J Mol Model (2014) 20:2204 DOI 10.1007/s00894-014-2204-x

ORIGINAL PAPER

Computational studies on the energetic properties of polynitroxanthines Mei Li & Hang Xu & Fengmin Wu

Received: 19 January 2014 / Accepted: 9 March 2014 / Published online: 8 April 2014 # Springer-Verlag Berlin Heidelberg 2014

Abstract Density function theory calculations were performed to find comprehensive relationships between the structures and properties of a series of highly energetic polynitroxanthines. The isodesmic reaction method was employed to estimate the gas-phase heat of formation. The solid-state heats of formation for the designed compounds were calculated by the Politzer approach using heats of sublimation. All of the designed compounds were found to possess solid-state heats of formation of >100 kJ mol−1. Detonation performances were evaluated by the Kamlet–Jacobs equations, based on the predicted densities and solid-state heats of formation. The results indicate that all of the compounds have excellent detonation velocities and pressures. The stabilities of the derivatives were calculated by evaluating their energy gaps, bond dissociation energies, and characteristic heights. The results indicate that all of the compounds have large bond dissociation energies and energy gaps. The characteristic height values of the compounds are more than or close to those of HMX and RDX. Thus, the polynitroxanthine derivatives show good thermodynamic and dynamic stability. Further, the present study may provide useful information on the structure–property relationships of these compounds, and for the development of novel high-energy materials.

Keyword High energy-density materials . Detonation performance . Isodesmic reaction . Computational chemistry

M. Li : H. Xu (*) : F. Wu Chemical Engineering and Pharmaceutics School, Henan University of Science and Technology, Luoyang 471003, People’s Republic of China e-mail: [email protected]

Introduction The design of new energetic materials—including propellants, explosives, and pyrotechnics—is a long-standing tradition in the chemical sciences. The synthesis of modern energetic materials is a scientific challenge [1–3]. Recently, because of many catastrophic explosions resulting from the unintentional initiation of munitions aboard ships, aircraft carriers, munitions trains, through impact or shock, considerable efforts have been made to develop new materials with good thermal stabilities, impact and shock insensitivities, with better performances, and which can be synthesized economically and in an environmentally friendly manner, in order to meet the requirements of future military and space applications [4, 5]. However, the desired characteristics of insensitivity and high energy are quite often contradictory to each other, making the development of new high energy-density materials (HEDMs) a difficult and challenging problem. Practical research into energetic materials is focused on developing increasingly highly performing explosives and propellants, and energetic materials that cause much less toxicological or environmental damage when used and are increasingly easy/safe to handle. However, new insights at the molecular level are needed to determine methods of increasing the energy content while retaining stability [6, 7]. Over the last few decades, heterocycles have received a great deal of attention from researchers in this field because they have high nitrogen contents and highly positive heats of formation, which can substantially increase molecular energy density. Furthermore, π aromatic bonding is present in these heterocycles, stabilizing them. These molecules are usually insensitive to static, friction, and impact [8]. It is well known that introducing –NO2 groups can enhance the explosive performance of an energetic material. Also, a furazan, tetrazine, tetrazole, or triazole ring is a useful structural unit upon which to base the design of a novel energetic

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material since it has an inherently high nitrogen content and good thermal stability. Many theoretical studies have attempted to design new high energy-density compounds by introducing different substituents while largely ignoring the effects of incorporating different nitrogen-containing heterocyclic rings. Xanthine is an important biomolecule because it is used to combine nucleonic acids,; as such it has been studied in depth in the field of biology [9, 10]. However, until we performed the present study, xanthine had not been researched as a building block for high-energy materials. The presence of carbonyl oxygens (such as those found in xanthine) can make a molecule quite susceptible to hydrolysis, and thus sensitive to water present in the air. However, we believe that this rule is not universally applicable, because some energetic materials with a carbonyl oxygen have been successful applied, such as 5-nitro-1,2,4-triazol-3-one (NTO), which has a high heat of reaction and a low sensitivity [11]. Xanthine is also fascinating because it has four hydrogen atoms on its rings that can be substituted by additional functional groups. In addition, it has a high molecular density, 1.6 g/cm3. In the work reported in the present paper, nitro groups were introduced at various positions on the xanthine skeleton. The stabilities and detonation performances of the resulting series of nitroxanthines (see Fig. 1) were then investigated systematically using quantum chemical methods. We expect that our results will provide useful information for the molecular design of novel HEDMs.

