J Mol Model (2014) 20:2326 DOI 10.1007/s00894-014-2326-1
ORIGINAL PAPER
Theoretical study of solvent effects on RDX crystal quality and sensitivity using an implicit solvation model Gang Chen & Wenyan Shi & Mingzhu Xia & Wu Lei & Fengyun Wang & Xuedong Gong
Received: 20 March 2014 / Accepted: 28 May 2014 # Springer-Verlag Berlin Heidelberg 2014
Abstract Density functional theory calculations using an SMD model were performed to investigate the effect of solvents (cyclohexanone, acetone, dimethyl formamide and dimethyl sulphoxide) on the crystal quality and sensitivity of RDX. The results indicate that the N–N bond length of the RDX molecule in solvents differs clearly from that in gas phase. The solvent effect on bond and dihedral angles of RDX molecule is small, however, the RDX molecule still maintains the AEE configuration. Natural population analysis shows that, due to solvation effects, RDX O atoms attract more electrons in solvents than in gas phase, while more positive charge distributes to the molecular skeleton. The calculations of N–NO2 bond BDE and nitro group charge as well as surface electrostatic potential parameters reveal that the solvent effect may be helpful to reduce the sensitivity of RDX, but this effect has an upper limit. Finally, it can be predicted qualitatively that the crystal quality of RDX crystallized from cyclohexanone and dimethyl sulphoxide will be higher than that from acetone and dimethyl formamide. Experimental results support these theoretical predictions. Keywords RDX . Sensitivity . Crystal quality . Solvent effect . Implicit solvation model
Introduction RDX (hexogen, C3H6N6O6) is one of the most important energetic materials, and is used widely in the preparation of plastic bonded explosives such as PBXN109 (composed of 64 % RDX, 20 % aluminium and 16 % binder [1]). However, G. Chen : W. Shi : M. Xia (*) : W. Lei : F. Wang : X. Gong Chemistry Department, Nanjing University of Science and Technology, Nanjing 210094, China e-mail: [email protected]
its high sensitivity impacts on the safety of RDX-based PBXs, thus restricting further application of RDX. The crystal quality of explosives, as characterized by particle size, shape and defect content, has an important effect on sensitivity, solid load and other factors [2, 3]. It has been reported [3–6] that RDX crystallized from a solvent is imperfect, with defects, impurities and irregular crystal shapes, which results in hot spot formation and high sensitivity as well as low load density. Crystal quality is influenced not only by internal molecular structures, but also by external environments such as crystallization technologies [4, 7], solvents [8] and additives [9]. Solvents play an important role in crystal quality, and can induce crystal defects, such as solvent inclusions [10, 11], affect product purity as foreign compounds [12], and change crystal morphology [13]. Consequently, to reduce sensitivity and improve performance, research of solvent effects on RDX crystal quality has an important practical significance. Many energetic material researchers believe that there is a strong relationship between sensitivity and the molecular structures of explosives. Cleavage of the weakest molecular bonds, which are generally regarded as trigger linkages, is widely considered as a key step in the explosive decomposition or initiation process [14]. In the past few decades, from the perspective of molecular structure, many scholars have focused on correlating configuration parameters with explosive sensitivity. As the linkage bond of nitramine compounds, the bond dissociation energy (BDE) of N–NO2 is suggested to be correlated with sensitivity [15]; however, any such relationship between BDE and sensitivity is not general, and it is insufficient to focus only on the BDE factor. Zhang et al. [16] have proposed a qualitative method in which the nitro group charge is regarded as a structural parameter that can be used to assess impact sensitivity. The method has wide application in almost all nitro compounds when the C–NO2, N–NO2, or O– NO2 bond is the weakest in the entire molecule. From the point of molecular electrostatic potential (MEP), Murray et al.
2326, Page 2 of 9
[17] found empirical evidence of a link, in that, if the N–NO2 bond is a trigger linkage, the anomalous electrostatic potential on the molecular surface can be correlated with the sensitivity of nitramines. Other methods, such as oxygen balance, molecular electronegative and band gap, that can approximately predict the sensitivity of explosives have also been proposed [18–20]. The molecular configuration and electronic structure of the solute, and the chemical reaction itself, are well known to be affected significantly by the solvent [21–24]. The solvents cyclohexanone (CYC), acetone (ACE), dimethyl formamide (DMF) and dimethyl sulfoxide (DMSO) are often used as crystallization solvents for RDX, and the solubility of RDX in these solvents is relatively high compared with other common solvents (Table 1) [25]. In practice, solvents used for the purification of RDX are often not fully recovery [26]. Obviously, any remaining solvent may impact on RDX crystal quality. As a result, it is very important to study solvent effects on the molecular structure of RDX that may be associated quantitatively with RDX sensitivity. So far, no such detailed investigation has been reported. The aim of our work was to investigate the effect of solvents on the sensitivity and crystal quality of RDX, to provide some theoretical support for high quality reduced sensitivity RDX. In this paper, DFT methods were combined with an implicit solvation model to investigate the effect of the solvents CYC, ACE, DMF and DMSO on RDX crystal quality. Changes in the molecular structure of RDX such as bond length, bond and dihedral angles in different solvents were analyzed, and charge distribution was also studied using natural population analysis (NPA). Following calculation of the bond dissociation energy of N–NO2 and the surface electrostatic potential parameter as well as nitro group charges, solvent effects on the sensitivity of RDX are discussed. Finally, by calculating the solvation free energies in different solvents, solvation effects on crystal quality of RDX were predicted and compared with experimental results.
