Designing and looking for novel cage compounds based on bicyclo-HMX as high energy density compounds

We designed four novel cage compounds 2,4,6,8,9-pentanitro-2,4,6,8,9-pentaazatricyclo[3.3.1.0 3,7 ] nonane (PATN), 2,4,6,8,9,9-hexanitro-2,4,6,8-tetraazatricyclo[3.3.1.0 3,7 ]nonane (HNTATN), 2,4,6,8,9-pentanitro-2,4,6,8-tetraazatricyclo[3.3.1.0 3,7 ]nonane (PNTATN), and 2,4,6,8-tetranitro-2,4,6,8-tetraaza-9-oxatricyclo[3.3.1.0 3,7 ]nonane (TAOTN) by introducing the intramolecular – N(NO 2 ) – , – C(NO 2 ) 2 – , – CH(NO 2 ) – , or – O – linkage into the bicyclo-HMX framework. Then, their molecular and electronic structures, energetic properties, thermal stability, and impact sensitivity were investigated using density functional theory. We discussed the e ﬀ ects of molecular geometry and electronic structure on their detonation properties. Their thermal stability was discussed based on bond dissociation energies and strain energies. We evaluated their impact sensitivity compared with known energetic compounds. Because of their detonation performance, thermal stability, and impact sensitivity, the potential candidates for high energy density compounds were selected. Our design strategy, constructing the novel cage skeleton by introducing a intramolecular linkage, may o ﬀ er another way to obtain potential energetic compounds with outstanding energetic performance and low sensitivity.


Introduction
Energetic materials such as explosives, propellants, and pyrotechnics are widely used for innumerable military and industrial applications.During the last several decades, the search for novel high energy density compounds (HEDCs) has become a hot spot in this eld and seems to be never-ending to meet with the requirements of the rapid development of military and modern industry.2][3][4][5][6] Generally, cage compounds with highly compact structure have higher densities than their acyclic or monocyclic analogues.Moreover, the cage strain inherent in the systems can led to high positive heat of formation (HOF) over traditional explosives such as 1,3,5,7tetranitro-1,3,5,7-tetraazacyclooctane (HMX) or hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX).Therefore, highly nitrated cage compounds usually exhibit high positive HOF, high density, excellent detonation performance, and acceptable thermal stability.1][12][13][14][15][16][17][18][19] Although the cage HEDCs have excellent energetic properties and lower sensitivity, these new energetic cage compounds, which usually had a complex structure and contained seven or more nitro groups, made them difficult to be synthesized.In addition, too many nitro groups made them very sensitive toward outer stimuli and further increases the difficulty and cost of the synthesis.To date, there are few impressive candidates of HEDCs with novel cage skeleton containing fewer substituents than CL-20 but exhibiting excellent energetic performance comparable with CL-20 or ONC.Thus, ingenious strategy is needed to design and develop new energetic materials with novel cage skeletons.
cis-2,4,6,8-Tetranitro-1H,5H-2,4,6,8-tetraazabicyclo[3.3.0]octane, commonly called "bicyclo-HMX" because of its structural analogy with HMX, is an important bicyclic nitramine explosive and can be used in solid propellants. 20,21Bicyclo-HMX has four nitramine moieties in the structure and exhibits outstanding detonation properties comparable with HMX. 22,23hus, it is reasonable to assume that its bicyclic framework is a good parent structure for developing novel polynitro cage compounds with improved energetic properties and induced sensitivity.Now, theoretical studies based on quantum chemical treatment have gained acceptance as a useful research tool to screen the candidates of HEDCs, thereby avoiding expensive and dangerous experimental tests. 24,25Furthermore, the molecular structures, HOFs, energetic properties, strain energy, thermal stability, and impact sensitivity for the title compounds were investigated by using density functional theory (DFT).The structure-property relationships were explored for the title compounds to understand the roles of different linkages in the designed cage skeleton.
The remainder of this paper is organized as follows.A description of our computational method is given in Section 2. The results and discussion are presented in Section 3, followed by a summary of our conclusions in Section 4.