Computational methods All quantum mechanical calculations were performed with the Gaussian 03 software suite [12]. The Becke three-parameter hybrid (B3) functional was used along with the Lee–Yang– Parr (LYP) correlation functional. The 6-311G** basis set was employed for all of the optimization and harmonic vibrational frequency calculations [13–15]. Previous studies have shown that the DFT-B3LYP method can be used to accurately predict the HOFs of many organic systems via isodesmic reactions [16, 17]. The heats of formation for the title compounds were derived from the following isodesmic reaction:

where ΔHf,p and ΔHf,R are the heats of formation of the reactants and products at 298 K, respectively. The heats of formation of the reference compounds are listed in Table 1. Thus, the heats of formation of xanthine derivatives can be calculated when the heat of reaction ΔH298 is known. ΔH298 can be calculated using the following formula: ΔH 298 ¼ ΔE þ ΔZPE þ ΔH T þ nRT

Here, ΔE is the difference in total energy between the reactants and products at 0 K. ΔZPE is the difference in zero-point energy between the reactants and products. ΔHT is the thermal correction from 0 to 298 K. ΔnRT is the work term, which equals zero here. The HOF in the solid state [ΔHf(s)] can then be estimated using ΔH f ðsÞ ¼ ΔH f ðgÞ−ΔH sub

ð4Þ

where ΔHsub is the sublimation enthalpy, which can be calculated according to the following equation (taken from [18]):

ΔH sub ¼ α1 ðSAÞ2 þ β 1 νσtot 2

1=2

þ γ1

ð5Þ

where SA is the area of the 0.001 electrons bohr−3 isodensity surface of the molecule. The values of coefficients α1, β1, and γ1 are taken from [19]. The strength of bonding, which can be evaluated using the bond dissociation energy (BDE), is fundamental to understanding chemical processes. The thermal stabilities of the title compounds were evaluated by calculating the BDE of the trigger bond in each compound. At 0 K, the bond dissociation energy can be obtained via BDEðA−BÞ ¼ EðA•Þ þ E ðB•Þ−E ðA−BÞ

ð6Þ

The bond dissociation energy corrected for the zero-point energy (ZPE) can be calculated via BDEðA−BÞZPE ¼ BDEðA−BÞ þ ΔZPE

C5 H4−n N4 O2 ðNO2 Þn þ nNH3 ¼ C5 H4 N4 O2 þ nNH2 NO2 ð1Þ

ð3Þ

ð7Þ

For reaction (1), the heat of reaction (ΔH298) can be calculated from the following equation:

where ΔZPE is the difference in ZPE between the products and the reactants. The characteristic height (H50), which reflects the impact sensitivity and the stability of a compound, was estimated using the following equation (taken from [20]):

ΔH 298 ¼ ΔH f ;p −ΔH f ;R

H 50 ¼ α2 σþ 2 þ β2 ν þ γ 2

ð2Þ

ð8Þ

J Mol Model (2014) 20:2204

Fig. 1 Structures and atom numbering of polynitroxanthines

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Table 1 Calculated total energy (E0, in a.u.), zero-point energy (ZPE, in a.u.), thermal correction (HT, in a.u.), and heats of formation (HOF, in kJ mol−1) of each reference compound Compound NH2NO2 C5H4N4O2 NH3

E0 (a.u.)

EZPE (a.u.)

HT (a.u.)

HOF(kJ mol−1)

−261.11379 −562.59248 −56.57604

0.03862 0.10505 0.03430

0.00470 0.00885 0.00381

6.69 −379.6 −45.94

The characteristic height also can be estimated using the following formula, as suggested by Cao [21]: H 50 ¼ 0:1926 þ 98:64QNO2 2 −0:03405OB100

ð9Þ

Here, QNO2 is the net charge on the nitro group and OB100 is the oxygen balance. The detonation velocity (D) and pressure (P) are the most important parameters for gauging the detonation characteristics of energetic materials. For a series of explosives containing the elements C, H, N, and O, the detonation velocities and pressures of the explosives can be calculated using the following Kamlet–Jacobs equations [22]:  1=2 1=2 D ¼ 1:01 N M¯ Q1=2 ð1 þ 1:3ρÞ

