Article pubs.acs.org/JPCA
Theoretical Study on the Effects of Hydrogen-Bonding and Molecule−Cation Interactions on the Sensitivity of HMX Yunlu Li, Junpeng Wu, Duanlin Cao, and Jianlong Wang* School of Chemical Engineering and Environment, North University of China, Taiyuan 030051, People’s Republic of China ABSTRACT: To assess the effects of weak interactions on the sensitivity of HMX, 11 complexes of HMX (where six of them are hydrogen-bonding complexes, and the other five are molecular−cation complexes) have been studied via quantum chemical treatment. The geometric and electronic structures were determined using DFTB3LYP and MP2(full) methods with the 6-311++G(2df, 2p) and aug-cc-pVTZ basis sets. The changes of the bond dissociation energy (BDE) of the trigger bond (N−NO2 in HMX) and nitro group charge have been computed on the detailed consideration to access the sensitivity changes of HMX. The results indicate that upon complex forming, the BDE increases and the charge of nitro group turns more negative in complexes, suggesting that the strength of the N−NO2 trigger bond is enhanced and then the sensitivity of HMX is reduced. Atom-in-molecules analyses have also been carried out to understand the nature of intermolecular interactions and the strength of trigger bonds.
1. INTRODUCTION With civil and military requirements, a great quantity of work has been done to develop new high-energy density materials (HEDMs) with good thermal stability, better performance, insensitivity, and environmentally friendly syntheses.1−4 Unfortunately, those characteristics are often contradictory to one another. Because of the nature of the explosive, most explosives having high performance show poor sensitivity, while explosives with excellent thermal stability and insensitivity usually exhibit poor performance.5,6 Therefore, one of the main research targets is tantamount to decrease the sensitivity of explosives, especially those with good detonation properties. Recently, much attention has been paid to investigate the relationship between the sensitivity and structure of the energetic compounds, especially the effects of the hydrogen-bonding/ molecular−cation interactions between explosive and small molecule/cations.7,8 Previous research has found that with increasing strength of the trigger bond (C−NO2 in the azolebased energetic compounds) after forming a complex, the bond dissociation energies increase, and thus the sensitivity of energetic compound is reduced.9−11 So, how about the situation on the energetic compounds with the trigger bond of N−NO2? HMX (1,3,5,7-tetranitro-1,3,5,7-tetraazacyclooctane), with four N−NO2 groups, is a typical nitroamine explosive, and has excellent detonation properties but relatively poor sensitivity. In this Article, the complexes with hydrogen bond forming from the nitro group of HMX to HF, HCl, HBr, HCN, HNC, and HCCH, and the complexes with molecular− cation interactions forming from the nitro group of HMX to Li+, Na+, K+, Mg2+, and Ca2+, have been studied via quantum chemical treatment. The MP2(full)/6-311++G(2df,2p) and DFT method at B3LYP/6-311++G(2df,2p) and B3LYP/augcc-pVTZ levels have been carried out to investigate the © XXXX American Chemical Society
geometric and electronic structures. The influences of those weak interactions on the strength of trigger bond and nitro charges have been accessed. By atom-in-molecules (AIM) analysis, the nature between the structure and sensitivity has been indicated, which can be a reference when designing new insensitive energetic materials, especially nitroamine energetic compounds with the trigger bond of N−NO2.
2. THEORY AND COMPUTATIONAL METHODS Using the Gaussian 09 package,12 DFT methods were used to study the monomer HMX (C0) and its complexes: HMX···HF (C1), HMX···HCl (C2), HMX···HBr (C3), HMX···HCN (C4), HMX···HNC (C5) (where the HNC is the isomer of HCN), and HMX···HCCH (C6); HMX···Li+ (C7), HMX··· Na+ (C8), HMX···K+ (C9), HMX···Mg+ (C10), and HMX··· Ca2+ (C11). The geometrical parameters of the above model compounds were optimized at the B3LYP/6-311++G(2df,2p) level. The choice of the level has already yielded reasonable molecular structures.13−15 The optimized structures have been identified as the local energy minimum by vibrational analysis. The interaction energy (Eint) was calculated at the B3LYP/6311++G(2df,2p), B3lyp/aug-cc-pVTZ, and MP2(full)/6-311+ +G(2df,2p) levels. Eint is defined as the difference between the energy of monomer and its complexes, which can be calculated from the following equation: E int = E(R−NO2 ··· X) − E(R−NO2 ) − E(X)
(1)
Eint has also been corrected from the Basis Set Superposition Error (BSSE).16 Received: August 28, 2016
A
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Figure 1. Optimized structures of model compounds at the B3LYP/6-311++G(2df, 2p) level.
is relatively most stable, and α-, γ-, and δ-HMX are unstable. To confirm the effects of weak interactions on the sensitivity of HMX, the α-HMX is used as a reference in this Article. Structures of α-HMX C0 and its complexes C1−C11 were optimized at the B3LYP/6-311++G(2df,2p) level, and those optimized structures are shown in Figure 1. Selected structural parameters of the model compounds are given in Table 1.