Computational methods
The hybrid DFT-B3LYP methods with the 6-311G(d,p) basis set were adopted for the optimizations of the molecular structures and the predictions of HOFs.Previous studies have shown that the basis set 6-311G(d,p) is able to precisely predict the molecular structures and energies of energetic organic compounds. 22,24,26,27he gas-phase HOFs were calculated by the isodesmic reactions based on total energies (E 0 ), zero-point energies (ZPE), and thermal correction (H T ) obtained from the DFT-B3LYP/6-311G(d,p) calculations.The isodesmic reactions in which the numbers of all kinds of bonds can keep invariable are widely used to decrease the calculation errors of HOFs. 24,25,28,29The corresponding isodesmic reactions used to obtain the gasphase HOFs of the title compounds at 298 K are as follows:  (1) For the isodesmic reaction, the heat of reaction DH 298 K at 298 K can be calculated from the following equation: where DH f,R and DH f,P are the HOFs of reactants and products at 298 K, respectively.At the same time, the DH 298 K can be calculated using the following expression: where DE 0 is the change in total energy between the products and the reactants at 0 K; DZPE is the difference between the zero-point energies (ZPE) of the products and the reactants at 0 K; DH T is thermal correction from 0 to 298 K.The D(PV) value in eqn ( 4) is the PV work term and equals DnRT for the reactions of ideal gas.
As most energetic compounds are usually solid, the calculation of detonation properties requires solid-phase HOF (DH f,solid ). 30According to Hess's law of constant heat summation, 31 the gas-phase HOF (DH f,gas ) and heat of sublimation (DH sub ) can be used to evaluate their solid-phase HOF: The DH sub can be calculated by the empirical expression suggested by Politzer et al.: 30,32 where A is the surface area of the 0.001 electrons per bohr 3 isosurface of electronic density of the molecule, n describes the degree of balance between positive and negative potential on the isosurface, and s tot 2 is a measure of variability of the electrostatic potential on the molecular surface.The coefficients a, b, and c were determined by Rice et al.: a ¼ 2.670 Â 10 À4 kcal mol À1 ÅÀ4 , b ¼ 1.650 kcal mol À1 , and c ¼ 2.966 kcal mol À1 . 33The descriptors A, n, and s tot 2 were calculated using the computational procedures proposed by Bulat et al. 34 This approach has been proved to be credible for evaluating heats of sublimation of many compounds. 33,35,36he detonation velocity and 28 pressure were estimated by the Kamlet-Jacobs equations 37 as where each term is dened as follows: D, the detonation velocity (km s À1 ); P, the detonation pressure (GPa); N, the moles of detonation gases per gram explosive; M, the average molecular weight of these gases; Q, the heat of detonation (cal g À1 ), which can be evaluated by the HOF difference between products and explosives according to the principle of exothermic reactions; and r, the crystal density of explosives (g cm À3 ).
The crystal density was obtained based on an improved approach proposed by Politzer et al., 38 in which the interaction index ns tot 2 was introduced.
in which M is the molecular mass (g mol À1 ), and n (0.001) is the volume of the 0.001 electrons per bohr 3 electronic density of the molecule (cm 3 per molecule).The coefficients b 1 , b 2 , and b 3 are 1.0462, 0.0021, and À0.1586, respectively. 39train energy (SE) 40 is an important index to correlate the structure with the stability and reactivity of the cage compounds.In this work, the strain energy of the azatricyclo [3.3.1.0 3,7]nonane cage skeleton were calculated from the change of total energies (E 0 ) with zero-point energies (ZPE) in the homodesmotic reaction: [40][41][42][43] The strength of bonding, which could be evaluated by bond dissociation energy (BDE), is fundamental to understand chemical processes. 44The energy required for bond homolysis at 298 K and 1 atm corresponds to the enthalpy of reaction A-B(g) / Ac(g) + Bc(g), which is the bond dissociation enthalpy of the molecule A-B by denition. 45For many organic molecules, the terms "bond dissociation energy" (BDE) and "bond dissociation enthalpy" oen appear interchangeably in the literature. 46Therefore, at 0 K, the homolytic bond dissociation energy can be given in terms of eqn (11).
The bond dissociation energy with zero-point energy (ZPE) correction can be calculated by eqn (12).
where DE ZPE is the difference between the ZPEs of the products and the reactants.Impact sensitivity is generally characterized through a drop weight test and reported as the height in cm, designated as h 50 .For the title compound, impact sensitivity was predicted by a simple method suggested by Pospíšil et al. 47,48 where h 50 is the height from which the sample is impacted by a 2.5 kg dropping mass and there is a 50% probability of causing an explosion, 49,50 s + 2 indicates the strengths and variabilities of the positive surface potentials, n is the balance of charges between positive potential and negative potential on the molecular surface, and the coefficients a, b, and g are À0.0064, 241.42, and À3.43, respectively.The calculations were performed with the Gaussian 09 package. 51The optimizations were performed without any symmetry restrictions using the default convergence criteria in the program.All of the optimized structures were characterized to be true local energy minima on the potential energy surfaces without imaginary frequencies.