J Mol Model (2014) 20:2326 Table 1 Solubility of RDX (hexogen, C3H6N6O6) (S, g/100 g) in various solvents at 298 K. CYC Cyclohexanone, ACE acetone, DMF dimethyl formamide, DMSO dimethyl sulfoxide. Data taken from [18] RDX
Benzene
CYC
ACE
Alcohol
DMF
DMSO
Water
S
–
7.5
8.2
–
37
41
–
parameter hybrid function [30] combined with the Lee, Yang and Parr correlation function [31]), has been confirmed to give reasonable configurations and electronic structures of the RDX molecule, which are good agreement with experimental results [32, 33]. Geometry optimization of RDX molecule in both the gas and solvent phase was performed at B3LYP/6311++G** level. The self-consistent reaction field (SCRF) based on the implicit solvation model-SMD model [34], which can correctly predict the solvation free energy, was applied to simulate solvent environments at the same computational level. The results of vibrational frequency analysis indicate that no imaginary frequencies are found, which means the optimized molecular structures are true minima on the potential energy surface. Furthermore, NPA implemented in Gaussian 09 software was performed to investigate solvation effects on the electronic structure of the RDX molecule. The N–NO2 bond strength can be characterized by the bond dissociation energy (BDE). The bond dissociation energy of N–NO2 is not only effective for characterizing such bond stability, but is also a major factor for assessing sensitivity. The BDE of N–NO2 was calculated by employing the following cleavage reaction:
Computational methods All DFT calculations were performed using Gaussian 09 software with a tight self-consistent field convergence threshold [27]. At ambient pressure and temperature, α-RDX (applied widely in practice) is the most stable crystallographic phase. The initial molecular structure was taken from an αRDX unit cell derived from the Cambridge Structural Database (CSD: CTMTNA for α-RDX) [28], as shown in Fig. 1. From Fig. 1, the α-RDX molecule (abbreviation RDX) consists of three CH2–N–NO2 units arranged in a six-membered ring, in which two nitro groups occupy axial A positions and the remaining nitro group is in the pseudo-equatorial E position, so that the molecular conformation of RDX is in the AAE form [29]. The DFT method with B3LYP (Becke-three
Fig. 1 Schematic view of the geometry configuration of RDX molecule
J Mol Model (2014) 20:2326
RNNO2 →RN þNO2 BDE ¼ E ðRNÞ þ E ðNO2 Þ−E ðRNNO2 Þ þ E ZPEC
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ð1Þ
Geometry configuration and charge distribution of RDX molecule in solvents
where E is the total energy, and EZPEC is zero point energy corrected. The quantitative analysis of molecular electrostatic potential of RDX on the van der Waals (vdW) surface in solvents was carried out using Multiwfn 3.2 software, which is a powerful multifunctional wavefunction analyzer [35, 36]. The statistical variable ν is defined as the surface electrostatic potentials imbalance, measured with the following formula:
ν¼
σ2þ σ2− σ2þ þ σ2−
2
ð2Þ
where ó+2 and ó−2 are the positive and negative surface potentials variances, which indicate the strength and variability of the positive and negative surface potentials [17]. The nitro group charge −QNO2 of the RDX molecule is defined as follows: −QNO2 ¼ −ðQN þ QO1 þ QO2 Þ
ð3Þ
where QN, QO1, and QO2 are the net charges on the N and O atoms of the nitro group, respectively [16]. The atom charge was calculated using the atom charge methods of Mulliken [37], NPA and CHELPG [38]. The molecular electrostatic potentials of RDX in solvents were mapped using the VMD 1.9.1 program [39]. In most continuum solvent models, such as SMD, solvation free energy is defined as: ΔGslov ¼ ðE slon þE nes Þ−E gas
Results and discussion
ð4Þ
where Eslon and Egas are the electronic energies of the solute in the presence and absence of the continuum solvent field; Enes denotes all non-electrostatic interaction energies, e.g., cavitation and dispersion-repulsion energies [40, 41]. Klamt [41] pointed out that the user should insist on the computational protocol used in the parametrization of the SMD model; only in this way can the accurate solvation free energy be obtained. The solvation free energies of RDX in different solvents were thus calculated at M052x/6-31G* level, which is consistent with the literature [34, 42].
The bond lengths, R, of the RDX molecule in different solvents optimized at B3LYP/6-311++G** level are listed in Table 2. It can be seen from Table 2 that, compared with the bond length in gas phase, the length changes of C–N covalent bonds on the molecular skeleton of RDX are slight. However, the distance of N–N bonds (N10–N13, N11–N14 and N12–N15) is decreased, with average changes of 0.031, 0.027 and 0.029 Å, respectively. And all N–O bond lengths are increased, with those belonging to the same nitro group being very close. This shows that the bond lengths of the RDX molecule in solvents is changed to some extent compared with those in gas phase, in which the change of N–N bonds is larger. That is to say, solvents have an important effect on the N–N bond length of the RDX molecule. Table 3 lists the computational bond and dihedral angles of the RDX molecule in different solvents at the B3LYP/6311++G** level. As seen from Table 3, the changes of RDX bond angles in solvents are small compared with those in vacuum, with the average changes of all bond angles being less than 3 %. For the dihedral angles of RDX molecule, only the N13–N10–C1–N11 and N13–N10–C1–N11 have a Table 2 Bond lengths of the RDX molecule in different solvents calculated at B3LYP/6-311++G** level Bonds
C1–N10 C3–N10 C1–N11 C2–N11 C2–N12 C3–N12 N10–N13 N11–N14 N12–N15 N13–O16 N13–O17 N14–O18 N14–O19 N15–O20 N15–O21 a
R(Å)
Average change
Gas
CYC
ACE
DMF
DMSO
1.474 1.474 1.449 1.463 1.463 1.449 1.405 1.433 1.433 1.220 1.220 1.214 1.215 1.214 1.215
