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Computational Screening of Nitrogen-Rich Energetic Salts Based on Substituted Triazine Vikas D Ghule J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp405631c • Publication Date (Web): 31 Jul 2013 Downloaded from http://pubs.acs.org on August 4, 2013
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Computational Screening of Nitrogen-Rich Energetic Salts Based on Substituted Triazine Vikas D. Ghule,*
Advanced Center for Research in High Energy Materials, University of Hyderabad, Hyderabad-500046, India.
Abstract In this work, 110 energetic salts were designed and studied for their applications in energetic materials. Density functional theory method was used to predict the heats of formation (HOFs), electronic structure, and energetic properties of a series of triazine-based ionic and non-ionic compounds. It is observed that the –N3 group, triazole, tetrazole, triazine, and tetrazine are effective structural units for increasing the HOFs in the designed compounds. The HOFs of cations, anions, and lattice energies of the salts were calculated separately to obtain the HOFs of the salts based on Born-Haber cycle. The combination of three cations within same framework is very useful for improving HOFs of energetic salts. Similarly, presence of the –NO2 and –NHNO2 groups in same structure found helpful in improving densities through strong inter- and intra-molecular hydrogen bonding. The detonation velocities and detonation pressures of the salts were predicted by the Kamlet-Jacobs equations using calculated densities and HOFs. The calculated energetic properties indicate that the combination of suitable anion and cation species is useful for modifying their detonation properties and oxygen balances (OB). The predicted results reveal that most of compounds outperform RDX and TATB and may be considered as potential candidate of high energy materials. These results provide basic information for molecular design of novel high energetic salts.
Key words: Energetic salts, Triazine, Energetic materials, Lattice energy, Heat of formation, Detonation velocity.
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Introduction Over the past several years, there has been a growing interest in the development of environmentally friendly energetic materials for military and civilian applications.1-4 Among this development, energetic materials composed of heterocyclic backbone are on the forefront of the research. These high-nitrogen compounds form a unique class of energetic materials whose energy is derived from their very high heats of formation rather than from the combustion of hydrocarbon skeleton. The high heat of formation is directly attributable to the large number of energetic N–N and C–N bonds in this compounds.5-7 In addition, heterocycles that contain large amounts of nitrogen are typically relatively dense, and the smaller amounts of hydrogen and carbon enhance good oxygen balance. In recent reports, the syntheses and design of new materials continues to focus on the heterocyclic-based energetic salt as they often exhibit low vapor pressures and higher density than their atomically similar nonionic analogues.8-16 s-Triazine is an intriguing heterocycle for high energy materials and possesses a high degree of thermal stability.17,18 With higher heats of formation and better performance, most of the derivatives of triazine are reported for energetic applications. Hydrogen atoms of triazine can be substituted with various energetic functional groups. In general, the good candidates for energetic materials contain high nitrogen/oxygen content which arises from their molecular backbone and typical energetic groups such as azo or azido groups.19-22 The nitrogen-rich azide compounds considered as energy power house because they can release enormous amounts of energy, which is due to the average bond energies: N–N (160 kJ/mol), N=N (418 kJ/mol) and N≡N (954 kJ/mol).23 In addition, the presence of nitro groups greatly improves the density results in increased detonation performance properties (pressure and velocity) that are related to the square of or proportional to the density.24-26 Normally more energetic groups
or
explosophores
enhance
the
nitrogen/oxygen
percentage
while
concomitantly increasing the sensitivity of the energetic materials. These groups are also supposed to be the trigger linkages in the energetic materials and affect their sensitivities and/or stabilities. Recently, Shreeve et al.27 reported 6-nitroamino-2,4-diazido[1,3,5]-triazine (NADAT) and its monoanionic energetic salts. These salts show good densities, moderate thermal stabilities, and better detonation performance, which were similar or higher than that of conventional explosives such as TNT or TATB. This work
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prompted us to study the energetic properties of various salts of the substituted triazine anion. Aiming at finding new super high energy density materials with high detonation velocity and pressure, triazine substituted with –N3, –NHNO2, –NO2, – NH2 groups and their salts were designed by replacing the proton of nitramino group. All designed compounds are of CHNO-type and their decomposition products expected predominantly in the generation of CO2, H2O and N2 and lead to promising candidates for green and environmentally friendly energetic materials. In this study, we reported a systematic study of the heats of formation (HOFs), density, and detonation performance of a series of energetic triazine salts using density functional theory (DFT).