Molecular geometry and electronic structure
It is necessary to examine the geometric structure of the title compounds before studying their various properties.The optimized structures of PATN and TAOTN are displayed in Fig. 3.And Table 1 lists some selected bond parameters of the title compounds and bicyclo-HMX.
Seen from Fig. 3, the molecule of PATN or TAOTN has a highly compact structure and may be considered to have two six-membered rings and two ve-membered rings.The cage skeleton of HNTATN or PNTATN is basically the same with PATN or TAOTN.
As shown in Table 1, the C-C bond, connecting two vemembered rings in the cage skeleton, is elongated due to the cage or ring strain in the system and its length is much longer than the normal C-C single bond length (1.54 Å).Furthermore, every cage compound has larger C-C bond length and average C-N bond length than their parent compound bicyclo-HMX, indicating that there is a larger inherent strain in the cage skeleton compared to the bicyclic skeleton of bicyclo-HMX.Among these compounds, TAOTN has the longest C-C bond length and PATN has the longest average C-N bond length.
Table 1 also lists the energies of HOMO, LUMO, and their energy gap (DE) of the title compounds and bicyclo-HMX.All of the title compounds have a smaller DE than bicyclo-HMX.Among them, TAOTN has the largest energy gap, whereas HNTATN has the smallest energy gap.It is known that the energy gap (DE) is an important stability index of the molecules and the molecule with a larger energy gap oen has high stability and low chemical reactivity. 8,52Thus, TAOTN may be less active and more stable than other three compounds in chemical processes with electron transfers or leaps, while HNTATN may exhibit a higher reactivity and lower stability in the chemical processes.The 3D plots of HOMO and LUMO for the title compounds were illustrated in Fig. 4, in which the positive phase is shown in red while the negative one is shown in green.It can be seen from Fig. 4 that all of the C-N orbits participate in both HOMO and LUMO levels.This shows that the removal of an electron from HOMO or addition of an electron to LUMO could weaken their cage skeleton.
The molecular electrostatic potentials (MEPs) for the title compounds were shown in Fig. 5.The MEPs for the 0.001 electron per bohr 3 isosurface of electron density were evaluated at the B3LYP/6-311G(d,p) level.The colors range from À0.02 to 0.02 hartree, with red denoting electron-rich regions (negative potential) and blue denoting electron-decient (positive potential) regions.
Electrostatic potentials can be used to analyzing the impact sensitivity of energetic compounds.According to previous studies, 53 the cage compounds with a larger electron deciency  at the center of the cage skeleton are oen more sensitive to outer impact than those with a lower electron deciency.Seen from the MEPs of these cage compounds, the positive potentials locates at the center of the cage skeleton, while the negative potentials appears to be distributed mostly on the N-NO 2 or C-NO 2 moiety.Clearly, PATN and HNTATN have stronger positive potential focused in the region than other two cage compounds.This indicates that they might have relatively high impact sensitivity.In addition, the positive potential within the inner structure for TAOTN is dispersed around the oxygen atoms in the cage skeleton, which might decrease the sensitivity.