ð10Þ

 1=2 1=2 P ¼ 1:558ρ2 N M¯ Q1=2

ð11Þ

Here, N is the number of moles of gaseous detonation  is the average molecproducts per gram of explosive and M ular weight of the gaseous products. Q is the chemical energy of detonation (cal/g), defined as the difference between the heats of formation of the products and those of the reactants (assuming that the most exothermic reactants are obtained). ρ is the density of the explosive (g/cm3), which was calculated by  Þ by the average molar volume dividing the molar weight ðM (Vm, obtained from the arithmetic average of 100 single-point molar volumes, defined as the volume of 0.001 electrons bohr−3 electron density envelope and computed by Monte Carlo integration. Moreover, a correction for electrostatic interaction that allows improved crystal density prediction was proposed by Peter Politzer et al. [23, 24]:  Crystal densityðρ0 Þ ¼ α2 ðM =V m Þ þ β2 νσ2 tot þ γ 2

m i 1X h þ þ 2 V ðri Þ−V s m i¼1 n 2 1X  −  þ V r j −V s n j¼1

σ2 tot ¼ σ2 þ þ σ2 − ¼

ð12Þ

ð13Þ

2 ν ¼ σ2 þ σ2 − = σ2 tot

ð14Þ

Vþ S ¼

m 1X V þ ðr i Þ m i¼1

ð15Þ

V −S ¼

n  1X V− rj n j¼1

ð16Þ

where ν is the balance parameter, V(r) is the electrostatic potential, V(ri) is the value of V(r) at any point ri on the surface, and V+S(ri) and V−S(rj) represent the positive and negþ − ative values of V(r) on the surface ( V¯S and V¯S are their 2 average values, respectively), while σ tot is the total variance.

Results and discussion Heat of formation (HOF) The HOF is one of the most important thermochemical properties of an energetic material because it is related directly to its detonation parameters. The HOF is frequently taken to be indicative of the energetic content of a material. Table 1 lists E0, EZPE, and thermal corrections (HT) for three reference compounds in isodesmic reactions. The experimental HOFs of many reference compounds are available for isodesmic reactions, while others are unavailable. The computational HOFs of NH2NO2 and C5H4N4O2 were taken from [25, 26], while the experimental HOF of NH3 was taken from [27]. Table 2 lists the HOFs in the gas state [ΔHf(g)] and solid state [ΔHf(s)] of all of the compounds and other relevant parameters. According to the data shown in Table 2, the HOFs are all positive, which is one of the requirements for an energetic material, and these compounds can all be considered endothermic materials. In general, the higher the HOF, the greater the energy content of the molecule. From Table 2, it is clear that the HOF increases as the number of nitro groups is increased. Thus, the contribution of the nitro groups to the HOFs of the polynitroxanthines complies with the group additivity rule. Comparison of the HOF values of A1, A2, A3, and A4 shows that A2 has the smallest HOF while A4 has the biggest HOF. This result indicates that energy contribution from the N–NO2 bond is higher than that from the C–NO2 bond. In other words, the C–NO2 bond is more stable than the N–NO2 bond. Inspecting the C series of polynitroxanthines, it is also notable that the HOFs of isomers with the same number of nitro groups are affected by the positions of the nitro groups. Generally speaking, the closer the nitro groups are to one another, the higher the HOF; in other words, the lower

J Mol Model (2014) 20:2204 Table 2 Total energies (E0, in a.u.), zero-point energies (ZPE, in a.u.), thermal correction values (HT, in a.u.), and heats of formation (in the gaseous and solid states) of the title compounds calculated at the B3LYP/6311G** level

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Compound

E

EZPE

HT

ΔHsub

ΔHf(g)

ΔHf(s)

A1 A2 A3 A4 B1

−767.09785 −767.13661 −767.09289 −767.09289 −971.62589

0.10622 0.10714 0.10589 0.10570 0.10750

0.01149 0.01142 0.01165 0.01176 0.01452

25.30 14.65 27.24 27.27 30.63

231.62 191.03 218.91 235.03 159.79

206.32 176.38 191.67 207.76 129.16

B2 B3 B4 B5 B6 C1 C2 C3 C4 D1

−971.59410 −971.59645 −971.63241 −971.63452 −971.58912 −1176.12089 −1176.12275 −1176.09067 −1176.12840 −1380.61613

