• Parabanic acid;
  • Explosive;
  • Detonation;
  • Density functional calculations


  1. Top of page
  2. Abstract
  3. Introduction
  4. Computational Methods
  5. Results and Discussion
  6. Conclusions

This work deals with certain parabanic acid (PA) derivatives because they possess great calculated density (>1.8 g·cm–3) and high content of nitrogen (26 %). Computed ballistic properties of eight different parabanic acid derivatives are presented. The structures were optimized at the B3LYP/6-31G(d, p) level. The calculated data for PA are found to be compatible with the experimental X-ray data. The detonation performance analyses were done using empirical Kamlet-Jacobs equations. Additionally, detonation products were assigned and power index were calculated. All the compounds considered are powerful candidates for high energy materials.


  1. Top of page
  2. Abstract
  3. Introduction
  4. Computational Methods
  5. Results and Discussion
  6. Conclusions

Lately, explosive scientists have concentrated on compounds of high density with high content of nitrogen and low content of hydrogen. These types of compounds attract both theoretical and practical considerations. They are not only applicable in conventional fields where high-energy substances are essential (propellants, explosives, etc.), but also applicable in some other purposes, e.g. gas-generating substances or components of pyrophobic compositions.1 Such compounds are used as components of energetic compositions on condition that they have promising detonation and/or combustion properties, which depend on the enthalpy of formation (or enthalpy of combustion) and molecular crystal density.26

One of the most remarkable energetic skeleton, rich in nitrogen, low in hydrogen is parabanic acid (PA).7 Parabanic acid, 2, 4,5-imidazolidinetrione, is a crystalline nitrogenous acid (C3N2H2O3) obtained by the oxidation of uric acid. It is also called oxalylurea (see Figure 1).8,9 Ulrich and Sayigh et al. have reported the synthesis of PA by the reaction of oxalychloride and urea.10

The great magnitude of the calculated density data (1.753 g·cm–3) of parabanic acid and high content of nitrogen (24.5 %) have inspired us to investigate the parabanic acid frame. We have designed a series of molecules (18) by nitration and imination. Figure 1 shows the structures of parabanic acid and its derivatives (compounds 18).

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Figure 1. The structures of PA and other derivatives.

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Computational Methods

  1. Top of page
  2. Abstract
  3. Introduction
  4. Computational Methods
  5. Results and Discussion
  6. Conclusions

The preliminary geometry optimizations resulting in energy minima were completed employing MM2 followed by semi-empirical PM3 self-consistent fields molecular orbital (SCF-MO) methods11 at the restricted level.12,13 Afterwards, geometry optimizations were done within the STO and various RHF levels. Finely framework of Density Functional Theory (DFT, B3LYP)14,15 at the restricted level16 of 6-31G(d, p) basis set were employed. The exchange term of B3LYP contains hybrid Hartree-Fock and local spin density (LSD) exchange functions with Becke's gradient correlation to LSD exchange.15,16 The correlation term of B3LYP consists of Vosko, Wilk, Nusair (VWN3) local correlation functional17 and Lee, Yang, Parr (LYP) correlation correction functional.18 Vibrational analyses and the calculation of total electronic energies were performed using B3LYP/6-31G(d, p) type calculations for closed-shell systems. The normal mode analysis for each compound yielded no imaginary frequency, which indicates each compound had at least a local minimum on the potential energy surface. The total electronic energies were corrected for zero point vibrational energies (ZPE). Gas phase heat of formations of all the molecules were calculated by a semi-empirical approach (PM3) over DFT (B3LYP/6-31G(d, p)) optimized geometries. All the computations, except for molar volume, were performed using Spartan 06 software package.19 Molar volume calculations were performed at the same theoretical level by Gaussian 03 software package.20 The normal mode analysis for each fragment resulted in no imaginary frequencies.

Results and Discussion

  1. Top of page
  2. Abstract
  3. Introduction
  4. Computational Methods
  5. Results and Discussion
  6. Conclusions

All the structures investigated were thought as the potential candidates for high explosives (Figure 1). The geometry optimizations of the structures shown in Figure 1 were done at the B3LYP/6-31G(d, p) level. The bond lengths for the geometry optimized structures are presented in Table 1 (Figure 2). The experimental X-ray diffraction21 and calculated bond length values of parabanic acid are also shown in Table 1. The similarity of the experimental and theoretical values of the bond lengths for PA guarantees satisfactory level of calculation for the geometry optimization. This compatibility also guarantees that bond lengths of other compounds are close to the actual values. Note that there are no experimental X-ray data for the new designed compounds 18 to the best of our knowledge.