Gas-phase and solid-phase heats of formation
The solid-phase HOF, DH f,solid , is an important property for energetic materials.Table 2 lists the total energies, ZPEs, thermal corrections, and gas-phase HOFs for reference compounds in the isodesmic reactions.The gas-phase HOFs of CH 4 , NH 3 , CH 3 NH 2 , CH 3 NO 2 , and CH 3 OCH 3 were taken from experimental results. 54The HOF value of NH 2 NO 2 was calculated from the atomization reaction at the G3 level.
Table 3 presents the total energies, ZPEs, thermal corrections, DH f,gas , and DH f,solid of the title compounds and bicyclo-HMX.It is found that the calculated DH f,solid value of bicyclo-HMX is in agreement with the previous report, 22 indicating that the predicted HOF method chosen for the title compounds is credible.As shown in Table 2, all the cage compounds exhibit high positive DH f,gas (357.13-619.01kJ mol À1 ) and DH f,solid (251.58-500.74kJ mol À1 ).Except for TAOTN, the title compounds have much larger DH f,gas and DH f,solid values than bicyclo-HMX, which shows that properly constructing a cage framework based on a bicyclic unit can remarkably increase energy extent of the parent compound.Especially, PATN has the highest DH f,gas and DH f,solid values among these cage compound.Although PATN possesses ve nitramine moieties, which has only more one N-NO 2 group than bicyclo-HMX, its HOF value increases 200 kJ mol À1 compared to bicyclo-HMX.Previous research suggested that energetic cage compounds derive most of their energies from substantial cage strain. 1,18This indicates that PATN may possess much higher cage   strain in the structure than parent bicyclo-HMX and other cage compounds.

Detonation properties
Detonation velocity (D) and detonation pressure (P) are two important performance parameters for energetic materials.Table 4 presents the calculated r, Q, D, P, and oxygen balance (OB) of the title compounds and bicyclo-HMX.For the purpose of comparison, the energetic properties of HNHAA are calculated, as HNHAA is only one more N-NO 2 group than the compound PATN in the structure.And the experimental detonation properties of two known explosives CL-20 and HMX are also listed in this table.The semi-empirical Kamlet-Jacobs formula has been proved to be reliable for predicting the explosive properties of energetic high-nitrogen compounds. 28,55he calculated r, D, and P values of bicyclo-HMX (1.860 g cm À3 , 9.14 km s À1 , and 37.82 GPa) agree well with the previous research results. 22,23This shows that our predictions for the title compounds are reliable.
As shown in Table 4, all the title compounds exhibit outstandingly high density with the predicted density ranging from 1.949 to 1.998 g cm À3 , which are signicantly higher than that of bicyclo-HMX (1.860 g cm À3 ).Moreover, all the designed cage compounds exhibit excellent detonation properties, which is to a great extent due to their unique cage structures.Their D and P values remarkably exceed those of bicyclo-HMX or HMX, showing that they can be regarded as promising candidates of HEDCs.Especially, PATN and HNTATN present extraordinary high detonation properties: D > 9.76 km s À1 and P > 44.95 GPa, which are even superior to those of famous explosive CL-20 (9.40 km s À1 and 42.00 GPa) or HNHAA (9.64 km s À1 and 44.10 GPa).TAOTN and PNTATN also exhibit remarkably high D and P values, which are superior to or comparable with those of CL-20.
In addition, all the title compounds possess higher heat of detonation (Q) and better oxygen balance compared to their parent compound bicyclo-HMX.PATN has the highest Q value (1736.84cal g À1 ) among them, while the TAOTN has the lowest one.Previous studies showed that the impact sensitivity of energetic compound roughly increases with Q. 56 Thus, it may be inferred that TAOTN or PNTATN has a relatively low sensitivity, while PATN or HNTATN may exhibit a relatively high sensitivity to external impact.In addition, it's worth noting that oxygen balance of PATN and HNTATN are equal to zero, making them combust completely to avoid releasing some toxic gases such as carbon monoxide during their decomposition.
Hence, constructing a cage skeleton based on the bicyclic framework by introducing -N(NO 2 )-, -C(NO 2 ) 2 -, -CH(NO 2 )-, or -Ocan substantially increase heat of detonation, density, and oxygen balance of the parent compound, which further dramatically increase detonation properties for the title cage compounds.