0.10690 0.10677 0.10784 0.10765 0.10638 0.10809 0.10792 0.10729 0.10819 0.10840

0.01437 0.01442 0.01429 0.01438 0.01463 0.01746 0.01755 0.01739 0.01733 0.02053

31.46 29.18 32.23 30.72 30.40 35.79 34.41 35.42 35.67 40.92

241.26 234.89 142.95 137.12 253.67 320.23 315.14 397.32 300.44 770.77

209.79 205.71 110.72 106.40 223.27 284.44 280.73 361.90 264.77 729.84

the thermodynamic stability. For example, in both C1 and C2, the two nitro groups are located on the same five-membered ring and are therefore close to each other, leading to a relatively high HOF, while the nitro groups are further apart in both C3 and C4, so they both have smaller HOFs than C1 and C2. Electronic structure and stability Table 3 lists the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energies and the energy gaps (ΔELUMO–HOMO) for the polynitroxanthines, as calculated at the B3LYP/6-311G(d,p) level. Molecular orbital analysis can provide useful information on electronic structures. Molecules with large energy gaps would be expected to have lower reactivities in chemical or photochemical processes involving electron transfer or an electron leap than molecules with small energy gaps. From Table 3, it is clear that all of the polynitroxanthines have lower ΔELUMO–HOMO values than the unsubstituted xanthine. However, the value of ΔELUMO–HOMO does not vary significantly among the polynitroxanthines. Inspecting the values for A1– A4, we find that once a nitro group has been attached to the six-membered ring, the entire molecule gains a large energy gap. The designed compounds have similar energy gaps to that of the commonly used stable explosive triaminotrinitrobenzene (TATB) [28, 29]; in other words, all of the compounds are stable. Recent works suggest that the bond dissociation (BDE) energy of the weakest bond in the explosive molecule may play an important role in initiating the explosion [30]. The initial stage of the thermal decomposition of an energetic material can be gauged on the basis of the BDE. In general, the

larger the BDE of the C–NO2 or N–NO2 bond, the more stable it is. The weakest bond is selected according to the principle of the smallest bond order [31]. Table 4 lists the trigger bond as well as its bond order, BDE without zero-point energy correction, and BDEZPE (with zero-point energy correction) for each compound investigated in the present work. From Table 5, we can see that the bond order of the weakest bond is less than 1, which indicates that it is vulnerable in explosive reactions. The BDE after zero-point energy correction is 17–23 kJ mol−1 Table 3 Calculated HOMO and LUMO energies (in a.u.) as well as the energy gaps (ΔELUMO–HOMO) of the polynitroxanthines, as calculated at the B3LYP/6-311G** level, as well as those of xanthine and TATB Compound

ELUMO

EHOMO

ΔELUMO–HOMO

C5H4N4 A1

−0.24207 −0.26608

−0.04848 −0.11806

0.19359 0.14802

A2 A3 A4 B1 B2 B3 B4 B5 B6 C1 C2 C3 C4 D1 TATB

−0.26974 −0.26338 −0.26006 −0.27968 −0.28450 −0.28207 −0.28817 −0.28542 −0.27773 −0.29613 −0.29348 −0.29697 −0.30054 −0.30682 −0.10280

−0.12870 −0.09711 −0.09308 −0.13764 −0.13013 −0.12917 −0.13790 −0.13959 −0.11031 −0.14540 −0.14710 −0.13936 −0.14719 −0.15328 −0.26480

0.14104 0.16627 0.16698 0.14204 0.15437 0.15290 0.15027 0.14583 0.16742 0.15073 0.14638 0.15761 0.15335 0.15354 0.16210

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Table 4 Calculated bond dissociation energy (BDE, in kJ mol−1) for the rupture of the weakest bond in each polynitroxanthine, as calculated at the UB3LYP/6-311 G** level, as well as those of RDX and HMX Compound