Computational details All computations were performed with Gaussian 03 package at B3PW91 method with 6-31G(d,p) basis set.28 The structural parameters were allowed to be optimized and no constraints were imposed on molecular structure during optimization process. All optimized structures were characterized to the true local energy minima on potential energy surfaces without imaginary frequencies. Figure 1 presents the non-ionic compounds selected for anionic moiety. The oxygen balance (OB) is used to indicate the degree to which an explosive can be oxidized and oxygen is needed in a molecule to oxidize it completely into their gaseous reaction products. OB is used in prediction of detonation velocity, detonation pressure, chemical energy of detonation, and decomposition products. The molecule is said to have a positive (negative) oxygen balance if it contains more (less) oxygen than is needed for complete combustion. OB (%) for an explosive containing the general formula CaHbNcOd with molecular mass M can be calculated as,
OB(%) =
(d − 2a − 0.5b) X 1600 M
(1)
In previous studies, isodesmic reactions have been successfully employed to estimate the HOFs from the total energies obtained from ab initio calculations.29-32 Therefore, isodesmic reactions are designed in which the basic structural units were retained to minimize errors. The isodesmic reactions used for the prediction of gasphase HOF (HOFGas) of designed compounds are shown in Figure 2. The total energy
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(E0), zero point energy (ZPE), and thermal corrections (∆HT) for reference compounds selected in isodesmic reactions and for ionic species are listed in Supporting Information. For estimation of the potential performance of the energetic material, it is also significant to calculate their solid-phase HOF (HOFSolid) because it is related directly with the detonation characteristics. According to Hess’ law, HOFSolid can be obtained from the HOFGas and heat of sublimation (HOFSub):
HOFSolid = HOFGas - HOFSub
(2)
Politzer et al.33-35 reported that the HOFSub can correlate well with the molecular surface area and the electrostatic interaction index for energetic compounds. The HOFSub can be evaluated by the Byrd and Rice method36 in the framework of the Politzer approach,33,37 using the following empirical relation,
2 0.5 HOFSub = β1A 2 + β 2 (vσ tot ) + β3
(3)
Where A is the area of the isosurface of 0.001 electrons/bohr3 electronic density, ν indicates the degree of balance between the positive and negative surface potentials,
σ tot2 is a measure of variability of the electrostatic potential, and β1, β2, and β3 are determined through a least-squares with the experimental HOFSolid of a selected set of known materials.36 Surface area, degree of balance between the positive and negative surface potentials and variability of the electrostatic potential are calculated using WFA program.38 Based on the Born–Haber cycle (shown in Figure 3), the heat of formation of an ionic compound can be simplified by subtracting the lattice energy of the salt (HL) from the total heat of formation of salt i.e. sum of the heats of formation of the cation and anion as shown in equation (4).
HOF (salt, 298 K) = HOF (cation, 298 K) + HOF (anion, 298 K) - HL
(4)
Lattice potential energy is the energy associated with the process in which a crystalline solid lattice, MpXq is converted into its constituent gaseous ions, pMq+ (g) and qXp− (g). The lattice energy can be predicted with reasonable accuracy by using Jenkins’ equation (5).39
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H L = U POT + [ p(
nM n - 2) + q( X - 2)]RT 2 2
(5)
where nM and nX depend on the nature of the ions Mp+ and Xq-, respectively, and are equal to 3 for monoatomic ions, 5 for linear polyatomic ions, and 6 for nonlinear polyatomic ions. When lattice potential energy (UPOT), is incorporated and made part of a Born–Haber cycle, it needs to be converted into a lattice enthalpy term. This lattice enthalpy (HL), involves correction of the UPOT term by an appropriate number of RT terms. The UPOT (kJ mol-1) can be predicted from four different equations (6-9) as suggested by Jenkins et al.40-42 using following equations,
U POT = AI ( 2VI )1/ 3
U POT = B( I 4
(6)
ρ 1/ 3 M
(7)
)
U POT = γ ( Mρ )1/ 3 + δ
(8)
U POT = 2 I [α (V) −1/ 3 + β ]
(9)
In above equations (6-9), I is the ionic strength factor, where I = 1/2Ʃnizi2. Here ni is the number of ions in the formula unit having a charge zi. For the salts with 3:1 charge ratio (cation:anion) listed in this work, the ionic strength, I=6. ρ is the density (g cm3
), V is the estimated volume of ionic material (nm3), and M is the chemical formula
mass of the ionic material (g mol-1). The coefficients A (121.4 kJ mol-1), B (1291.7 kJ mol-1), γ (2342.6·I kJ mol-1.cm), δ (55.2·I kJ mol-1) and generalised parameters α and β for salts (3:1) are 138.7 kJ mol-1.nm and 27.6 kJ mol-1, respectively, taken from Ref. 40. Equation (6) is normally employed for salts likely to have lattice energy greater than 5000 kJ mol-1 but it seems to work quite well in this case and for these materials. The empirical Kamlet-Jacobs24-26 equations were employed to estimate the values of detonation velocity (D) and detonation pressure (P) for the high energy materials containing C, H, O and N as following equations:
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D = 1.01( NM 0.5Q 0.5 ) 0.5 (1 + 1.30ρ )
(10)
P = 1.55ρ 2 NM 0.5Q 0.5
(11)
where in above equations D is detonation velocity (km/s), P is detonation pressure (GPa), N is moles of gaseous detonation products per gram of explosives, M is average molecular weights of gaseous products, Q is chemical energy of detonation (cal/g) defined as the difference of the HOFs between products and reactants, and ρ is the density of explosive (g/cm3).
Results and discussion The aim of developing energetic salts is to achieve higher performance for real applications. Computational design of new energetic salts at molecular level based on pairing of selective energetic cations and anions allows for producing energetic salts with diverse physiochemical properties. Often, their properties are manipulated by making structural modifications. Therefore, the optimization of molecules with high energy and density to achieve higher performance for real applications is the primary step for searching high energy density materials. The triazine derivatives considered in this study tend to be acidic as a result of the electron withdrawing effect of triazine ring and the nitro group substituted on the NH. The designed compounds are organized in five different series including A, B, C, D, and E. Figure 4 presents the molecular frameworks and numbering of a series of anions and cations selected for energetic salts.