Strain energies
Table 5 lists the energies of the cage strain for the title compounds at the B3LYP/6-311G(d,p) level via homodesmotic reactions.It is found that when the structure converts from a s tot 2 is in kcal mol À1 and A is in Å2 .The scaling factor is 0.98 for ZPE. 24b The calculated value in parentheses was from ref. 22.
Table 4 Predicted densities (r), heats of detonation (Q), detonation velocities (D), detonation pressures (P), and oxygen balance (OB) for the title compounds a Compd.View Article Online a bicyclic framework into a cage skeleton, the strain energy remarkably increases in the cage molecule.Especially, the strain energy of the cage compound PATN is the highest value among them, almost double the strain energy of bicyclo-HMX.
The high strain energy in the cage system will be released during the explosion and result in producing an additional energy for the title compounds.
In addition, although PATN, TAOTN, HNTATN, and PNTATN have similar cage skeleton, their strain energies differ quite a bit.For example, when the N-NO 2 group in the structure of PATN is replaced by oxygen atom or the -CH-NO 2 group, the strain energy of the cage skeleton decreases more than 56 kJ mol À1 .It indicates that TAOTN and PNTATN have better thermal stability than PATN.Table 5 also presents the BDEs of the relatively weaker bonds of the title compounds.For the purpose of comparison, the BDEs of the relatively weaker bonds of HNHAA are given.Seen from Table 5, the N-NO 2 bonds linked to the cage have the lowest BDE values in the molecule of PATN, TAOTN, and PNTATN, respectively, which means that the N-NO 2 bonds are the weakest one and easier to rupture than other bonds in thermal decomposition for the three compounds.However, the weakest C-NO 2 bond of HNTATN have lower BDE value (122.90 kJ mol À1 ) than other bonds in the molecule, showing the rupture of C-NO 2 bonds appear to be the initial step in thermal decomposition or detonation.
Among them, TAOTN has the highest BDE value (150.67 kJ mol À1 ) of the relatively weaker bond and possesses better thermal stability than other cage compounds.Also, the BDEs of the relatively weaker N-NO 2 , C-N, and C-C bond of HNTATN are lower than those of other three cage compounds.It manifests that HNTATN may be less stable compared to other three compounds.This is because containing gem-dinitro groups on the bridge carbon atom decreases thermal stability of the cage compound.Generally, these conclusions are consistent with molecular structure analysis or cage strain analysis as mentioned above.
On the whole, all the title compounds possess good thermal stability and meet the thermal stability requirement as HEDMs.

Impact sensitivity
Impact sensitivity, generally reported as the height in cm and designated h 50 , is oen used to judge whether energetic compounds are sensitive or insensitive to external impact. 57The higher h 50 is, the more sensitive is the explosive.Table 6 lists the estimated impact sensitivity (h 50 ) of the title compounds.For the purpose of comparison, the h 50 values of HNHAA, CL-20, and HMX are calculated.The evaluated h 50 value of CL-20 or HMX is very close to the experimental results, 53 indicating that our predicted results are reliable.
Seen from Table 6, the title compounds exhibit higher h 50 values than HNHAA or CL-20, except that compound HNTATN has a slightly lower h 50 value than CL-20.According to the estimated h 50 values, PATN, TAOTN, and PNTATN are anticipated to be more insensitive to external impact than HNHAA or CL-20 but more sensitive than HMX.In addition, TAOTN has the highest h 50 value of 19.14 cm among the title cage compounds, showing that the introduction of the intramolecular oxy-bridge can effectively decrease the sensitivity of the cage compound.However, HNTATN has the lowest estimated h 50 values among these compounds and exhibit relatively high impact sensitivity, which also indicates that containing gem-dinitro groups on the bridge carbon atom increases impact sensitivity for the cage compounds.
Overall, PATN, TAOTN, or PNTATN exhibits high positive HOF, high density, excellent detonation properties superior to or comparative with CL-20, and lower impact sensitivity than CL-20 or HNHAA.As it is only ve or four nitramine moieties in the relatively simple structure, the three cage compounds may be regards as very attractive potential HEDCs.In addition, although the thermal stability and impact sensitivity of HNTATN is a bit poor compared to other three cage compounds, it possesses ideal oxygen balance, good thermal stability, and excellent detonation properties superior to CL-20 or HNHAA.Thus, HNTATN is also regarded as promising candidates for HEDCs.

