached at the same C-atom in the ring and are very near to each other. This may yield a very strong repulsive interaction energy, causing instability to the molecule and ultimately, resulting in a higher heat of formation than that of the mononitramino derivative. Placing the third nitroamino group at the B atom drastically reduces the heat of formation in the case of the trinitroamino group. This may be due to the interaction of the empty p-orbital of the boron atom with the additional lone pair of electrons available with the N atom of the nitroamino group bonded to it. The specific enthalpies of combustion of the title compounds are also listed in Table 3. The results show that specific enthalpy of combustion decreases as the number of nitramino groups increases. This shows that the increase in the number of the substituent group increases the molecular mass more significantly than their energy content.

Table 3 Parameters involved in the estimation of sublimation enthalpies using WFA program using the structures of the designed molecules optimized at B3LYP/6-31G(d)

Compound	ν	σ+^2	σ−^2	SA (Å^2)	ΔHsub (kJ mol^−1)	ΔfH^0 (g) (kJ mol^−1)	ΔfH^0 (s) (kJ mol^−1)	ΔHsp,comb (kJ g^−1)
1-Amino-3-nitramino-1,2-azaboriridine	0.24	155.88	98.45	145.42	89.66	284.37	194.71	16.7
1-Amino-3,3-dinitramino-1,2-azaboriridine	0.18	180.40	57.73	183.17	95.67	317.83	222.16	11.2
1-Amino-2,2,3-trinitramino-1,2-azaboriridine	0.14	196.61	40.43	224.97	108.93	252.35	143.41	8.0

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Explosive performance

The two important explosive characteristics, the detonation velocity (D) and the detonation pressure (P), calculated using Kamlet–Jacobs equation,²⁶ are listed in Table 4. In order to infer the reliability of the approaches applied during the present investigation to calculate the detonation parameters, we calculated the detonation performances of two well-known explosives, i.e. RDX (1,3,5-trinitro-1,3,5-triazinane) and HMX (1,3,5,7-tetranitro-1,3,5,7-tetrazocine), and the values are also listed in Table 4. The calculated values of RDX and HMX using the methods adopted during the present investigation yielded the density and D and P comparable to the experimental values, as listed in Table 4. This gave us confidence in the procedure adopted to yield reliable values of detonation parameters and loading density of the titled molecules. Results show that D and P of the designed compounds considered during the present study are in the range of 8.0–9.0 km s⁻¹ and 26–35 GPa, respectively. The loading density (ρ) is in the range of 1.58–1.80 g cm⁻³. These loading densities are comparable to commercial explosives RDX (1.82 g cm⁻³). For the three title compounds considered during the present investigation, OB₁₀₀ values are also listed in Table 4. The results show that increasing the number of nitramino groups drastically increases the oxygen balance. In the case of the trinitramino derivative, OB₁₀₀ value is calculated to be 0.00. This shows that the trinitroamino derivative of 1-amino-1,2-azaboriridine should be considered to be a preferred compound in terms of the maximum exothermic heat release.

Table 4 Detonation properties of the title compounds

Compound	OB100	ρ (g cm^−3)	Q (cal g^−1)	D (km s^−1)	P (GPa)
a Values are calculated during the present study.b Values are taken from ref. 41.
1-Amino-3-nitramino-1,2-azaboriridine	−55.17	1.58	1913.72	8.0	26.17
1-Amino-3,3-dinitramino-1,2-azaboriridine	−18.18	1.71	1863.62	9.0	34.14
1-Amino-2,2,3-trinitramino-1,2-azaboriridine	0.00	1.80	1800.50	9.0	35.17
RDX^a	−21.62	1.80^a	1488.28	8.70^a	33.26^a
		1.82^b		8.75^b	34.00^b
HMX^a	−21.62	1.90^a	1477.02	9.0^a	35.15^a
		1.91^b		9.10^b	39.00^b

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Impact sensitivity

Impact sensitivity of the title compounds measured in terms of h₅₀ (cm) are listed in Table 5. Lower values of h₅₀ signify the compounds to be more sensitive towards impact. In order to assess the reliability of the calculation of impact sensitivity on the basis of eqn (18), the same is calculated for known commercial explosives such as RDX and HMX, which were found to be 28 and 47 cm, respectively. The predicted value of RDX is in close agreement with the experimental value (29 cm), whereas for HMX, the predicted value is slightly higher than the experimentally determined one (33 cm). This gives us confidence that the use of eqn (18) for determining the impact sensitivity of designed or yet to be synthesized high energetic materials would yield reliable values. Results recorded in Table 5 show that the values of h₅₀ of the title molecules are in the range of 30–52 cm. The results show that the trinitramino derivative has explosive properties comparable to HMX.

Table 5 Density Data and impact sensitivity (h₅₀/cm) of the designed molecules along with the reference compounds

Compound	ν	σ+^2	σ−^2	σtotal^2	νσtotal^2	V(0.001) Å^3	ρ (g cm^−3)	h50 (cm)
a Calculated values during the present study.
1-Amino-3-nitramino-1,2-azaboriridine	0.23	163.69	98.97	262.66	61.68	129.56	1.58	52.21
1-Amino-3,3-dinitramino-1,2-azaboriridine	0.18	186.97	58.20	245.16	44.38	173.72	1.71	39.08
1-Amino-2,2,3-trinitramino-1,2-azaboriridine	0.14	199.68	41.28	240.96	34.21	217.98	1.80	29.57
RDX^a	0.13	164.19	30.75	194.94	25.90	204.52	1.80	27.59
HMX^a	0.21	127.16	55.24	182.39	38.51	264.76	1.90	46.73

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Conclusion

On the basis of theoretical studies, we have studied the electronic structure, enthalpy of formation, enthalpy of combustion and thermal stability of nitramino derivatives of 1-amino-1,2-azaboriridine. On the basis of overall performance parameters we find that 1-amino-2,3,3-trinitramino-1,2-azaboriridine falls in the category of HEDMs. The present study shows that BNC ring compounds have a great potential to be used as HEDMs.

Acknowledgements

One of the authors (SG) is thankful to University Grants Commission (UGC), New Delhi, for providing DSA (BSR) fellowship under its SAP program sanctioned to the Chemistry Department. Authors are also thankful to Uttar Pradesh State Government for providing financial support under its Center of Excellence Program for the upgradation of the computational facility. Thanks are also due to DRDO, Government of India for providing financial support to undertake this study.

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