1.474 1.474 1.454 1.468 1.467 1.454 1.376 1.408 1.406 1.227 1.227 1.221 1.222 1.221 1.222
1.473 1.473 1.454 1.468 1.468 1.454 1.373 1.406 1.405 1.227 1.227 1.221 1.222 1.221 1.222
1.473 1.474 1.454 1.468 1.468 1.454 1.373 1.406 1.403 1.228 1.228 1.221 1.222 1.221 1.223
1.473 1.474 1.454 1.468 1.468 1.454 1.373 1.405 1.403 1.228 1.228 1.221 1.223 1.222 1.223
Decrease in bond length
−0.001a 0 0.005 0.005 0.005 0.005 −0.031a −0.027 −0.029a 0.008 0.008 0.007 0.007 0.007 0.008
2326, Page 4 of 9 Table 3 Bond and dihedral angles of the RDX molecule in different solvents calculated at B3LYP/6-311++G** level
a
Decrease in bond length
J Mol Model (2014) 20:2326
Bond and dihedral angles
Angle(°)
Average change (%)
Gas
CYC
ACE
DMF
DMSO
N10–C1–N11
109
107.8
107.8
107.8
107.7
−1.1a
N11–C2–N12 N10–C3–N12 C1–N10–C3 C1–N10–N13 C3–N10–N13 N10–N13–O16 N10–N13–O17 O16–N13–O17 C1–N11–C2 C1–N11–N14 C2–N11–N14 N11–N14–O18 N11–N14–O19 O18–N14–O19 C2–N12–C3 C2–N12–N15 C3–N12–N15 N12–N15–O20 N12–N15–O21
112.5 109.0 114.5 115.5 115.5 116.6 116.6 126.7 115.5 116.4 116.9 116.1 116.6 127.1 115.5 116.9 116.4 116.1 116.6
110.9 108.0 114.6 118.8 118.7 117.3 117.3 125.3 114.9 116.9 117.7 116.8 117.3 125.7 115.2 117.9 117.4 116.8 117.4
110.9 108.0 114.7 119.0 119.0 117.4 117.4 125.2 114.9 117.0 117.8 116.9 117.4 125.6 115.1 118.0 117.3 116.9 117.4
110.8 108.0 114.6 119.0 119.0 117.4 117.4 125.2 114.8 117.0 117.7 116.9 117.4 125.6 115.1 118.0 117.5 116.9 117.4
110.7 108.0 114.6 119.0 118.9 117.4 117.4 125.1 114.8 117.0 117.7 116.9 117.4 125.5 115.2 118.0 117.5 116.9 117.4
−1.5a −0.9a 0.1 3.0 2.9 0.7 0.7 −1.2a −0.6a 0.5 0.7 0.7 0.7 −1.2a −0.3a 0.9 0.9 0.7 0.7
O20–N15–O21 N13–N10–C1–N11 N13–N10–C3–N12 N14–N11–C2–N12 N14–N11–C1–N10 N15–N12–C3–N10 N15–N12–C2–N11 O16–N13–N10–C1 O17–N13–N10–C3 O18–N14–N11–C1 O19–N14–N11–C2 O20–N15–N12–C3 O21–N15–N12–C2
127.1 166.8 −166.8 95.6 −92.4 92.5 −95.6 159.7 −159.7 167.7 −158.7 −167.7 158.7
125.6 154.2 −154.7 93.1 −90.7 93.5 −95.4 165.6 −164.0 169.4 −157.8 −170.1 158.8
125.6 153.1 −153.4 93.4 −91.3 93.3 −95.1 166.1 −164.8 169.1 −158.4 −169.2 159.5
125.5 153.0 −153.6 92.9 −90.6 93.5 −95.3 166.2 −164.6 169.5 −157.7 −170.3 158.7
125.5 153.3 −153.8 92.8 −90.5 93.6 −95.3 166.1 −164.4 169.4 −157.7 −170.3 158.7
−1.2a −8.0 −7.7a −2.7a −1.8a 1.0 −0.3a 3.9 3.0 1.0 −0.5a 1.4 0.1
larger variation, of which the average change percentages come to 8 %. It can be seen that the largest changes of RDX bond and dihedral angles in solvents both occur in the E position, showing that the N–NO2 unit placed in this location tends to be slightly vertical, as seen in Fig. 2. In a word, the solvent effect on the molecular structure of RDX is small, and the RDX molecule maintains the AEE configuration in solvents. The atom charges on the RDX molecule calculated by NPA analysis in different solvents at B3LYP/6-311++G** level, are presented in Table 4. As seen from Table 4, compared with the natural charges in gas phase, charges of both N and C atoms of RDX molecule decrease in solvents, and with the increase
of solvent polarity, the negative charges of these atoms gradually reduce. On the contrary, the negative charge numbers of all O atoms increase, with the nitro O atoms in the E position have the most average charge transfer numbers (0.010 e). The charge change of H atoms is small, except for atoms H6 and H7 whose charge numbers reduce slightly. The results of NPA analysis indicate that RDX O atoms may attract more electrons in solvent than in the gas phase, while the more positive charges are transferred to the molecular skeleton. From the perspective of MEP, the negative potentials of the RDX molecule are concentrated on nitro O atoms due to solvation effects, while positive potentials distribute in nitro N atoms and molecular ring, as shown in Fig. 3.
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Fig. 3 Mapped charts of molecular electrostatic potentials (ESPs) of RDX in gas phase and solvent. Left Gas phase, right DMSO solvent Fig. 2 Diagram comparing RDX molecular structures in gas phase and solvent. Color codes: green molecular structure of RDX in gas phase; gray molecular structure of RDX in DMSO solvent
Solvent effect on RDX sensitivity Bond dissociation energy of N–NO2 The BDE of N–NO2 of the RDX molecule in different solvents calculated according to Eq. (1) is listed in Table 5. The dielectric constants ε of CYC, ACE, DMF and DMSO solvents are shown in Table 6, which can qualitatively represent the solvent polarity. The relationship between BDE of N–NO2 and the dielectric constant is shown in Fig. 4. Table 4 Atom charges of the RDX molecule in different solvents calculated by NPA analysis at B3LYP/6-311++G** level
a
Decrease in bond length
Atom
From Table 5, it can be observed that the BDE of N–NO2 is enhanced in these solvents compared with that in gas phase. Figure 4 shows that, with the increase of dielectric constants, both curves of BDEmax and BDEave first go up; after reaching 20.49, ε then tends to equilibrium. This result indicates that solvent polarity has a large effect on the N–NO2 BDE, but this effect has an upper limit because the difference of BDE in different solvents is relatively small. The cleavage of N–NO2 bonds regarded as linkage bonds has been considered as the key step in detonation initiation of nitramines, which can be characterized by the BDE. Generally speaking, the larger BDE of linkage bonds means that, if subjected to external environment stimuli such that the weakest bond will be not
Natural charge Gas
CYC
ACE
DMF
DMSO
Average transfer number
C1 C2 C3 H4 H5 H6 H7 H8 H9 N10 N11 N12 N13 N14 N15 O16 O17
−0.024 −0.032 −0.024 0.281 0.201 0.284 0.218 0.201 0.281 −0.354 −0.345 −0.345 0.624 0.624 0.624 −0.380 −0.380
−0.018 −0.024 −0.018 0.285 0.202 0.284 0.218 0.201 0.286 −0.343 −0.336 −0.336 0.623 0.619 0.620 −0.389 −0.389
−0.018 −0.024 −0.018 0.286 0.202 0.284 0.218 0.202 0.286 −0.342 −0.335 −0.336 0.623 0.619 0.620 −0.39 −0.39