To measure bond strength and the relative stability of the monomer and its complexes, trigger bond dissociation energies (BDEs) were calculated using the above three methods, where the BDE is the difference between the energies of complex and free radicals, which can be calculated from the following equations:17 BDE = E(R−NO2 ) − E(R•) − E(•NO2 ) for monomer (2)
Table 1. Selected Bond Lengths (in Å) of Model Compounds
BDE = E(R−NO2 ··· X) − E(R•) − E(•NO2 ··· X) for complex
compound
(3)
C0 C1 C2 C3 C4 C5 C6 C7 C8 C10
The previous works show that increasing the negative charge of the nitro group (−QNO2) can reduce the sensitivity of energetic materials.18−20 The nitro charge (QNO2), where the nitro group is at the position of forming the interaction, can be calculated with the following equation: Q NO = Q N + Q O1 + Q O2 2
(4)
The QN, QO1, and QO2 are the charges on the nitrogen and oxygen atoms of the nitro group, respectively. Atom-in-molecule (AIM)21 analysis of the optimized geometries of model monomer and its complexes has also been carried out using the AIMPAC package at the B3LYP/6-311+ +G(2df,2p) level to understand the nature of the intermolecular interaction and the strength of the trigger bond. Generally, the bigger is the value of electron density ρ(r), the more stable is the bond. Furthermore, the value of Laplacian ∇2ρ(r) is usually used to describe the nature of a bond. When the value of the ∇2ρ(r) is negative, the bond is covalent, and if the value of ∇2ρ(r) is positive, the bond then is ionic.
C9 C11
HMX HMX···HF HMX···HCl HMX···HBr HMX···HCN HMX···HNC HMX···HCCH HMX···Li+ HMX···Na+ HMX···Mg2+ compound HMX···K+ HMX···Ca2+
O13···H 1.831 2.080 2.174 2.214 1.970 2.397
O18···Mn+ 2.930 2.439
O13···Mn+
N9−O13
N1−N9
1.216 1.400 1.229 1.383 1.224 1.389 1.223 1.391 1.223 1.388 1.228 1.384 1.219 1.395 2.011 1.245 1.322 2.565 1.231 1.355 2.154 1.259 1.309 N11−O18 N5−N11 1.229 1.252
1.361 1.317
According to Table 1, Figure 2 was obtained. In monomer C0, all of the carbon atoms lie in the same plane, all of the amino nitrogen atoms lie in another plane, and the distributions of both groups’ para-positions nitro groups are symmetry. One group in the para-position nitro groups (N1−NO2 and N5− NO2) is relatively upright, and another group (N3−NO2 and N7−NO2) is procumbent. This is a consequence of the repulsion between the neighboring nitro group. This distribution reduces the steric hindrance and makes the compound more stable. The average distance of the N−N
3. RESULTS AND DISCUSSION 3.1. Optimized Structures. There are four stable crystal structures for HMX at room temperature, in which the β-HMX B
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in complexes is relatively stronger than in monomer. As a result, the complexes are more stable than monomer, where the stability is said to be thermal stability, which is associated with thermal and mechanical sensitivity performance for an energetic compound. That means forming complexes that contain the hydrogen bond forming between hydrogen atoms in small molecules and nitro oxygen atoms in HMX can reduce the sensitivity of HMX. This conclusion is meaningful for commercial production. In C4−C6 complexes, hydrogen-bond lengths are 2.214, 1.970, and 2.397 Å, respectively. The hydrogen bond in C5 is stronger than that of the other two complexes. The bond length of N1−N9 is shorter than that of monomer. As a result, the complexes of C4−C6 are more stable and less sensitive than monomer. Thus, based on the hydrogen-bond length, the possible decreasing order of stability of the model compounds for C1−C6 is as follows: C1 > C5 > C2 > C3 > C4 > C6. Also based on the trigger bond length, that order is as follows: C1 > C5 > C4 > C2 > C3 > C6. For molecule−cation complexes, the effect of molecule− cation interaction is more obvious as shown in Figure 2. In C7−C11 complexes, the trigger bond length N1−N9 (or N5− N11) is 1.322, 1.355, 1.309, 1.361, and 1.317 