Heat of formation Heat of formation (HOF) is one of the most important parameter to estimate the performance of energetic material and indicates the energy content of corresponding material. Table 1 lists the total energies, ZPEs, thermal corrections and molecular surface properties for the non-ionic triazine derivatives. Unfortunately, no experimental HOFs are available for the designed non-ionic and ionic salts in the literature. The HOFSolid of the designed non-ionic compounds have been obtained through application of the Politzer approach as outlined in Computational Details. We investigated the effects of –NO2, -NHNO2, -NH2, and -N3 substituents on the HOFGas
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and HOFSolid of the compounds selected for anionic moiety. Table 2 presents the HOFs, HOFSub and relevant energetic properties of the triazine compounds selected for anionic moiety. It is seen that all the compounds have positive HOFSolid ( >100 kJ/mol), which is one of the necessary characteristics of energetic materials. Among these triazine derivatives, IV possesses the highest HOFSolid (419 kJ/mol). It is also observed that replacing the –NO2 with –NHNO2 groups on triazine backbone improves the HOF (II and V). However, replacement of –NO2 in II with –NH2 group reduces the HOFSolid of III by ~84 kJ/mol. The calculated HOFs of the designed salts are listed in Table 3-7. Among each series of salts, anionic species in combination with 5, 8, 13, 19, 21, and 22 cations possess higher HOFs than other salts. This is attributable to the presence of –N3 group, energetic triazole and tetrazole skeleton in cation and the increase of the number of energetic C-N bonds in these derivatives. It is noteworthy that the HOFs of designed isomers with the same number of nitro and amino groups are affected by the positions of C-NH2 and N-NH2 linkages. Thus, the replacement of 3-amino-1,2,4triazole cation (14) with 4-amino-4H-1,2,4-triazole cation (13) is very favorable for increasing its HOF greatly. It is seen that cations with tetrazine backbone (21 and 22) have highest HOFs in all series of salts. Comparing the HOFs of salts containing 4, 6, 7, and 8 cations reveals that the substitution of –NH2 can enhance the HOFs of the corresponding compounds. However, reverse effect found in case of 14 and 15 cations, where introduction of additional –NH2 group on triazole reduces the HOF of corresponding cations by ~30-65 kJ/mol. Figure 5 compares the effects of different cations and their combinations on HOF of the corresponding salts. It is obvious that the salts with 3:1 (cation:anion) charge ratio represent higher HOFs due to significant energy contribution from three cations. Overall, compared with other functional groups, the –N3 group has the highest impact on the HOFs of the cation and anion and is the first choice to increase the HOF of high energy materials. It is observed that with the increase in number of cations in salts improves their HOFs considerably. Further, it is also found that the transformation of the non-ionic molecules to corresponding cations or anions is very helpful for increasing their HOFs.
Density Density is the crucial factor for the prediction of performance and high density also desirable in terms of the amount of material can be packed into volume-limited
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warhead or propulsion configurations. The Hofmann approach has been used to predict the densities in which an average atom volume calculated to estimate the cell volume for a title compound.43 Table 2 lists the densities of the substituted non-ionic triazine derivatives and Table 3-7 lists the densities of the designed salts. The densities for non-ionic compounds have been found to be in the range of 1.79−1.95 g/cm3. Among the designed compounds, the molecule III shows the lowest density (1.79 g/cm3) whereas I show the highest density of about 1.95 g/cm3. As evident from Table 2, when the substituent on triazine ring is –NO2 (II), an increase in the density value is observed compared to its corresponding –NH2 (III) and –N3 (IV) substituted derivatives. The presence of –NO2 groups and N−H in the molecular framework increases the opportunity for hydrogen bonding and may responsible for the better densities in the designed compounds. Figure 6 presents a comparison of the densities of the series A, B and E, in which –NO2 groups replaced with –NHNO2 groups and changes the cation:anion charge ratio from 1:1 to 2:1 to 3:1. In energetic salts, when the selected cations are 3, 5, 9, 17, 18, and 19 its corresponding salts have the largest densities among the salts with the same anion. Incorporating the –NO2 and –N3 group into the cationic species (cations 5, 9 and 17) enhances the density of corresponding salts, whereas for the substituent –CH3 or –NH2, the case is quite the contrary. Figure 7 represents the effect of –NO2 (series B), –NH2 (series C) and –N3 (series D) substituents on the densities of various salts. As expected in 2:1 (series B) and 3:1 (series E) salts, the increase in volume due to two and three cations, respectively decreases the density. The densities for the salts comprised of the 5-aminotetrazole cations (18, 19 and 20) shows decrement with incorporation of –NH2 and –CH3 groups. A similar trend is also observed in the guanidine salts (4, 6, 7 and 8), where introduction of –NH2 group in guanidine derivative reduces the density. We also noted that replacement of 1,2,4triazole with tetrazole show a great effect on the density. This shows that incorporating different cations alters the trend of the densities under the influence of different substituents. Overall, the presence of nitrogen-rich rings and nitro groups are essential to improve the density.