−0.018 −0.024 −0.017 0.286 0.202 0.284 0.217 0.201 0.286 −0.342 −0.335 −0.335 0.622 0.619 0.619 −0.39 −0.39
−0.018 −0.024 −0.017 0.286 0.202 0.284 0.217 0.201 0.286 −0.342 −0.335 −0.335 0.622 0.618 0.619 −0.39 −0.39
0.006 0.008 0.006 0.005 ≈0 ≈0 ≈0 ≈0 0.005 0.012 0.010 0.010 −0.002a −0.005a −0.004a −0.010a −0.010a
O18 O19 O20 O21
−0.362 −0.366 −0.362 −0.366
−0.368 −0.373 −0.369 −0.374
−0.368 −0.374 −0.369 −0.374
−0.368 −0.373 −0.370 −0.374
−0.369 −0.373 −0.370 −0.375
−0.006a −0.007a −0.008a −0.008a
2326, Page 6 of 9
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Table 5 Bond dissociation energy (BDE) of N–NO2 (kJ mol−1) in different solvents calculated at UB3LYP/6-311++G** level. Geometry optimization and vibrational analysis for RDX molecule and free radicals were performed at UB3LYP/6-311++G** level, and all molecule structures are true minimum on potential energy surface BDE
Gas
CYC
ACE
DMF
DMSO
BDEmaxa
143.78
151.51
151.14
152.73
153.71
BDEaveb
140.80
149.99
149.36
151.34
152.42
a
Maximum value of BDE of N-NO2
b
Average value of BDE of N-NO2
easy to break, which increases molecular stability, the sensitivity of the energetic material will be lower [15]. This relationship suggests that the effect of solvents may contribute to reducing the sensitivity of RDX, with the bond strength of N– NO2 in the RDX molecule in solvents being stronger than in the gas phase. Quantitative analysis of ESP of RDX Quantitative analysis of ESP of RDX on vdW surfaces in solvents is tabulated in Table 7, as performed at B3LYP/6311++G** level. From Table 7, it can be seen that the variables VS,max, ó+2, and ó−2 increase in solvents compared with gas phase. However, the increase tendency of these parameters is slight as solvent polarities strengthen, with values in different solvents being quite close. This indicates that the ESP of RDX is influenced by solvent polarities, but it also has an upper limit. Murray et al. [17] have successfully correlated the anomalous surface potential imbalance ν with the sensitivity of nitramine compounds containing RDX. It is found that when the electrostatic balance ν is larger (ν ≤0.250), the sensitivity is lower. Seen from Table 7, the variable ν calculated based on Eq. (2) in solvents is larger than that in gas phase. Hence, it is predicted that the sensitivity of RDX may be reduced via solvent effects. Nitro group charges of RDX It is well known that atom charges cannot be observed physically. Avoiding the inaccuracy of the single atom charge definition method, we adopted the Mulliken and NPA as well as CHELPG charge methods to calculate atom charges of the RDX molecule. The calculation of nitro group charges −QNO2 Table 6 Dielectric constants of solvents at 298 K Solvents
CYC
ACE
DMF
DMSO
εa
15.62
20.49
37.22
46.83
a
Static dielectric constant
Fig. 4 Relationship between the bond dissociation energy (BDE) of N– NO2 of the RDX molecule and the dielectric constants of solvents
of the RDX molecule according to Eq. (3) in different solvents are shown in Table 8, and the relationship of the nitro group charge with ε is plotted in Fig. 5. From Table 8, we see that nitro group charges of the RDX molecule calculated by different atom charge methods in solvents are larger than those in the gas phase. Figure 5 shows that, with the increase of dielectric constants, all curves rise rapidly from gas to acetone, and thereafter tend to be in equilibrium. The relationship between ε and –Qmax or –Qave indicates that there is a large influence of solvent polarity on nitro group charges, but this effect also has an upper limit, at which the changes of –Qmax or –Qave are very small. This result is consistent with the discussion on the BDE of N–NO2. The nitro group charges also correlate well with the sensitivity of explosive. Research shows that if N–NO2 bonds are the weakest bond of nitroamine compounds, nitro group charges are larger and sensitivity is lower [16]. We conjecture that the insensitivity of RDX may be improved by solvent effects, i.e., that −QNO2 values of the RDX molecule are larger in solvents compared with gas phase. Calculating structural parameters such as BDE of N–NO2, which are affected by solvents, and imbalances in surface electrostatic potential as well as in nitro group charge, suggests that solvent effects may contribute to reducing the sensitivity of RDX. However, we should keep in mind that it is unreasonable to make a conclusion that solvent effect Table 7 Quantitative analysis of MEPs of RDX on vdW surfaces in different solvents at B3LYP/6-311++G** level Parametersa
Gas
CYC
ACE
DMF
DMSO
ó+2 ó−2 ν
181.92 38.64 0.144
207.27 45.59 0.148
206.90 46.24 0.149
208.42 46.39 0.149
209.10 46.41 0.149
a
Units for σ+2 and σ−2 are (kcal mol−1 )2 ; ν is unitless
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Table 8 Nitro group charges of the RDX molecule in different solvents calculated by Mulliken, NPA and CHELPG charge methods Method
Mulliken
NPA
CHELPG
Table 9 Solvation free energies of CYC, DMF and DMSO in respective solvents calculated by SMD model with M052x/6-31G* level at 298 K, and compared with reference values Solvation free energy (kcal mol−1)
−Qmaxa
−Qaveb
−Qmax
−Qave
−Qmax
−Qave
Gas
0.363
0.363
0.136
0.114
0.125
0.049
CYC ACE DMF DMSO
0.459 0.463 0.467 0.470
0.424 0.427 0.429 0.432
0.156 0.158 0.158 0.158
0.134 0.135 0.136 0.136
0.172 0.174 0.175 0.175
0.064 0.067 0.066 0.066
CYC
a
Maximum value of nitro group charge
b
Average value of nitro group charge, defined as:−Qave =−(QNO2–1 + QNO2–2 +QNO2–3)/3
determines the final sensitivity of RDX from just a single structural parameter. In fact, solvents impact on many aspects of explosives such as crystal morphology and crystal defects, which also play an important role in sensitivity. Hence, solvent effects may help to polish up RDX sensitivity to some extent by means of the prediction methods applied above.