Trigger bond

Bond order

BDE

BDEZPE

A1 A2 A3 A4 B1 B2 B3 B4 B5

N14–NO2 C12–NO2 N8–NO2 N6–NO2 N13–NO2 N8–NO2 N6–NO2 N8–NO2 N6–NO2

0.8966 0.9230 0.8499 0.8290 0.7186 0.6628 0.8172 0.8323 0.8135

138.55 295.11 124.68 210.77 99.16 121.12 207.02 121.01 209.92

120.09 277.70 107.70 188.87 83.37 103.96 184.41 104.18 188.57

B6 C1 C2 C3 C4 D1 RDX HMX

N6–NO2 N12–NO2 N12–NO2 N6–NO2 N6–NO2 N11–NO2 – –

0.8074 0.6953 0.6993 0.7971 0.7919 0.6769 -

197.75 111.49 103.47 200.93 199.04 113.82 166.19 178.77

174.58 94.67 87.39 179.52 175.91 96.87 145.62 160.41

BDE bond dissociation energy without zero-point energy correction, BDEZPE bond dissociation energy including zero-point energy correction

lower than the BDE without zero-point energy correction. However, the BDE and BDEZPE show the same trend across the series of compounds, and the pyrolysis mechanism is not Table 5 Calculated characteristic height (H 50 , in cm) of each polynitroxanthine, as well as those of RDX and HMX Compound

QNO22

OB100

a

H50

σ+2

υ

b

A1 A2 A3 A4 B1 B2 B3 B4 B5 B6 C1 C2 C3 C4 D1 RDX HMX

0.000732 0.000002 0.000118 0.000051 0.001167 0.000011 0.000002 0.000283 0.000250 0.000217 0.000671 0.000668 0.000092 0.001444 0.002194

−2.37 −2.37 −2.37 −2.37 0.00 0.00 0.00 0.00 0.00 0.00 1.52 1.52 1.52 1.52 2.58

34.55 27.35 28.50 27.83 30.78 19.37 19.26 22.05 21.72 21.40 20.70 20.67 14.99 28.32 32.13

108.41 142.31 194.37 207.08 146.69 147.59 163.98 172.90 197.97 180.26 160.78 193.23 150.34 221.19 154.85

0.2478 0.2015 0.1861 0.1683 0.1947 0.2145 0.1480 0.1939 0.1233 0.1346 0.1470 0.1204 0.1516 0.0926 0.1061

55.70 44.29 40.26 35.88 42.63 47.40 31.26 42.28 25.07 27.90 31.03 24.41 32.20 17.50 21.18 24.0 26.0

a

H50 and b H50 are H50 values derived using different methods

H50

affected by the zero-point energy. Among the A series of compounds, A2 has the biggest BDEZPE; this result shows that the C–NO2 bond is more stable than the N–NO2 bond. The same conclusion can be drawn for the other series, and it correlates with the HOF. Among the C series of compounds, C3 and C4 have larger BDEZPE values than C1 and C2, which can be explained by the intramolecular hydrogen bonding present in C3 and C4. This implies that hydrogen bonding plays an important role in increasingthermodynamic stability. Most of the compounds have higher BDE ZPE values (>120 kJ mol−1) than those of RDX and HMX. Fortunately, the BDEZPE values of all of the polynitroxanthines are >80 kJ mol−1, meeting the requirement of an HEDM [32]. All of the designed compounds show good stability. Predicting the impact sensitivities of HEDMs is a very important step in the development of new highly energetic materials. Impact sensitivity is usually characterized by the drop hammer test. It is defined as the height H50 from which a given weight falling upon the compound has a 50 % probability of producing an explosion. Recently, the Politzer group investigated the possibility of a link between the impact sensitivity and the space available to the molecules in the crystal lattice of an energetic material, and obtained interesting conclusions [33]. Table 5 lists aH50 and bH50, which are H50 values obtained using two different methods, and other relevant parameters. For comparison, the relevant values for RDX and HMX also are listed in this table. Inspecting the values of aH50, A1 has the biggest value while C3 has the smallest value. This result Table 6 Predicted detonation properties of the polynitroxanthines investigated in the present work, as calculated at the B3LYP/6-311G** level, as well as those of RDX and HMX Compound OB (%) ρ (g/cm3)

Q (cal/g) D (km/s)

P (GPa) 26.79 26.68

A1 A2

−2.37 −2.37

1.84 1.85

1201.77 1167.85

A3 A4 B1 B2 B3 B4 B5 B6 C1 C2 C3 C4 D1 RDX HMX

−2.37 −2.37 0.00 0.00 0.00 0.00 0.00 0.00 1.52 1.52 1.52 1.52 2.58 0.00 0.00

1.87 1.84 2.01 2.00 2.02 2.05 2.02 2.03 2.13 2.11 2.15 2.12 2.25 1.78(1.82) 1.88(1.91)