Design of synthetic route
Although the title compounds have not been synthesized so far, the synthesis of some compounds with similar cage skeletons such as trioxatricyclo[3.3.1.0 3,7]nonane and triphosphatricyclo [3.3.1.0 3,79][60] Thus, it may be expected that the synthesis of the title compounds can be realized successfully in the future.Here we designed the synthetic routes for the two compounds TAOTN and PATN.Considering that there are only four or ve nitro groups in the molecules, the main difficulty of the synthesis may be how to synthesize 2,4,6,8-tetraazaoxatricyclo[3.

Conclusions
In this work, the structures, HOFs, energetic properties, strain energy, thermal stability, and impact sensitivity of the four novel cage compounds based on the bicyclo-HMX framework were systematically studied using the DFT-B3LYP method and compared with the parent compound or some famous energetic compounds.
It is found that all the title compounds have much higher density, heat of detonation, and detonation properties and better oxygen balance than the parent compound bicyclo-HMX.Compared to famous explosives CL-20 or HNHAA, all the title compounds possess relatively simple structures, good thermal stability, superior or comparative detonation properties, and much lower impact sensitivity, except that HNTATN has slightly higher impact sensitivity than CL-20.Especially, PATN and TAOTN exhibit a best combination of high density, good thermal stability, better detonation properties, and lower impact sensitivity than CL-20.Furthermore, designed feasible synthetic routes of PATN and TAOTN shows that they can be synthesized successfully in the future.Thus, all of the four cage compounds are promising candidates for HEDCs.
In addition, these results indicate that our design strategy of constructing new cage skeleton by introducing the intramolecular -N(NO 2 )-, -C(NO 2 ) 2 -, -CH(NO 2 )-, or -Olinkage based on the bicyclic nitramine is proven to be very useful and gives more options for designing novel cage compounds with excellent energetic performance and induced sensitivity.The new approach may be applied to design and develop energetic compounds with high denotation properties, good thermal stability, and low sensitivity.

Fig. 2
Fig. 2 Molecular frameworks of four designed cage compounds based on bicyclo-HMX.

Fig. 4
Fig. 4 HOMO and LUMO energy levels and energy gaps of four cage compounds.

Fig. 5
Fig. 5 Electrostatic potentials of the title compounds, color coding for MEPs are from red (negative) to blue (positive).

da
Oxygen balance (%) for C a H b O c N d : 1600 Â (c À 2a À b/2)/M w ; M w : molecular weight of the title compounds.b Calculated values from ref. 22. c Calculated values from ref. 23.d Experimental values from ref. 4.This journal is © The Royal Society of Chemistry 2018 RSC Adv., 2018, 8, 44-52 | 49 Paper RSC Advances Open Access Article.Published on 19 December 2017.Downloaded on 3/20/2024 4:32:09 PM.This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.

3. 5
Thermal stability BDE can provide useful information for understanding the stability of the investigated molecules.Generally, the smaller the BDE of a bond is, the weaker the bond is, and the easier the bond becomes a trigger bond.To investigate thermal stability of the title compounds, four possible bond dissociations have been considered: (1) the N-NO 2 bond linked to the cage; (2) the C-NO 2 bond linked to the cage; (3) the C-N bond in the cage; (4) the C-O bond in the cage only for the compound TAOTN.

Table 1
Selected bond lengths (Å), energies of HOMO and LUMO and their energy gaps DE (eV) of the title compounds at the B3LYP/6-311G (d, p) level The values in parentheses are the average one. a

Table 2
Calculated total energies (E 0 , a.u.), zero-point energies (ZPE, a.u.), thermal corrections (H T , kJ mol À1 ), and gas-phase HOFs (kJ mol À1 ) for the reference compounds a 24(8.00 d ) a The scaling factor is 0.98 for ZPE.24bThe experimental values were from ref.54.cThe value was calculated at the G3 level from the atomization reaction.dThe calculated value was taken from ref.12.

Table 5
Strain energies (SE, kJ mol À1 ) of the title compounds via homodesmotic reactions, and bond dissociation energies (BDE, kJ mol À1 ) of the relatively weak bonds for the title compounds a Calculated values from ref.9.

Table 6
The impact sensitivity (h 50 , cm) of the title compounds a Experimental values from ref.53.