Solvent effects on crystal quality of RDX Due to the lack of experimental solvation free energies of RDX in these solvents, we first applied the SMD model to predict the solvation free energies of CYC, DMF or DMSO as solutes with respect to themselves to prove the accuracy of this model. The predicted solvation free energies based on Eq. (4) at M052x/6-31G* level are shown in Table 9, and compared with reference values from [34]. From Table 9, it can be seen that the free energies calculated by the SMD model are very close to the corresponding reference values, with the maximum energy deviation less than 1 kcal mol−1. Thus, the SMD
Prediction −7.17
DMF Ref. [34] −6.25
DMSO
Prediction −6.39
Ref. [34] −6.47
Prediction −7.57
Ref. [34] −7.63
model reliably predicts RDX solvation free energies in solvents. The SMD model was used at a computation level of M052x/6-31G* to calculate solvation free energies of RDX in different solvents at 298 K. The values listed in Table 10 reveal that the RDX solvation free energies in ACE and DMF solvents are larger than those in DMSO and CYC. The order of solvation free energies (absolute value) of RDX in different solvents is that DMSO≈CYC
ORIGINAL PAPER
Theoretical study of solvent effects on RDX crystal quality and sensitivity using an implicit solvation model Gang Chen & Wenyan Shi & Mingzhu Xia & Wu Lei & Fengyun Wang & Xuedong Gong
Received: 20 March 2014 / Accepted: 28 May 2014 # Springer-Verlag Berlin Heidelberg 2014
Abstract Density functional theory calculations using an SMD model were performed to investigate the effect of solvents (cyclohexanone, acetone, dimethyl formamide and dimethyl sulphoxide) on the crystal quality and sensitivity of RDX. The results indicate that the N–N bond length of the RDX molecule in solvents differs clearly from that in gas phase. The solvent effect on bond and dihedral angles of RDX molecule is small, however, the RDX molecule still maintains the AEE configuration. Natural population analysis shows that, due to solvation effects, RDX O atoms attract more electrons in solvents than in gas phase, while more positive charge distributes to the molecular skeleton. The calculations of N–NO2 bond BDE and nitro group charge as well as surface electrostatic potential parameters reveal that the solvent effect may be helpful to reduce the sensitivity of RDX, but this effect has an upper limit. Finally, it can be predicted qualitatively that the crystal quality of RDX crystallized from cyclohexanone and dimethyl sulphoxide will be higher than that from acetone and dimethyl formamide. Experimental results support these theoretical predictions. Keywords RDX . Sensitivity . Crystal quality . Solvent effect . Implicit solvation model
Introduction RDX (hexogen, C3H6N6O6) is one of the most important energetic materials, and is used widely in the preparation of plastic bonded explosives such as PBXN109 (composed of 64 % RDX, 20 % aluminium and 16 % binder [1]). However, G. Chen : W. Shi : M. Xia (*) : W. Lei : F. Wang : X. Gong Chemistry Department, Nanjing University of Science and Technology, Nanjing 210094, China e-mail: [email protected]
its high sensitivity impacts on the safety of RDX-based PBXs, thus restricting further application of RDX. The crystal quality of explosives, as characterized by particle size, shape and defect content, has an important effect on sensitivity, solid load and other factors [2, 3]. It has been reported [3–6] that RDX crystallized from a solvent is imperfect, with defects, impurities and irregular crystal shapes, which results in hot spot formation and high sensitivity as well as low load density. Crystal quality is influenced not only by internal molecular structures, but also by external environments such as crystallization technologies [4, 7], solvents [8] and additives [9]. Solvents play an important role in crystal quality, and can induce crystal defects, such as solvent inclusions [10, 11], affect product purity as foreign compounds [12], and change crystal morphology [13]. Consequently, to reduce sensitivity and improve performance, research of solvent effects on RDX crystal quality has an important practical significance. Many energetic material researchers believe that there is a strong relationship between sensitivity and the molecular structures of explosives. Cleavage of the weakest molecular bonds, which are generally regarded as trigger linkages, is widely considered as a key step in the explosive decomposition or initiation process [14]. In the past few decades, from the perspective of molecular structure, many scholars have focused on correlating configuration parameters with explosive sensitivity. As the linkage bond of nitramine compounds, the bond dissociation energy (BDE) of N–NO2 is suggested to be correlated with sensitivity [15]; however, any such relationship between BDE and sensitivity is not general, and it is insufficient to focus only on the BDE factor. Zhang et al. [16] have proposed a qualitative method in which the nitro group charge is regarded as a structural parameter that can be used to assess impact sensitivity. The method has wide application in almost all nitro compounds when the C–NO2, N–NO2, or O– NO2 bond is the weakest in the entire molecule. From the point of molecular electrostatic potential (MEP), Murray et al.
2326, Page 2 of 9
[17] found empirical evidence of a link, in that, if the N–NO2 bond is a trigger linkage, the anomalous electrostatic potential on the molecular surface can be correlated with the sensitivity of nitramines. Other methods, such as oxygen balance, molecular electronegative and band gap, that can approximately predict the sensitivity of explosives have also been proposed [18–20]. The molecular configuration and electronic structure of the solute, and the chemical reaction itself, are well known to be affected significantly by the solvent [21–24]. The solvents cyclohexanone (CYC), acetone (ACE), dimethyl formamide (DMF) and dimethyl sulfoxide (DMSO) are often used as crystallization solvents for RDX, and the solubility of RDX in these solvents is relatively high compared with other common solvents (Table 1) [25]. In practice, solvents used for the purification of RDX are often not fully recovery [26]. Obviously, any remaining solvent may impact on RDX crystal quality. As a result, it is very important to study solvent effects on the molecular structure of RDX that may be associated quantitatively with RDX sensitivity. So far, no such detailed investigation has been reported. The aim of our work was to investigate the effect of solvents on the sensitivity and crystal quality of RDX, to provide some theoretical support for high quality reduced sensitivity RDX. In this paper, DFT methods were combined with an implicit solvation model to investigate the effect of the solvents CYC, ACE, DMF and DMSO on RDX crystal quality. Changes in the molecular structure of RDX such as bond length, bond and dihedral angles in different solvents were analyzed, and charge distribution was also studied using natural population analysis (NPA). Following calculation of the bond dissociation energy of N–NO2 and the surface electrostatic potential parameter as well as nitro group charges, solvent effects on the sensitivity of RDX are discussed. Finally, by calculating the solvation free energies in different solvents, solvation effects on crystal quality of RDX were predicted and compared with experimental results.