Detonation properties Detonation velocity and detonation pressure are two important performance parameters for an energetic materials. The calculated heats of detonation (Q),
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detonation velocities (D), and pressures (P) for the starting non-ionic compounds and their corresponding ionic salts are given in Table 2-7. As evident from Table 2-7 that the –NO2 group is an effective substituent for increasing the density and thus the performance. Among the non-ionic compounds (I-V), I shows better detonation performance (D=9.05 km/s and P=38.07 GPa) over the other compounds due to the higher HOF, density and oxygen balance. The chemical energies of detonations for non-ionic compounds composed of nitramino groups are above 1082 cal/g indicate that the energetic densities of these derivatives are large. Among the designed salts, anion combined with 3, 9, 17, and 21 cations have chemical energy of detonation over 1100 cal/g. The performance of salts with 3, 9 and 17 cations is better due to the higher densities and oxygen balance (OB), which increases the concentration of detonation products like CO, CO2, and H2O. In the present study, the designed compounds composed only of the atoms C, H, N, and O and hence, N2(g), H2O(g), CO2(g), and C(s) are assumed as important detonation products, explained by Kamlet et al.24-26 and Politzer and Murray.34 Furthermore, assuming the detonation product composition to be N2(g)/H2O(g)/CO2(g)/C(s) gives overall quite satisfactory results for CHNO-based energetic compounds using an H2O−CO2 arbitrary decomposition scheme. A comparison of the detonation velocity and detonation pressure with TNT, TATB and RDX for the designed salts is displayed in Fig. 8. A3 (D = 8.88 km/s, P = 35.70 GPa), A9 (D = 8.64 km/s, P = 33.64 GPa) and A17 (D = 8.66 km/s, P = 34.12 GPa) possess a detonation performance comparable to that of RDX (D = 8.60 km/s, P = 33.92 GPa). The high performances of these compounds originate mainly from their high density and high oxygen balance. As observed, designed compounds exhibit better detonation performance than the TNT (D = 7.21 km/s, P = 22.49 GPa) whereas most of the designed compounds show higher/comparable performance than TATB (D = 8.13 km/s, P = 30.17 GPa). This indicates that the selective designed compounds could also be used as energetic compounds.
Conclusions In this work, we have studied the heats of formation, densities, and detonation properties for a series of energetic triazine-based nitrogen-rich salts by using the DFTB3PW91 method. Various cationic species have been combined with triazine anionic moieties to study the systematic structure-property relationship. The results reveal that
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the –NO2 group is an effective substituent for increasing the densities of the ionic and non-ionic compounds. The substitution of the –NO2 and –N3 groups are found helpful in increasing the HOFs of the corresponding salts. The calculated detonation properties using Kamlet-Jacobs equation indicate that the NO2 and N3 explosophores are an effective structural unit for enhancing the detonation performance for the designed salts. Most of the designed salts exhibit good performance and are worthy of synthesis and further investigation. The predicted results for 110 energetic salts also expected to provide some useful information for the molecular design of novel highenergy salts.
Associated Content Supporting Information: The total energy (E0), zero point energy (ZPE), and thermal correction (∆HT) at the B3PW91/6-31G(d,p) level and experimental HOFGas for the reference compounds, cationic and anionic species. Selective structural parameters of the compound I-V. The electrostatic potentials for the 0.001 electron/bohr3 isosurfaces of electron density evaluated at the B3PW91 level of theory for compound I-V. Thermodynamic properties of compounds I-V. Information for the prediction of density for Series A-E salts.
Author Information Corresponding Author *e-mail:
[email protected] (VDG)
Notes The author declare no competing financial interest.
Acknowledgement The author thanks ACRHEM, University of Hyderabad for financial support and computational facilities. The author also thanks Dr. K. Muralidharan, School of Chemistry, University of Hyderabad and Dr. S. Radhakrishnan, Mr. P. M. Jadhav, and Mr. R. S. Patil, High Energy Materials Research Laboratory, Pune, for their help and support.
