Computational Evaluation of Polycyclic Bis-Oxadiazolo-Pyrazine Backbone in Designing Potential Energetic Materials

Abstract 4H,8H-bis[1,2,5]oxadiazolo[3,4-b:3',4'-e]pyrazine (bis-oxadiazolo-pyrazine) represents a versatile CHNO backbone for the design of energetic materials. In this paper, we report a comprehensive computational study using density functional theory to improve detonation properties of this CHNO backbone by introducing pyrazine rings, nitro groups, and N-oxide functionalities. The heat of formation, oxygen balance, density, and detonation properties of a series of furazan-pyrazine fused ring derivatives are computed. Their sensitivity and stability has been correlated with bandgap (ΔELUMO-HOMO), maximum heat of detonation (Q), and impact energy (h50). Introduction of –NO2 and N–oxide on the parent furazan-pyrazine fused ring derivatives is favorable for improving the heat of formation, oxygen balance and density. The heat of formation varies between 464.46 and 1043.57 kJ/mol, and the densities range from 1.75 to 2.01 g/cm3. The positive heat of formation and high densities achieved good detonation velocities (6.74 to 9.61 km/s) and pressures (19.96–43.65 GPa). Among the bis-oxadiazolo-pyrazine derivatives, P5, P6, Q5, Q6, R4, R5, and R6 are fascinating due to their high detonation performances, have calculated detonation velocities and pressures above 9.30 km/s and 40.0 GPa, respectively. Some furazan-pyrazine fused ring derivatives reveal good performance parameters with reasonable stability, confirming them as potential energetic compounds relative to RDX and HMX. Graphical Abstract


Computational methods
All the density functional theory (DFT) calculations and optimization of bis-oxadiazolo-pyrazine derivatives were performed by using Gaussian 09 program at the B3PW91/6-31G(d,p). 28 The geometry of all the compounds were fully optimized without any symmetry restriction and confirmed on true local energy minima free from imaginary frequencies. The computational methods and equations [29][30][31][32] which are used for the estimation of energetic properties are summarized in the Supplemental data.

Heat of formation
The heat of formation (HOF) is the crucial parameter to indicate the energy content of explosives. The calculated HOF values (HOF Gas , HOF Solid and HOF Sublimation ), total energy, zero-point energy and thermal correction of all bis-oxadiazolo-pyrazine derivatives are summarized in Table 1. The gas-phase heat of formation (HOF Gas ) of the designed compounds is evaluated by using an isodesmic reaction ( Figure S19 in Supplemental data). In general, energetic materials were always in the solid rather than the gas phase. [33][34][35] It is seen that the calculated HOF Solid of P1 (387.20 kJ/mol), P4 (572.04 kJ/mol), and Q4 (723.72 kJ/mol) are close to the reported values, 403.46/420.63, 658.61, and 782.0 kJ/mol, respectively. [36][37][38] The computed HOF Gas value for R6 (1043.57 kJ/mol) is very close to the reported result (1146.85 kJ/mol). 39 As given in Table 1, all the designed compounds have positive HOF Solid ranges from 405.27 (P2) to 828.50 (R6) kJ/mol due to significant energy contribution from parent fused rings P1 (387.20 kJ/mol), Q1 (429.23 kJ/mol), and R1 (458.67 kJ/mol). The incorporation of piperazine rings in the P1 structure helps to increase the HOF of Q1 and R1 by 42 and 71 kJ/mol. Therefore, the HOF Solid values of title compounds increase in the order of P-series < Q-series <R-series. The comparison of HOF Solid of P1, P3, and P4 reveals that -NO 2 groups (P1!P4 by 185 kJ/mol) significantly improve energy content over N-oxide (P1!P3 by 34 kJ/mol) linkages. Figure 3 compares the HOF Solid of selected P, Q, and R-series compounds. In all series, the introduction of N-oxide, N-NO 2 , and their combination increases the energy content, suggesting the potential of these groups in enhancing the HOF of corresponding compounds. However, it can be noted that the -NO 2 groups are a very good substituent for increasing the HOF over the Noxides. Figure 4 compares the HOF Solid , density, and detonation characteristics for selective bis-oxadiazolo-pyrazine derivatives with RDX and HMX. The bis-oxadiazolo-pyrazine derivatives show four to ten times higher HOF Solid than HMX (76 kJ/mol). Qualitatively, the predicted HOF Gas and HOF Solid values reproduce similar variation trends under the influence of different functional groups ( Figure S20 in the Supplemental data). Overall, increasing piperazine rings in the backbone and substituting -NO 2 , and N-oxide groups is an effective way to improve HOFs.