J Mol Model (2014) 20:2326 Table 1 Solubility of RDX (hexogen, C3H6N6O6) (S, g/100 g) in various solvents at 298 K. CYC Cyclohexanone, ACE acetone, DMF dimethyl formamide, DMSO dimethyl sulfoxide. Data taken from [18] RDX
Benzene
CYC
ACE
Alcohol
DMF
DMSO
Water
S
–
7.5
8.2
–
37
41
–
parameter hybrid function [30] combined with the Lee, Yang and Parr correlation function [31]), has been confirmed to give reasonable configurations and electronic structures of the RDX molecule, which are good agreement with experimental results [32, 33]. Geometry optimization of RDX molecule in both the gas and solvent phase was performed at B3LYP/6311++G** level. The self-consistent reaction field (SCRF) based on the implicit solvation model-SMD model [34], which can correctly predict the solvation free energy, was applied to simulate solvent environments at the same computational level. The results of vibrational frequency analysis indicate that no imaginary frequencies are found, which means the optimized molecular structures are true minima on the potential energy surface. Furthermore, NPA implemented in Gaussian 09 software was performed to investigate solvation effects on the electronic structure of the RDX molecule. The N–NO2 bond strength can be characterized by the bond dissociation energy (BDE). The bond dissociation energy of N–NO2 is not only effective for characterizing such bond stability, but is also a major factor for assessing sensitivity. The BDE of N–NO2 was calculated by employing the following cleavage reaction:
Computational methods All DFT calculations were performed using Gaussian 09 software with a tight self-consistent field convergence threshold [27]. At ambient pressure and temperature, α-RDX (applied widely in practice) is the most stable crystallographic phase. The initial molecular structure was taken from an αRDX unit cell derived from the Cambridge Structural Database (CSD: CTMTNA for α-RDX) [28], as shown in Fig. 1. From Fig. 1, the α-RDX molecule (abbreviation RDX) consists of three CH2–N–NO2 units arranged in a six-membered ring, in which two nitro groups occupy axial A positions and the remaining nitro group is in the pseudo-equatorial E position, so that the molecular conformation of RDX is in the AAE form [29]. The DFT method with B3LYP (Becke-three
Fig. 1 Schematic view of the geometry configuration of RDX molecule
J Mol Model (2014) 20:2326
RNNO2 →RN þNO2 BDE ¼ E ðRNÞ þ E ðNO2 Þ−E ðRNNO2 Þ þ E ZPEC
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ð1Þ
Geometry configuration and charge distribution of RDX molecule in solvents
where E is the total energy, and EZPEC is zero point energy corrected. The quantitative analysis of molecular electrostatic potential of RDX on the van der Waals (vdW) surface in solvents was carried out using Multiwfn 3.2 software, which is a powerful multifunctional wavefunction analyzer [35, 36]. The statistical variable ν is defined as the surface electrostatic potentials imbalance, measured with the following formula:
ν¼
σ2þ σ2− σ2þ þ σ2−
2
ð2Þ
where ó+2 and ó−2 are the positive and negative surface potentials variances, which indicate the strength and variability of the positive and negative surface potentials [17]. The nitro group charge −QNO2 of the RDX molecule is defined as follows: −QNO2 ¼ −ðQN þ QO1 þ QO2 Þ
ð3Þ
where QN, QO1, and QO2 are the net charges on the N and O atoms of the nitro group, respectively [16]. The atom charge was calculated using the atom charge methods of Mulliken [37], NPA and CHELPG [38]. The molecular electrostatic potentials of RDX in solvents were mapped using the VMD 1.9.1 program [39]. In most continuum solvent models, such as SMD, solvation free energy is defined as: ΔGslov ¼ ðE slon þE nes Þ−E gas
Results and discussion
ð4Þ
where Eslon and Egas are the electronic energies of the solute in the presence and absence of the continuum solvent field; Enes denotes all non-electrostatic interaction energies, e.g., cavitation and dispersion-repulsion energies [40, 41]. Klamt [41] pointed out that the user should insist on the computational protocol used in the parametrization of the SMD model; only in this way can the accurate solvation free energy be obtained. The solvation free energies of RDX in different solvents were thus calculated at M052x/6-31G* level, which is consistent with the literature [34, 42].
The bond lengths, R, of the RDX molecule in different solvents optimized at B3LYP/6-311++G** level are listed in Table 2. It can be seen from Table 2 that, compared with the bond length in gas phase, the length changes of C–N covalent bonds on the molecular skeleton of RDX are slight. However, the distance of N–N bonds (N10–N13, N11–N14 and N12–N15) is decreased, with average changes of 0.031, 0.027 and 0.029 Å, respectively. And all N–O bond lengths are increased, with those belonging to the same nitro group being very close. This shows that the bond lengths of the RDX molecule in solvents is changed to some extent compared with those in gas phase, in which the change of N–N bonds is larger. That is to say, solvents have an important effect on the N–N bond length of the RDX molecule. Table 3 lists the computational bond and dihedral angles of the RDX molecule in different solvents at the B3LYP/6311++G** level. As seen from Table 3, the changes of RDX bond angles in solvents are small compared with those in vacuum, with the average changes of all bond angles being less than 3 %. For the dihedral angles of RDX molecule, only the N13–N10–C1–N11 and N13–N10–C1–N11 have a Table 2 Bond lengths of the RDX molecule in different solvents calculated at B3LYP/6-311++G** level Bonds
C1–N10 C3–N10 C1–N11 C2–N11 C2–N12 C3–N12 N10–N13 N11–N14 N12–N15 N13–O16 N13–O17 N14–O18 N14–O19 N15–O20 N15–O21 a
R(Å)
Average change
Gas
CYC
ACE
DMF
DMSO
1.474 1.474 1.449 1.463 1.463 1.449 1.405 1.433 1.433 1.220 1.220 1.214 1.215 1.214 1.215
1.474 1.474 1.454 1.468 1.467 1.454 1.376 1.408 1.406 1.227 1.227 1.221 1.222 1.221 1.222
1.473 1.473 1.454 1.468 1.468 1.454 1.373 1.406 1.405 1.227 1.227 1.221 1.222 1.221 1.222
1.473 1.474 1.454 1.468 1.468 1.454 1.373 1.406 1.403 1.228 1.228 1.221 1.222 1.221 1.223
1.473 1.474 1.454 1.468 1.468 1.454 1.373 1.405 1.403 1.228 1.228 1.221 1.223 1.222 1.223
Decrease in bond length