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27. Huang, Y.; Zhang, Y.; Shreeve, J. M. Nitrogen-Rich Salts Based on Energetic Nitroaminodiazido[1,3,5]triazine and Guanazine. Chem. Eur. J. 2011, 17, 1538–1546. 28. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A.; Vreven, T., Jr.; Kudin, K. N.; Burant, J. C.; et al. Gaussian 03, revision A.1; Gaussian, Inc.: Pittsburgh, PA, 2003. 29. Ju, X. H.; Wang, X.; Bei, F. L. Substituent effects on heats of formation, group interactions, and detonation properties of polyazidocubanes. J. Comput. Chem. 2005, 26, 1263−1269. 30. Xu, X. J.; Xiao, H. M.; Ju, X. H.; Gong, X. D.; Zhu, W. H. Computational Studies on Polynitrohexaazaadmantanes as Potential High Energy Density Materials. J. Phys. Chem. A 2006, 110, 5929−5933. 31. Ghule, V. D.; Jadhav, P. M.; Patil, R. S.; Radhakrishnan, S.; Soman, T. QuantumChemical Studies on Hexaazaisowurtzitanes. J. Phys. Chem. A 2010, 114, 498−503. 32. Ghule, V. D.; Radhakrishnan, S.; Jadhav, P. M.; Tewari, S. P. Theoretical Studies on Nitrogen Rich Energetic Azoles. J. Mol. Model. 2011, 17, 1507−1515. 33. Politzer, P.; Murray, J. S.; Grice, M. E.; DeSalvo, M.; Miller, E. Calculation of Heats of Sublimation and Solid Phase Heats of Formation. Mol. Phys. 1997, 91, 923– 928. 34. Politzer, P.; Murray, J. S. Some Perspectives on Estimating Detonation Properties of C,H,N,O Compounds. Cent. Eur. J. Energ. Mater. 2011, 8, 209–220. 35. Politzer, P.; Lane, P.; Murray, J. S. Computational Characterization of a Potential Energetic Compound: 1,3,5,7-Tetranitro-2,4,6,8-Tetraazacubane. Cent. Eur. J. Energ. Mater. 2011, 8, 39–52. 36. Byrd, E. F. C.; Rice, B. M. Improved Prediction of Heats of Formation of Energetic Materials Using Quantum Mechanical Calculations. J. Phys. Chem. A 2006, 110, 1005−1013. 37. Politzer, P.; Murray, J. S. Computational Prediction of Condensed Phase Properties from Statistical Characterization of Molecular Surface Electrostatic Potentials. Fluid Phase Equilib. 2001, 185, 129−137. 38. Bulat, F. A.; Toro-Labbe, A.; Brinck, T.; Murray, J. S.; Politzer, P. Quantitative Analysis of Molecular Surfaces: Areas, Volumes, Electrostatic Potentials and Average Local Ionization Energies. J. Mol. Model. 2010, 16, 1679−1691. 39. Jenkins, H. D. B. Thermodynamics of the Relationship between Lattice Energy and Lattice Enthalpy. J. Chem. Educ. 2005, 82, 950-952.
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Page 14 of 27
40. Jenkins, H. D. B.; Tudela, D.; Glasser, L. Lattice Potential Energy Estimation for Complex Ionic Salts from Density Measurements. Inorg. Chem. 2002, 41, 2364-2367. 41. Glasser, L.; Jenkins, H. D. B. Lattice Energies and Unit Cell Volumes of Complex Ionic Solids. J. Am. Chem. Soc. 2000, 122, 632-638. 42. Jenkins, H. D. B.; Roobottom, H. K.; Passmore, J.; Glasser, L. Relationships among
Ionic
Lattice
Energies,
Molecular
(Formula
Unit)
Volumes,
and
Thermochemical Radii. Inorg. Chem. 1999, 38, 3609-3620. 43. Hofmann, D. W. M. Fast Estimation of Crystal Densities. Acta Cryst. B 2002, 57, 489-493.
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The Journal of Physical Chemistry
List of Tables
Table 1. Total Energy (E0), Zero Point Energy (ZPE), and Thermal Correction (∆HT) at the B3PW91/6-31G(d,p) Level and molecular surface properties for the non-ionic triazine derivatives (I-V).
a
Compd
E0 a
ZPEb
∆HTc
Ad
σ2tote
vf
I
-948.71128
0.0890
0.0127
213.57
240.84
0.07
II
-1004.03410
0.1067
0.0154
224.31
225.89
0.14
III
-854.98139
0.1219
0.0142
208.87
238.28
0.19
IV
-963.15927
0.1079
0.0153
228.99
181.28
0.21
V
-1059.35555
0.1241
0.0166
237.74
179.52
0.13
b
c
d
Total energy (a.u.). Zero point energy (a.u.). Thermal correction (a.u.). Area of the isosurface of
0.001 electrons/bohr3 electronic density (Å2). eMeasure of variability of the electrostatic potential (kJ/mol). fDegree of balance between the positive and negative surface potentials.
Table 2. Energetic properties of non-ionic triazine derivatives (I-V). OBa
HOFGasb
HOFSubc
HOFSolidd
ρe
Df
Pg
Qh
(%)
(kJ/mol)
(kJ/mol)
(kJ/mol)
(g/cm3)
(km/s)
(GPa)
(cal/g)
I
-3.5
274.09
92.55
181.54
1.95
9.05
38.07
1432
II
-6.5
291.52
107.42
184.10
1.91
8.89
36.27
1369
III
-29.6
207.88
107.23
100.65
1.79
7.94
27.87
1082
IV
-19.8
532.80
113.50
419.30
1.89
8.52
33.13
1235
V
-9.2
312.58
108.81
203.77
1.88
8.78
35.07
1329
Compd
a
b
c
d
Oxygen balance. Gas-phase heat of formation. Heat of sublimation. Solid-phase heat of formation.
e
Density. fDetonation velocity. gDetonation pressure. hChemical energy of detonation.
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Page 16 of 27
Table 3. Energetic properties of series A salts (1-22). Compd.