Oxygen balance and density
On detonation, energetic compounds undergo extreme rapid reactions, the intense release of energy, and hot decomposition products. 40,41 In CHNO-based explosives, oxygen is necessary for the complete oxidation of carbon and hydrogen to CO 2 and H 2 O, respectively. Oxygen balance (OB) indicates the percentage sufficiency or insufficiency of oxygen present in the explosive for the complete oxidation reaction. Further, sufficient oxygen content for complete oxidation of explosives helps to achieve maximum heat of explosion. In other words, the greater the OB value, the better is the energetic performance. The maximum density value ensures the packing of the explosive in a confined space and positively influences the detonation properties. The performance characteristics (detonation velocity and pressure) of energetic compounds are proportional to their densities. The density was estimated by the Politzer approach 42 in which the electrostatic interaction index is used to account for the intermolecular contacts. As shown in Table 2, except P6 all the bis-oxadiazolo-pyrazine derivatives are oxygen-deficient and their OB values range from À109.3 to À3.7%. It is observed that the molecules with the combination of À NO 2 and Noxide groups have higher OB and densities than that of parent frameworks (P1, Q1 and R1). Incorporating more piperazine rings in the backbone increases the hydrocarbon content and affects the OB values. Compared to P1, OB in Q1 and R1 decreased by 26 and 42%, respectively. The calculated densities of these compounds range from 1.77 to 2.02 g/cm 3 . The computed densities of compounds P1 (1.77 g/cm 3 ), Q4 (1.97 g/cm 3 ), and R6 (2.02 g/cm 3 ) are very close to the reported results, 1.75, 1.98, and 2.05 g/cm 3 , respectively. 37-39 Among the fifteen bis-oxadiazolopyrazine derivatives studied here, nine molecules show higher density than HMX (1.90 g/cm 3 ) and thirteen molecules are better than RDX (1.80 g/cm 3 ) except for Q2 and R2 (Figure 4). It is observed that the insertion of N-oxide groups in the parent backbone (P1, Q1, and R1) increases the density of individual molecules by 0.03-0.09 g/cm 3 , while -NO 2 groups improve the density by 0.16-0.23 g/cm 3 . This shows that -NO 2 groups are more favorable to improve density than Noxide groups. Our observations specify that designing energetic molecules with nitro groups and N-oxide functionalities effectively enhances oxygen balance, density, and overall performance.

Detonation properties
Detonation velocity (D) and pressure (P) are crucial parameters that reflect the potential and performance of explosives. The empirical Kamlet-Jacobs equations 43,44 and EXPLO5 thermochemical software (version 6.06.02) were used to compute performance parameters. It is observed that detonation properties computed with EXPLO5 code are slightly higher than that predicted from Kamlet-Jacobs equations. The calculated D and P values are summarized in Table 2 and found in the range 6.74-9.61 km s À1 and 19.96-43.65 GPa, respectively. Our calculated detonation properties for P1, Q4, and R6 are comparable with the reported values (Table 2). Comparing the predicted D and P values of P1, Q1 and R1 compounds indicate that increasing the piperazine rings in the molecular framework negatively impacts detonation properties. In Q1 and R1, detonation velocity decreased by 420-640 m/s while pressure reduced by 2.83-3.99 GPa. As can be seen from Figure 4, all the bis-oxadiazolo-pyrazine derivatives with -NO 2 functional groups in the structure possess D in the range of 9.06 to 9.61 km/s which is greater than that of RDX (8.60 km/s) and HMX (8.90 km/s), similarly, their P values found between 37.89 to 43.65 GPa, relatively higher than RDX (33.92 GPa) and comparable/higher than HMX (38.39 GPa). 45 This specifies that the -NO 2 groups are influential functional groups for enhancing the detonation properties of the title compounds. Similarly, incorporating N-oxide functionalities plays a positive role in increasing detonation properties. The introduction of N-oxide functionalities in P2, P3, Q2, Q3, R2, and R3 increases the D values by 420-1060 m/s, while P values are enhanced by 2.76-8.23 GPa compared to their corresponding parent rings. Among the designed compounds, R6 derivative has the highest detonation characteristics (9.61 km/s and 43.65 GPa) due to its highest density, HOF and explosophoric groups. Our results indicate that introducing piperazine rings in the 4H,8Hbis [1,2,5]oxadiazolo[3,4-b:3 0 ,4 0 -e]pyrazine (P1) structure increase the -NH sites for substitution of functional groups and overall effective way to improve the detonation performance. The comparison of fully substituted derivatives (P4-6, Q4-6 and R4-6) reveals that the incorporation of two or three piperazine rings in the backbone does not significantly improve the performance over 4H,8H-bis [1,2,5]oxadiazolo[3,4-b:3 0 ,4 0 -e]pyrazine but responsible for the destabilization of the corresponding molecules. This shows that the backbone structure with one or two piperazine rings can lead to satisfactory energetic properties with better stability.