Å, respectively, which is substantially shorter than monomer. The maximum difference of the bond length is 0.091 Å, and the minimum difference is 0.045 Å. It is reported that the complexes forming by metal cation can reduce the sensitivity of HMX remarkably. This effect also has periodic trends. Thus, based on the trigger bond length, the descending order of stability of the model compounds for C7−C11 is as follows: C10 > C11 > C7 > C8 > C9. As compared to all of the model compounds, the descending order of stability for C0−C11 is as follows: C10 > C11 > C7 > C8 > C9 > C1 > C5 > C4 > C2 > C3 > C6 > C0. The above analyses suggest that forming a complex hydrogen-bonding or molecule−cation interaction can reduce the sensitivity of HMX, especially forming molecule−cation interactions. Thus, hydride or metal cation can be introduced appropriately in the commercial process of nitroamine. 3.2. Interaction Energy and Dissociation Energy. Further, to determine the effects of the hydrogen-bonding and molecule−cation interactions, B3LYP/[6-311++G(2df,2p), aug-cc-pVTZ] and MP2(full)/6-311++G(2df,2p) methods have been carried out to calculate the Eint and BDEs using the optimized structure. The results are shown in Tables 2 and 3. Where the Eint contains the hydrogen-bonding interaction
Figure 2. Two kinds of bond lengths in model compounds.
single bond in C0 is 1.400 Å, between the length of the N−N single bond (1.450 Å) and a double bond (1.250 Å), which is the result of electron transfer. In C1−C3 complexes, the hydrogen bonds forming between the hydrogen atoms in small molecules and nitro oxygen atoms in HMX are 1.831 (C1), 2.080 (C2), and 2.174 Å (C3), respectively. For HMX···HX (X = F, Cl, Br), the hydrogenbond length showing periodic changes decreases with the increase of atomic number, which is showing in Figure 2. This is the result of that with the increasing atomic number, the atomic radius increases, then the ability of bounding electron abates, which decreases the strength of the hydrogen bond. According to the literature,22 the hydrogen bonds are very strong when the bond length of H···A is 1.2−1.5 Å and the sum of van der Waals radii of X···A is 2.5−3.2 Å; strong when H···A is 1.5−2.2 Å with X···A 2.2−2.5 Å; and weak when H···A is 2.0−3.0 Å with X···A 3.0−4.0 Å. Thus, Table 1 indicates that the hydrogen bond in C3 is a weak hydrogen bond, and those in C1 and C2 are strong. With the changes of hydrogen bonds in C1−C3 complexes, the bond lengths of N9−O13 and N1− N9 are changed regularly. It is noted that the N1−N9 is the trigger bond in HMX, so the changes of this bond length indicate the changes of the strength, eventually leading to the changes of sensitivities of the complexes. As compared to reference compound C0, the bond length of N1−N9 in C1−C3 is shorter, suggesting that the trigger bond Table 2. Interaction Energies Calculated at Three Levelsa
B3LYP C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 a
MP2(full)
complex
6-311++G(2df,2p)
aug-cc-pVTZ
HMX···HF HMX···HCl HMX···HBr HMX···HCN HMX···HNC HMX···HCCH HMX···Li+ HMX···Na+ HMX···K+ HMX···Mg2+ HMX···Ca2+
4.88 2.17 1.73 2.90 4.55 1.00 50.17 42.72 33.20 196.98 144.65
5.39 2.62 1.96 2.97 4.68 1.06 51.30 43.88 200.47
6-311++G(2df,2p) 3.72 2.07 2.68 4.63 1.17 45.74 38.09 32.54 184.92 137.00
The values of Eint are in −kcal/mol. C
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The Journal of Physical Chemistry A Table 3. Trigger Bond Dissociation Energies Calculated at Three Levelsa B3LYP C0 C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 a
MP2(full)
complex
6-311++G(2df,2p)
aug-cc-pVTZ
6-311++G(2df,2p)
HMX HMX···HF HMX···HCl HMX···HBr HMX···HCN HMX···HNC HMX···HCCH HMX···Li+ HMX···Na+ HMX···K+ HMX···Mg2+ HMX···Ca2+
51.92 56.73 54.84 54.25 55.21 56.52 53.37 96.58 90.89 82.59 209.89 174.26
50.96 55.52 53.69 53.17 54.18 55.45 52.38 94.99 89.04
72.66 81.46 77.59 77.46 80.43 74.92 119.96 117.45 108.82 236.55 200.10
208.23
The BDEs are in −kcal/mol.