OBa
HOFcb
HOFac
UPotd
HLe
HOFsaltf
ρg
VODh
DPi
Qj
1
-12.9
634.8
-92.2
512
517
26
1.84
8.53
32.66
1249
2
-15.2
761.2
-92.2
501
506
163
1.82
8.63
33.25
1323
3
-6.1
674.2
-92.2
504
509
73
1.86
8.88
35.70
1394
4
-27.6
567.2
-92.2
484
489
-14
1.78
7.93
27.71
1073
5
-20.3
914.3
-92.2
478
483
339
1.85
8.41
31.86
1221
6
-28.9
657.7
-92.2
476
481
85
1.76
7.98
27.90
1115
7
-30.0
775.6
-92.2
468
473
210
1.75
8.09
28.55
1174
8
-31.0
894.3
-92.2
461
466
336
1.74
8.18
29.08
1227
9
-11.9
700.6
-92.2
469
474
134
1.85
8.64
33.64
1299
10
-31.2
381.6
-92.2
464
469
-180
1.77
7.65
25.70
973
11
-20.9
530.6
-92.2
478
483
-45
1.80
8.18
29.65
1146
12
-22.4
619.5
-92.2
470
475
52
1.78
8.21
29.72
1181
13
-33.0
946.9
-92.2
474
479
376
1.80
8.17
29.58
1266
14
-33.0
796.4
-92.2
474
479
225
1.80
7.97
28.21
1152
15
-33.9
753.8
-92.2
466
471
191
1.78
7.85
27.16
1090
16
-34.8
841.2
-92.2
459
464
285
1.77
7.92
27.56
1124
17
-16.2
909.5
-92.2
468
473
344
1.88
8.66
34.12
1376
18
-20.3
954.4
-92.2
478
483
379
1.85
8.45
32.21
1248
19
-21.8
1019.1
-92.2
470
475
452
1.83
8.45
31.99
1260
20
-33.9
925.2
-92.2
466
471
362
1.78
8.07
28.67
1215
21
-32.2
1324.3
-92.2
450
455
777
1.79
8.40
31.23
1355
22
-46.8
1180.6
-92.2
429
434
654
1.74
7.73
25.95
1140
a
b
Oxygen balance (%). Heat of formation of cation (kJ mol ). Heat of formation of anion (kJ mol-1).
d
-1
c
Lattice potential energy (kJ mol-1). eLattice energy (kJ mol-1). fHeat of formation of salt (kJ mol-1).
g
Density (g cm-3). hVelocity of detonation (km s-1). iDetonation pressure (GPa). jChemical energy of
detonation (cal g-1).
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The Journal of Physical Chemistry
Table 4. Energetic properties of series B salts (1-22). Compd.
OBa
HOFcb
HOFac
UPotd
HLe
HOFsaltf
ρg
VODh
DPi
Qj
1
-22.9
634.8
59.9
1458
1465
-136
1.74
7.96
27.56
1045
2
-25.8
761.2
59.9
1409
1416
166
1.72
8.25
29.37
1212
3
-10.3
674.2
59.9
1422
1429
-21
1.78
8.67
33.12
1328
4
-44.0
567.2
59.9
1335
1342
-148
1.68
7.23
22.21
856
5
-30.8
914.3
59.9
1309
1316
573
1.79
8.06
28.70
1110
6
-44.7
657.7
59.9
1301
1309
66
1.66
7.41
23.14
948
7
-45.3
775.6
59.9
1271
1279
332
1.65
7.62
24.40
1057
8
-45.8
894.3
59.9
1244
1252
597
1.64
7.79
25.38
1150
9
-17.6
700.6
59.9
1276
1282
179
1.79
8.44
31.48
1247
10
-46.2
381.6
59.9
1256
1263
-440
1.68
6.96
20.59
770
11
-32.3
530.6
59.9
1310
1318
-197
1.71
7.67
25.32
994
12
-33.8
619.5
59.9
1279
1287
12
1.70
7.82
26.21
1067
13
-50.2
946.9
59.9
1294
1302
652
1.72
7.74
25.84
1188
14
-50.2
796.4
59.9
1294
1302
351
1.72
7.44
23.88
1014
15
-50.5
753.8
59.9
1265
1272
296
1.70
7.30
22.85
940
16
-50.6
841.2
59.9
1238
1246
496
1.69
7.45
23.69
1005
17
-23.6
909.5
59.9
1270
1277
602
1.84
8.51
32.52
1363
18
-30.8
954.4
59.9
1309
1316
653
1.79
8.14
29.30
1157
19
-32.3
1019.1
59.9
1278
1285
813
1.77
8.18
29.42
1189
20
-50.5
925.2
59.9
1265
1272
638
1.70
7.64
24.99
1125
21
-45.3
1324.3
59.9
1206
1213
1496
1.72
8.17
28.82
1349
22
-62.7
1180.6
59.9
1134
1142
1279
1.67
7.35
22.86
1073
a
b
Oxygen balance (%). Heat of formation of cation (kJ mol ). Heat of formation of anion (kJ mol-1).
d
-1
c
Lattice potential energy (kJ mol-1). eLattice energy (kJ mol-1). fHeat of formation of salt (kJ mol-1).
g
Density (g cm-3). hVelocity of detonation (km s-1). iDetonation pressure (GPa). jChemical energy of
detonation (cal g-1).
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Page 18 of 27
Table 5. Energetic properties of series C salts (1-22). Compd.