−0.001a 0 0.005 0.005 0.005 0.005 −0.031a −0.027 −0.029a 0.008 0.008 0.007 0.007 0.007 0.008
2326, Page 4 of 9 Table 3 Bond and dihedral angles of the RDX molecule in different solvents calculated at B3LYP/6-311++G** level
a
Decrease in bond length
J Mol Model (2014) 20:2326
Bond and dihedral angles
Angle(°)
Average change (%)
Gas
CYC
ACE
DMF
DMSO
N10–C1–N11
109
107.8
107.8
107.8
107.7
−1.1a
N11–C2–N12 N10–C3–N12 C1–N10–C3 C1–N10–N13 C3–N10–N13 N10–N13–O16 N10–N13–O17 O16–N13–O17 C1–N11–C2 C1–N11–N14 C2–N11–N14 N11–N14–O18 N11–N14–O19 O18–N14–O19 C2–N12–C3 C2–N12–N15 C3–N12–N15 N12–N15–O20 N12–N15–O21
112.5 109.0 114.5 115.5 115.5 116.6 116.6 126.7 115.5 116.4 116.9 116.1 116.6 127.1 115.5 116.9 116.4 116.1 116.6
110.9 108.0 114.6 118.8 118.7 117.3 117.3 125.3 114.9 116.9 117.7 116.8 117.3 125.7 115.2 117.9 117.4 116.8 117.4
110.9 108.0 114.7 119.0 119.0 117.4 117.4 125.2 114.9 117.0 117.8 116.9 117.4 125.6 115.1 118.0 117.3 116.9 117.4
110.8 108.0 114.6 119.0 119.0 117.4 117.4 125.2 114.8 117.0 117.7 116.9 117.4 125.6 115.1 118.0 117.5 116.9 117.4
110.7 108.0 114.6 119.0 118.9 117.4 117.4 125.1 114.8 117.0 117.7 116.9 117.4 125.5 115.2 118.0 117.5 116.9 117.4
−1.5a −0.9a 0.1 3.0 2.9 0.7 0.7 −1.2a −0.6a 0.5 0.7 0.7 0.7 −1.2a −0.3a 0.9 0.9 0.7 0.7
O20–N15–O21 N13–N10–C1–N11 N13–N10–C3–N12 N14–N11–C2–N12 N14–N11–C1–N10 N15–N12–C3–N10 N15–N12–C2–N11 O16–N13–N10–C1 O17–N13–N10–C3 O18–N14–N11–C1 O19–N14–N11–C2 O20–N15–N12–C3 O21–N15–N12–C2
127.1 166.8 −166.8 95.6 −92.4 92.5 −95.6 159.7 −159.7 167.7 −158.7 −167.7 158.7
125.6 154.2 −154.7 93.1 −90.7 93.5 −95.4 165.6 −164.0 169.4 −157.8 −170.1 158.8
125.6 153.1 −153.4 93.4 −91.3 93.3 −95.1 166.1 −164.8 169.1 −158.4 −169.2 159.5
125.5 153.0 −153.6 92.9 −90.6 93.5 −95.3 166.2 −164.6 169.5 −157.7 −170.3 158.7
125.5 153.3 −153.8 92.8 −90.5 93.6 −95.3 166.1 −164.4 169.4 −157.7 −170.3 158.7
−1.2a −8.0 −7.7a −2.7a −1.8a 1.0 −0.3a 3.9 3.0 1.0 −0.5a 1.4 0.1
larger variation, of which the average change percentages come to 8 %. It can be seen that the largest changes of RDX bond and dihedral angles in solvents both occur in the E position, showing that the N–NO2 unit placed in this location tends to be slightly vertical, as seen in Fig. 2. In a word, the solvent effect on the molecular structure of RDX is small, and the RDX molecule maintains the AEE configuration in solvents. The atom charges on the RDX molecule calculated by NPA analysis in different solvents at B3LYP/6-311++G** level, are presented in Table 4. As seen from Table 4, compared with the natural charges in gas phase, charges of both N and C atoms of RDX molecule decrease in solvents, and with the increase
of solvent polarity, the negative charges of these atoms gradually reduce. On the contrary, the negative charge numbers of all O atoms increase, with the nitro O atoms in the E position have the most average charge transfer numbers (0.010 e). The charge change of H atoms is small, except for atoms H6 and H7 whose charge numbers reduce slightly. The results of NPA analysis indicate that RDX O atoms may attract more electrons in solvent than in the gas phase, while the more positive charges are transferred to the molecular skeleton. From the perspective of MEP, the negative potentials of the RDX molecule are concentrated on nitro O atoms due to solvation effects, while positive potentials distribute in nitro N atoms and molecular ring, as shown in Fig. 3.
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Fig. 3 Mapped charts of molecular electrostatic potentials (ESPs) of RDX in gas phase and solvent. Left Gas phase, right DMSO solvent Fig. 2 Diagram comparing RDX molecular structures in gas phase and solvent. Color codes: green molecular structure of RDX in gas phase; gray molecular structure of RDX in DMSO solvent
Solvent effect on RDX sensitivity Bond dissociation energy of N–NO2 The BDE of N–NO2 of the RDX molecule in different solvents calculated according to Eq. (1) is listed in Table 5. The dielectric constants ε of CYC, ACE, DMF and DMSO solvents are shown in Table 6, which can qualitatively represent the solvent polarity. The relationship between BDE of N–NO2 and the dielectric constant is shown in Fig. 4. Table 4 Atom charges of the RDX molecule in different solvents calculated by NPA analysis at B3LYP/6-311++G** level
a
Decrease in bond length
Atom
From Table 5, it can be observed that the BDE of N–NO2 is enhanced in these solvents compared with that in gas phase. Figure 4 shows that, with the increase of dielectric constants, both curves of BDEmax and BDEave first go up; after reaching 20.49, ε then tends to equilibrium. This result indicates that solvent polarity has a large effect on the N–NO2 BDE, but this effect has an upper limit because the difference of BDE in different solvents is relatively small. The cleavage of N–NO2 bonds regarded as linkage bonds has been considered as the key step in detonation initiation of nitramines, which can be characterized by the BDE. Generally speaking, the larger BDE of linkage bonds means that, if subjected to external environment stimuli such that the weakest bond will be not
Natural charge Gas
CYC
ACE
DMF
DMSO
Average transfer number
C1 C2 C3 H4 H5 H6 H7 H8 H9 N10 N11 N12 N13 N14 N15 O16 O17
−0.024 −0.032 −0.024 0.281 0.201 0.284 0.218 0.201 0.281 −0.354 −0.345 −0.345 0.624 0.624 0.624 −0.380 −0.380
−0.018 −0.024 −0.018 0.285 0.202 0.284 0.218 0.201 0.286 −0.343 −0.336 −0.336 0.623 0.619 0.620 −0.389 −0.389
−0.018 −0.024 −0.018 0.286 0.202 0.284 0.218 0.202 0.286 −0.342 −0.335 −0.336 0.623 0.619 0.620 −0.39 −0.39
−0.018 −0.024 −0.017 0.286 0.202 0.284 0.217 0.201 0.286 −0.342 −0.335 −0.335 0.622 0.619 0.619 −0.39 −0.39
−0.018 −0.024 −0.017 0.286 0.202 0.284 0.217 0.201 0.286 −0.342 −0.335 −0.335 0.622 0.618 0.619 −0.39 −0.39
0.006 0.008 0.006 0.005 ≈0 ≈0 ≈0 ≈0 0.005 0.012 0.010 0.010 −0.002a −0.005a −0.004a −0.010a −0.010a
O18 O19 O20 O21
−0.362 −0.366 −0.362 −0.366
−0.368 −0.373 −0.369 −0.374
−0.368 −0.374 −0.369 −0.374
−0.368 −0.373 −0.370 −0.374
−0.369 −0.373 −0.370 −0.375
−0.006a −0.007a −0.008a −0.008a
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Table 5 Bond dissociation energy (BDE) of N–NO2 (kJ mol−1) in different solvents calculated at UB3LYP/6-311++G** level. Geometry optimization and vibrational analysis for RDX molecule and free radicals were performed at UB3LYP/6-311++G** level, and all molecule structures are true minimum on potential energy surface BDE