Table 4. Mulliken Charges of Model Compounds Calculated at the B3LYP/6-311++G(2df,2p) Level atom
C0
−QNO2
C1
−QNO2
C2
−QNO2
C3
−QNO2
C4
−QNO2
C5
−QNO2
N9 O13 O14 N10 O15 O16 N11 O17 O18 N12 O19 O20 atom
−0.074 −0.151 −0.151 −0.062 −0.144 −0.144 −0.074 −0.151 −0.151 −0.062 −0.144 −0.144 C6
0.376
−0.412 −0.098 −0.111 −0.082 −0.134 −0.135 −0.054 −0.148 −0.149 −0.060 −0.138 −0.136 C7
0.621
−0.257 −0.156 −0.109 −0.075 −0.136 −0.134 −0.067 −0.149 −0.149 −0.060 −0.139 −0.137 C8
0.522
−0.252 −0.127 −0.108 −0.075 −0.137 −0.134 −0.069 −0.149 −0.150 −0.059 −0.140 −0.138 C9
0.487
−0.332 −0.139 −0.099 −0.075 −0.135 −0.134 −0.066 −0.148 −0.148 −0.063 −0.138 −0.136 C10
0.570
−0.392 −0.157 −0.094 −0.081 −0.133 −0.132 −0.061 −0.147 −0.146 −0.061 −0.138 −0.135 C11
0.643
N9 O13 O14 N10 O15 O16 N11 O17 O18 N12 O19 O20
−0.332 −0.139 −0.099 −0.075 −0.135 −0.134 −0.065 −0.148 −0.148 −0.063 −0.138 −0.136
0.570
−0.581 −0.106 −0.106 −0.081 −0.097 −0.112 −0.267 −0.100 −0.100 −0.081 −0.112 −0.097
0.793
−0.538 −0.089 −0.089 −0.108 −0.109 −0.109 −0.537 −0.090 −0.090 −0.108 −0.109 −0.109
0.716
−0.512 0.017 0.017 −0.080 −0.061 −0.061 −0.512 0.016 0.016 −0.080 −0.061 −0.061
0.478
−0.467 −0.111 −0.111 −0.110 −0.066 −0.066 −0.467 −0.111 −0.111 −0.110 −0.066 −0.066
0.689
0.350
0.376
0.350
0.344
0.361
0.337
0.351
0.351
0.334
0.290
0.467
0.290
−0.610 −0.026 −0.026 −0.112 −0.105 −0.105 −0.611 −0.026 −0.025 −0.113 −0.105 −0.105
0.345
0.365
0.336
0.662
0.322
0.662
0.323
0.346
0.368
0.337
0.326
0.717
0.326
0.343
0.362
0.337
0.202
0.480
0.202
0.346
0.354
0.334
0.242
0.689
0.242
deemed to be a strong hydrogen bond. In Table 2, the value of Eint for C5 is 4.63, greater than 4 −kcal/mol, which indicates that the hydrogen bond in C5 is strong. This result is consistent with the previous conclusion in section 3.1. Yet values of Eint for C1−C3 are all less than 4 −kcal/mol, indicating that the hydrogen bonds in C1−C3 are weak, which is partly different with the previous conclusion in section 3.1. On the basis of values of Eint in Table 2, the descending order of stability of the model compounds for C1−C11 is as follows: C10 > C11 > C7 > C8 > C9 > C5 > C1 > C4 > C2 > C3 > C6 (where the value of Eint for C3 is referenced to the other two algorithms). Referring to the BDEs in Table 3, the decreasing order of stability of the model compounds for C1−C11 is as follows: C10 > C11 > C7 > C8 > C9 > C5 > C1 > C4 > C2 > C3 > C6 > C0. It is noted that the orders referring to Eint and BDEs are relatively consistent with each other.