OBa
HOFcb
HOFac
UPotd
HLe
HOFsaltf
ρg
VODh
DPi
Qj
1
-44.8
634.8
113.4
1480
1488
-105
1.64
7.24
21.95
868
2
-45.7
761.2
113.4
1428
1435
201
1.62
7.63
24.17
1074
3
-28.4
674.2
113.4
1442
1449
13
1.69
8.12
28.14
1202
4
-62.3
567.2
113.4
1350
1357
-109
1.60
6.61
18.02
711
5
-45.6
914.3
113.4
1322
1330
612
1.72
7.60
24.89
1006
6
-61.5
657.7
113.4
1314
1322
107
1.59
6.88
19.45
824
7
-60.9
775.6
113.4
1283
1290
375
1.58
7.15
20.89
951
8
-60.4
894.3
113.4
1255
1262
640
1.58
7.38
22.29
1059
9
-30.2
700.6
113.4
1289
1296
219
1.73
8.07
28.17
1163
10
-61.0
381.6
113.4
1267
1274
-397
1.62
6.45
17.31
651
11
-48.1
530.6
113.4
1324
1331
-156
1.64
7.17
21.55
875
12
-48.5
619.5
113.4
1292
1299
53
1.63
7.36
22.61
962
13
-66.7
946.9
113.4
1307
1314
693
1.65
7.29
22.31
1090
14
-66.7
796.4
113.4
1307
1314
392
1.65
6.95
20.30
902
15
-65.7
753.8
113.4
1276
1284
337
1.64
6.85
19.63
831
16
-64.9
841.2
113.4
1249
1256
540
1.63
7.03
20.60
908
17
-36.0
909.5
113.4
1282
1289
643
1.78
8.15
29.28
1290
18
-45.6
954.4
113.4
1322
1330
692
1.72
7.69
25.50
1055
19
-46.2
1019.1
113.4
1290
1297
855
1.70
7.76
25.77
1098
20
-65.7
925.2
113.4
1276
1284
680
1.64
7.22
21.84
1029
21
-57.6
1324.3
113.4
1215
1222
1540
1.66
7.83
25.85
1285
22
-73.7
1180.6
113.4
1141
1149
1326
1.63
7.06
20.78
1008
a
b
Oxygen balance (%). Heat of formation of cation (kJ mol ). Heat of formation of anion (kJ mol-1).
d
-1
c
Lattice potential energy (kJ mol-1). eLattice energy (kJ mol-1). fHeat of formation of salt (kJ mol-1).
g
Density (g cm-3). hVelocity of detonation (km s-1). iDetonation pressure (GPa). jChemical energy of
detonation (cal g-1).
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The Journal of Physical Chemistry
Table 6. Energetic properties of series D salts (1-22). Compd.
OBa
HOFcb
HOFac
UPotd
HLe
HOFsaltf
ρg
VODh
DPi
Qj
1
-34.8
634.8
359.9
1459
1467
163
1.72
7.70
25.60
979
2
-36.6
761.2
359.9
1410
1417
465
1.70
8.02
27.54
1154
3
-20.8
674.2
359.9
1423
1431
277
1.77
8.48
31.59
1272
4
-53.3
567.2
359.9
1336
1343
151
1.66
7.00
20.67
802
5
-38.8
914.3
359.9
1310
1317
872
1.78
7.90
27.47
1067
6
-53.3
657.7
359.9
1302
1309
366
1.65
7.23
21.95
900
7
-53.3
775.6
359.9
1272
1279
632
1.64
7.46
23.28
1013
8
-53.3
894.3
359.9
1245
1252
897
1.63
7.64
24.32
1110
9
-24.9
700.6
359.9
1277
1285
476
1.78
8.30
30.33
1209
10
-53.8
381.6
359.9
1256
1264
-141
1.67
6.79
19.50
726
11
-40.8
530.6
359.9
1311
1319
102
1.70
7.50
24.10
947
12
-41.7
619.5
359.9
1280
1288
311
1.68
7.63
24.76
1024
13
-58.5
946.9
359.9
1295
1302
952
1.70
7.55
24.43
1145
14
-58.5
796.4
359.9
1295
1302
651
1.70
7.24
22.47
969
15
-58.2
753.8
359.9
1266
1273
595
1.69
7.14
21.77
898
16
-57.9
841.2
359.9
1239
1246
796
1.68
7.30
22.65
966
17
-30.6
909.5
359.9
1271
1278
901
1.83
8.37
31.41
1327
18
-38.8
954.4
359.9
1310
1317
952
1.78
7.98
28.07
1113
19
-39.8
1019.1
359.9
1279
1286
1112
1.76
8.03
28.25
1149
20
-58.2
925.2
359.9
1266
1273
937
1.69
7.49
23.91
1084
21
-51.7
1324.3
359.9
1206
1214
1795
1.71
8.05
27.84
1317
22
-68.1
1180.6
359.9
1135
1142
1579
1.66
7.23
22.05
1045
a
b
Oxygen balance (%). Heat of formation of cation (kJ mol ). Heat of formation of anion (kJ mol-1).
d
-1
c
Lattice potential energy (kJ mol-1). eLattice energy (kJ mol-1). fHeat of formation of salt (kJ mol-1).
g
Density (g cm-3). hVelocity of detonation (km s-1). iDetonation pressure (GPa). jChemical energy of
detonation (cal g-1).
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Table 7. Energetic properties of series E salts (1-22). Compd.