Sensitivity trend
Sensitivity is a key parameter in deciding the practical applicability of energetic materials. [46][47][48] The sensitivity indicates the ease with which an energetic material detonates or its ability to withstand against external mechanical stimuli. In literature, theoretical studies have considered the energy gap (DE) between the highest occupied molecular orbital (E HOMO ) and lowest unoccupied molecular orbital (E LUMO ), heat of detonation (Q), and the drop weight impact height (h 50 ) to provide useful information regarding the relative order of sensitivity and stability of energetic compounds. [49][50][51] In general, the smaller energy gap (DE) reveals the easier electron transition between frontier molecular orbitals and the corresponding compound is more unstable, and its sensitivity is higher. Similarly, higher values of Q are to be avoided from the perspective of impact sensitivity. The higher value of h 50 state that greater impact energy is necessary to initiate a detonation reaction and the compound is more insensitive. In Table 3 Figure 5). It is noteworthy that computational methods play an ever-increasing role in designing energetic materials and minimizing the experimental research due to the risks associated with these compounds. Great development has been done in predicting accurate crystal densities, heats of formation, and detonation properties; however, predicting the sensitivity of new compounds toward external mechanical stimuli remains very challenging and prone to large uncertainties as it is governed by various factors. [52][53][54][55][56][57][58] The DE, Q, and h 50 values only indicate the sensitivity trend and cannot be described with a simple computational approach.

Conclusion
In this work, a series of compounds containing high-nitrogen fused bis-oxadiazolo-pyrazine backbone with nitro and N-oxide functional groups were designed and their HOFs, detonation performance, and sensitivity properties were studied by using density functional theory. It is observed that adding piperazine rings in the bis-oxadiazolo-pyrazine framework significantly improves the energy content and stability of the backbone; however, it leads to reduced oxygen balance and lower detonation performance. The computed results reflect that nitro and N-oxide groups are crucial in increasing oxygen balance, density, and detonation properties. Furthermore, P5, P6, Q5, Q6, R5, and R6 show better energetic performance than RDX and are close to HMX. In addition, all bis-oxadiazolo-pyrazine derivatives are expected to be stable and less sensitive as judged by the energy gap (DE), heat of detonation (Q), and the drop weight impact height (h 50 ) values. An analysis of the energetic properties and sensitivity parameters indicates that the increasing piperazine rings in the backbone add more NH sites for nitration but are less favorable for insensitivity. Considering all physicochemical properties, the bis-oxadiazolo-pyrazine framework could be considered a potential backbone for discovering new energetic materials with higher energy and enhanced stability. Computational details and selective structural parameters of bis-oxadiazolo-pyrazine derivatives are given in the Supplemental data.

Acknowledgments
Anjali thank UGC-CSIR, the Ministry of Education, Government of India for the Junior Research Fellowship. SD gratefully acknowledges the support of the Start-up Research Grant (No. SRG/2020/000023) and EMEQ scheme (No. EEQ/2020/000025), Science and Engineering Research Board, Department of Science and Technology, Government of India for research funding.

Disclosure statement
No potential conflict of interest was reported by the author(s).