energies and molecule−cation interaction energies, the BEDs are the trigger bond (N1−N9 or N5−N11) dissociation energies. In Table 2, the values calculated using B3LYP methods are distinct from one another. According to the previous works, the MP2(full)/aug-cc-pVTZ method is reasonable and yields good results.23,24 Thus, discussions by Eint are based on the results calculated at MP2/6-311++G(2df,2p) level. Without consideration of the electron delocalization effect, the values calculated using the B3LYP method in Table 3 are smaller and reasonable. Thus, discussions for BDEs are based on the results calculated at the B3LYP/aug-cc-pVTZ level. The hydrogen-bond energy is the most reliable stander to evaluate the strength of the hydrogen bond. Depending on the literature,25 if the bond energy (−kcal/mol) is less than 4, it suggests a weak hydrogen bond. If the value is 4−15, then it is D
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The Journal of Physical Chemistry A Table 5. Electron Density of the Bond Critical Point Calculated at the B3LYP/6-311++G(2df,2p) Levela ρ(O6···H7) ∇2ρ(O6···H7) ρ(N4···O6) ∇2ρ(N4···O6) ρ(N1···N4) ∇2ρ(N1···N4)
C0
C1
C2
C3
C4
C5
0.5152 −1.0072 0.3345 −0.4712
0.0291 0.0951 0.4984 −0.9290 0.3472 −0.5299
0.0182 0.0592 0.5054 −00.9566 0.3428 −0.5090 C8
0.0153 0.0496 0.5062 −0.9641 0.3413 −0.5020 C9
0.0133 0.0472 0.5053 −0.9603 0.3436 −0.5125
0.0215 0.0757 0.5002 −0.9376 0.3471 −0.5292
C7 ρ(O6···M ) ∇2ρ(O6···Mn+) ρ(N4···O6) ∇2ρ(N4···O6) ρ(N1···N4) ∇2ρ(N1···N4) n+
a
0.0256 0.1649 0.4798 −0.8244 0.3973 −0.7745
0.0116 0.0626 0.4961 −0.9047 0.3697 −0.6351
0.0105 0.0458 0.4992 −0.9220 0.3650 −0.6117
ρ in au.
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3.3. Electron Structure. In nitro compounds, the C−NO2 bond or N−NO2 bond is generally the weakest bond in the molecule, and the rupture of this bond is the initial step in the decomposition or detonation.26,27 Table 4 shows the Mulliken charges and the nitro group charges (QNO2, the sum of the charges of the nitrogen and oxygen atoms), respectively. The previous works have suggested that the higher −QNO2 indicates plausible lower impact sensitivity of the energetic compound.18−20,28−30 Table 4 gives the values of −QNO2 in HMX monomer and its complexes, and the values in all complexes are higher than that in monomer, which indicates that the trigger bonds of complexes are substantially more strong, and as a consequence, the complexes are more stable than monomer. On the basis of the highest −QNO2 value, the probable decreasing order is as follows: C7 > C9 > C11 > C8 > C5 > C1 > C4 (C6) > C2 > C3 > C10 > C0. Furthermore, to understand the nature of intermolecular interactions in the complexes, the atom-in-molecule (AIM) theory of Bader has been applied to the C0−C11 compounds. Table 5 gives the electron density ρ of the bond critical point corresponding to the N−NO2 bonds of designed molecules.The ρ(O···H and O···Mn+) of C1−C11 are between 0.0013 and 0.0332 au, and the ∇2ρ(N···N) are positive, which indicate the interactions are of closed-shell. The ρ(N···O) values of complexes are smaller than that of monomer. This is the result of forming weak interactions leading to the N−O bond being elongated. Furthermore, the ρ(N···N) values of complexes are greater than that of monomer, which also indicates that, after forming an interaction, the trigger bond is more strong, and the sensitivity of the compound is decreased. This result is consistent with the above conclusions.
C10 0.0332 0.1972 0.4637 −0.7390 0.4084 −0.8291
C6 0.0088 0.0314 0.5105 −0.9854 0.3382 −0.4879 C11 0.0013 0.1493 0.4717 −0.07839 0.4018 −0.7930
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We are grateful to the referees for their useful comments. Y.L. acknowledges the sustaining financial support from The Science Research Foundation for Graduate Students of North University of China (no. 20151227).
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REFERENCES
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4. CONCLUSION The B3LYP/[6-311++G(2df,2p), aug-cc-pVTZ] and MP2(full)/6-311++G(2df,2p) methods were used to determine the geometric and electronic structures, interaction energies, and bond dissociation energies for the HMX monomer and its 11 complexes. After complexes are formed, the trigger bond lengths are shorter, the bond dissociation energies are bigger, and the sum of nitro negative charge is higher than those of monomer. By AIM analysis, the electron densities are greater than those of monomer. Those effects make the HMX (nitroamine explosive) less sensitive and more stable. E
DOI: 10.1021/acs.jpca.6b08681 J. Phys. Chem. A XXXX, XXX, XXX−XXX
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DOI: 10.1021/acs.jpca.6b08681 J. Phys. Chem. A XXXX, XXX, XXX−XXX