OBa
HOFcb
HOFac
UPotd
HLe
HOFsaltf
ρg
VODh
DPi
Qj
1
-30.8
634.8
502.5
2627
2637
-230
1.67
7.61
24.51
935
2
-33.6
761.2
502.5
2509
2519
267
1.65
8.07
27.39
1196
3
-13.3
674.2
502.5
2540
2550
-25
1.73
8.62
32.20
1338
4
-54.8
567.2
502.5
2339
2349
-145
1.62
6.91
19.84
787
5
-37.2
914.3
502.5
2281
2291
954
1.76
7.99
27.91
1114
6
-54.7
657.7
502.5
2265
2275
201
1.61
7.21
21.50
918
7
-54.5
775.6
502.5
2200
2210
619
1.60
7.49
23.10
1060
8
-54.5
894.3
502.5
2142
2152
1033
1.59
7.69
24.29
1177
9
-20.9
700.6
502.5
2211
2221
383
1.76
8.45
31.22
1285
10
-55.0
381.6
502.5
2167
2177
-530
1.63
6.70
18.74
723
11
-39.5
530.6
502.5
2285
2295
-201
1.66
7.51
23.77
972
12
-40.7
619.5
502.5
2217
2227
134
1.65
7.70
24.95
1070
13
-60.8
946.9
502.5
2249
2259
1084
1.67
7.59
24.38
1213
14
-60.8
796.4
502.5
2249
2259
633
1.67
7.23
22.17
1003
15
-60.2
753.8
502.5
2186
2196
568
1.65
7.10
21.19
923
16
-59.7
841.2
502.5
2130
2140
886
1.64
7.29
22.25
1007
17
-27.9
909.5
502.5
2197
2207
1024
1.82
8.53
32.47
1422
18
-37.2
954.4
502.5
2281
2291
1075
1.76
8.08
28.60
1170
19
-38.5
1019.1
502.5
2214
2224
1336
1.73
8.12
28.58
1216
20
-60.2
925.2
502.5
2186
2196
1082
1.65
7.49
23.59
1143
21
-52.4
1324.3
502.5
2062
2072
2403
1.68
8.13
28.11
1412
22
-70.7
1180.6
502.5
1917
1927
2117
1.64
7.27
22.11
1100
a
b
Oxygen balance (%). Heat of formation of cation (kJ mol ). Heat of formation of anion (kJ mol-1).
d
-1
c
Lattice potential energy (kJ mol-1). eLattice energy (kJ mol-1). fHeat of formation of salt (kJ mol-1).
g
Density (g cm-3). hVelocity of detonation (km s-1). iDetonation pressure (GPa). jChemical energy of
detonation (cal g-1).
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The Journal of Physical Chemistry
List of Figure Captions
Figure 1. Molecular frameworks of a series of substituted 1,3,5-triazine molecules (IV). Figure 2. Designed isodesmic reactions to calculate gas-phase heat of formation for the non-ionic compounds (I-V). Figure 3. Born-Haber cycle for the formation of energetic salts. Figure 4. Molecular structures of cations (1-22) and anions (A-E) selected for the design of energetic salts. Figure 5. Comparison of the HOFs of energetic salts of the Series A (cation:anion ratio is 1:1), Series B (cation:anion ratio is 2:1), and Series E (cation:anion ratio is 3:1). Figure 6. Comparison of the densities of the series A, B and E. Cation:anion charge ratio of the series A, B and E are 1:1, 2:1 and 3:1, respectively. Figure 7. Effect of –NO2 (series B), –NH2 (series C) and –N3 (series D) substituents on the densities of corresponding salts. Figure 8. Comparison of the detonation velocities and detonation pressures of the designed energetic salts.
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Figure 1
Figure 2
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The Journal of Physical Chemistry
-∆HOF
Cation+ Anion- (Solid)
mC(s) + nH2(g) + oN2(g) + pO2(g)
∆HL -∆HOFanion
Cation+ (gas) + Anion- (gas)
-∆HOFcation
Figure 3
O2N N O2N
O2N
N N N
N NO2
O2N
N
N
N
O2N
N
N
A
NO2
H2N
O2N
N
N
B
N
N N
NO2
N3
C
O2N
N N
N N
N
N
NO2
O2N
N
N N
N
D
NO2
E
[Anions]
NH2 NH4
NH2NH3
NH3OH
1
2
3
N H
NO2
H2N
16
HN N N H 17
H2N
NH2
H2N
NH2 NH2
N H
H2N
H2N
N H
N H
N H
N NH N NH2 N NH2
18
19
13
H2N HN
NH2 NH
H2N
N N NH 22 [Cations]
Figure 4
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N H
NH2
N NH2
N NH N NH2 N CH3
NH
N H
NH2
NH2
HN
20
N N
H2N
8
N NH NH3
12
11
N NH N NH2 N H
N H
NH2
7
O NH3
H2N
NH2
6
O
NH2
NO2
N NH
HN
5
10
NH2 N NH2
N3
NH2 N H
9
H2N
NH2 4
O
NH2 H2N
H2N
NH2
HN N
N H 14
H2N
N N H 15
N N H2NHN
NHNH3 N N 21
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Figure 5
Figure 6
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The Journal of Physical Chemistry
Figure 7
Figure 8
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Table of Contents (ToC)
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