Gas
CYC
ACE
DMF
DMSO
BDEmaxa
143.78
151.51
151.14
152.73
153.71
BDEaveb
140.80
149.99
149.36
151.34
152.42
a
Maximum value of BDE of N-NO2
b
Average value of BDE of N-NO2
easy to break, which increases molecular stability, the sensitivity of the energetic material will be lower [15]. This relationship suggests that the effect of solvents may contribute to reducing the sensitivity of RDX, with the bond strength of N– NO2 in the RDX molecule in solvents being stronger than in the gas phase. Quantitative analysis of ESP of RDX Quantitative analysis of ESP of RDX on vdW surfaces in solvents is tabulated in Table 7, as performed at B3LYP/6311++G** level. From Table 7, it can be seen that the variables VS,max, ó+2, and ó−2 increase in solvents compared with gas phase. However, the increase tendency of these parameters is slight as solvent polarities strengthen, with values in different solvents being quite close. This indicates that the ESP of RDX is influenced by solvent polarities, but it also has an upper limit. Murray et al. [17] have successfully correlated the anomalous surface potential imbalance ν with the sensitivity of nitramine compounds containing RDX. It is found that when the electrostatic balance ν is larger (ν ≤0.250), the sensitivity is lower. Seen from Table 7, the variable ν calculated based on Eq. (2) in solvents is larger than that in gas phase. Hence, it is predicted that the sensitivity of RDX may be reduced via solvent effects. Nitro group charges of RDX It is well known that atom charges cannot be observed physically. Avoiding the inaccuracy of the single atom charge definition method, we adopted the Mulliken and NPA as well as CHELPG charge methods to calculate atom charges of the RDX molecule. The calculation of nitro group charges −QNO2 Table 6 Dielectric constants of solvents at 298 K Solvents
CYC
ACE
DMF
DMSO
εa
15.62
20.49
37.22
46.83
a
Static dielectric constant
Fig. 4 Relationship between the bond dissociation energy (BDE) of N– NO2 of the RDX molecule and the dielectric constants of solvents
of the RDX molecule according to Eq. (3) in different solvents are shown in Table 8, and the relationship of the nitro group charge with ε is plotted in Fig. 5. From Table 8, we see that nitro group charges of the RDX molecule calculated by different atom charge methods in solvents are larger than those in the gas phase. Figure 5 shows that, with the increase of dielectric constants, all curves rise rapidly from gas to acetone, and thereafter tend to be in equilibrium. The relationship between ε and –Qmax or –Qave indicates that there is a large influence of solvent polarity on nitro group charges, but this effect also has an upper limit, at which the changes of –Qmax or –Qave are very small. This result is consistent with the discussion on the BDE of N–NO2. The nitro group charges also correlate well with the sensitivity of explosive. Research shows that if N–NO2 bonds are the weakest bond of nitroamine compounds, nitro group charges are larger and sensitivity is lower [16]. We conjecture that the insensitivity of RDX may be improved by solvent effects, i.e., that −QNO2 values of the RDX molecule are larger in solvents compared with gas phase. Calculating structural parameters such as BDE of N–NO2, which are affected by solvents, and imbalances in surface electrostatic potential as well as in nitro group charge, suggests that solvent effects may contribute to reducing the sensitivity of RDX. However, we should keep in mind that it is unreasonable to make a conclusion that solvent effect Table 7 Quantitative analysis of MEPs of RDX on vdW surfaces in different solvents at B3LYP/6-311++G** level Parametersa
Gas
CYC
ACE
DMF
DMSO
ó+2 ó−2 ν
181.92 38.64 0.144
207.27 45.59 0.148
206.90 46.24 0.149
208.42 46.39 0.149
209.10 46.41 0.149
a
Units for σ+2 and σ−2 are (kcal mol−1 )2 ; ν is unitless
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Table 8 Nitro group charges of the RDX molecule in different solvents calculated by Mulliken, NPA and CHELPG charge methods Method
Mulliken
NPA
CHELPG
Table 9 Solvation free energies of CYC, DMF and DMSO in respective solvents calculated by SMD model with M052x/6-31G* level at 298 K, and compared with reference values Solvation free energy (kcal mol−1)
−Qmaxa
−Qaveb
−Qmax
−Qave
−Qmax
−Qave
Gas
0.363
0.363
0.136
0.114
0.125
0.049
CYC ACE DMF DMSO
0.459 0.463 0.467 0.470
0.424 0.427 0.429 0.432
0.156 0.158 0.158 0.158
0.134 0.135 0.136 0.136
0.172 0.174 0.175 0.175
0.064 0.067 0.066 0.066
CYC
a
Maximum value of nitro group charge
b
Average value of nitro group charge, defined as:−Qave =−(QNO2–1 + QNO2–2 +QNO2–3)/3
determines the final sensitivity of RDX from just a single structural parameter. In fact, solvents impact on many aspects of explosives such as crystal morphology and crystal defects, which also play an important role in sensitivity. Hence, solvent effects may help to polish up RDX sensitivity to some extent by means of the prediction methods applied above.
Solvent effects on crystal quality of RDX Due to the lack of experimental solvation free energies of RDX in these solvents, we first applied the SMD model to predict the solvation free energies of CYC, DMF or DMSO as solutes with respect to themselves to prove the accuracy of this model. The predicted solvation free energies based on Eq. (4) at M052x/6-31G* level are shown in Table 9, and compared with reference values from [34]. From Table 9, it can be seen that the free energies calculated by the SMD model are very close to the corresponding reference values, with the maximum energy deviation less than 1 kcal mol−1. Thus, the SMD
Prediction −7.17
DMF Ref. [34] −6.25
DMSO
Prediction −6.39
Ref. [34] −6.47
Prediction −7.57
Ref. [34] −7.63
model reliably predicts RDX solvation free energies in solvents. The SMD model was used at a computation level of M052x/6-31G* to calculate solvation free energies of RDX in different solvents at 298 K. The values listed in Table 10 reveal that the RDX solvation free energies in ACE and DMF solvents are larger than those in DMSO and CYC. The order of solvation free energies (absolute value) of RDX in different solvents is that DMSO≈CYC