1185.17 7.78 1203.40 7.71 1199.23 8.53 1270.61 8.61 1267.00 8.67 1182.91 8.59 1179.09 8.52 1282.55 8.72 1366.47 9.36 1363.77 9.31 1422.74 9.53 1352.18 9.32 1661.55 10.37 1591.03 8.87(8.75) 1633.90 9.28(9.10)

7.72 7.69

27.49 26.72 34.41 34.94 35.66 35.25 34.39 36.17 42.68 42.16 44.54 42.26 53.97 34.67(34.00) 39.19(39.00)

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shows that C3 is the most sensitive of all the molecules. Moreover, it is clear that a larger absolute charge on the nitro group is correlated with a higher aH50 value. Compared with the a H 5 0 values of RDX and HMX, most of the polynitroxanthines have higher sensitivities. Inspecting the b H50 values in Table 5, A1 again has the biggest value, but, in contrast to aH50, C4 has the smallest value. An apparent trend is that the bH50 value decreases as the number of substituent groups increases, which indicates that the sensitivity increases from A to D. Based on the values of bH50, we can see that almost all of the compounds have lower sensitivities than RDX and HMX, which indicates that these compounds are stable with respect to impact. However, we also note that the conclusions drawn based on the values of aH50 and bH50 are not very consistent with those drawn from the BDE values. For example, the BDE of A1 is smaller than that of A2, but this is not the case for aH50 and bH50. This supports the viewpoint of Politzer [34] that there is no general correlation between bond strength and impact sensitivity; any such correlation is limited to a certain class of molecules.

Detonation performance Two key measures of explosive performance are the detonation velocity (D) and the detonation pressure (P). These refer to the stable velocity of the shock front that characterizes detonation and the stable pressure that is developed behind the front, respectively. Many studies have indicated that D and P can be accurately calculated using the K–J equations [35, 36]. Table 6 reports the oxygen balance, molecular density, energy of detonation, detonation velocity, and pressure for each of the polynitroxanthines investigated in the present work, as well as RDX and HMX. It can also be seen from Table 6 that the energy of detonation increases linearly when NO2 groups are added to the molecule. The smallest and largest values of Q are 1167.85 and 1661.55 kJ mol−1, respectively, which shows that all of the compounds have good energy densities. In addition, there are strong linear relationships between ρ and n (the number of nitro groups), D and n, and P and n: ρ=0.131n+1.735 (R2 =0.990), D=0.886n+6.87 (R2 =0.997), and P=8.909n+17.42 (R2 =0.993), respectively. This strongly supports the claim that introducing more nitro substituents (moderately increasing the oxygen balance) into an energetic molecule usually helps to improve its detonation performance. Compared with the detonation performances of RDX and HMX [37, 38], the B, C, and D series of polynitroxanthines have outstanding detonation properties. Furthermore, the detonation performances of the C and D series meet the requirements (i.e., ρ≈1.9 g/cm3, D≈9.0 km/ s, and P≈40 GPa) of HEDMs [39].

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Conclusions In the work reported here, we studied the heats of formation, electronic structures, energetic properties, and thermal stabilities of a series of polynitroxanthines using the DFT-B3LYP method. All of the compounds were found to have positive solid-state heats of formation, and the heat of formation was observed to be affected by the number of nitro groups present and their positions on the rings of the polynitroxanthine. In addition, more energy was contributed by the N–NO2 bond than by the C–NO2 bond. Stability correlations were established for these molecules by evaluating the energy gap, the dissociation energy of the weakest bond, and the characteristic height of each compound. The energy gaps for all of the compounds were close to that of TATB, and the bond dissociation energies were >80 kJ mol−1. Furthermore, most of the polynitroxanthines had satisfactory H50 values. The calculated detonation velocities and pressures indicate that the nitro group is an effective structural unit for enhancing the detonation performances of polynitroxanthine derivatives. The molecular density, detonation velocity, and detonation pressure increase linearly with the number of nitro groups. Because of their outstanding detonation performances and thermal stabilities, the “C series” and “D series” compounds explored in this work are considered to be the target compounds with the greatest potential to be synthesized and used as HEDMs. Acknowledgments This work is supported by the National Nature Science Foundation of China (no. 21006057) and the Provincial Science and Technology Foundation of Henan (no. 122102310568).

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Computational studies on the energetic properties of polynitroxanthines.

Density function theory calculations were performed to find comprehensive relationships between the structures and properties of a series of highly en...
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