Table 1. The bond lengths /Å of the geometry optimized parabanic acid and its nitro derivatives (compounds 18) calculated at the theoretical level of B3LYP/6-31G(d, p).
 PA a)PA12345678
  1. a

    a) Literature experimental values reported in Ref. 21. b) X represents nitrogen and/or oxygen atoms (see Figure 1).

C1X3 b)1.2031.2061.1981.1921.2521.2741.2761.2741.2761.276
C2X4 b)1.2131.2041.1961.1951.1991.1961.2581.2751.2791.269
C3X5 b)1.2101.2041.2021.1951.1941.1941.2001.1941.2571.276
thumbnail image

Figure 2. The numbering scheme of the structures presented in this paper.

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An evaluation between the experimental and theoretical bond lengths of PA indicates that the calculated results are a little greater than the experimental values. One possible source of this slight discrepancy is the inadequate modeling of dispersion forces in most forms of DFT. Other reason is due to the solid-state effect, i.e., intermolecular interactions. Such interactions are not considered in the DFT calculations.22

Total Energies

Table 2 shows the Zero Point Energy (ZPE) corrected absolute total electronic energies of the geometry optimized compounds calculated at the theoretical level of B3LYP/6-31G(d, p). When Table 2 is considered, it is obvious that the ZPE corrected total electronic energies (Ecorr) of compounds get lower from compound 1 to 8. It is known that as the molecular weight of compounds get higher, the total electronic energy values get lower.

Table 2. The calculated corrected total electronic energies of PA and derivatives at (DFT) B3LYP/6-31G(d, p) theoretical level.
 FormulaE /kJ·mol–1Ecorr /kJ·mol–1

Ballistic Properties

Hazardous effects of explosives can be assessed by the determination of the ballistic properties, i.e. detonation velocity (D) and detonation pressure (P). The experimental Kamlet-Jacobs equations26 are employed for the calculations of these properties as follows:

  • D = 1.01 (N M1/2 Q1/2)1/2 (1+1.30 ρ) ((1))
  • P = 1.558 ρ2 N M1/2 Q1/2 ((2))

where each term in Equation (1) and Equation (2) is expressed as follows: detonation velocity D (km·s–1); detonation pressure P (GPa); density of a compound ρ (g·cm–3); moles of gaseous detonation products per gram of explosive N; average molecular weight of gaseous products M; chemical energy of detonation Q (kJ·g–1). The parameters N, M, and Q are calculated along with the chemical composition of each explosive as listed in Table 3.22 The parameters N, M, and Q were calculated according to the chemical composition of each explosive as listed in the second column of Table 3.

Table 3. Stoichiometric relations for the calculations of the N, Mave and Q parameters of CaHbOcNd type explosives.22
Parameterc ≥ 2a + b/22a + b/2 > c ≥ b/2b/2 > c
N(b + 2c + 2d)/4M(b + 2c + 2d)/4M(b + d)/2M
Mave4M/(b + 2c + 2d)(56d + 88c – 8b)/(b + 2c + 2d)(2b + 28d + 32c)/(b + d)
Q × 10–3(28.9b + 94.05a + 0.239ΔHof)/M[28.9b + 94.05(c/2 – b/4) + 0.239ΔHof]/M(57.8c + 0.239ΔHof)/M

In Table 3, M is the molecular weight of the compound (in g·mol–1); ΔHof is the gas phase standard heat of formation of the compound (in kJ·mol–1). Former studies2325 have stated that the gas phase standard heat of formation (ΔHof) calculated at the PM3 level over DFT (B3LYP/6-31G(d, p)) optimized geometries could substitute the experimental data reasonably. PM3 is a semi empirical method and some parameters involved in it are essentially based on experimental data. Due to that fact, ΔHof prediction is quite trustworthy on condition that correct geometry is adjusted prior to ΔHof calculations. Therefore, PM3 method was applied over (B3LYP/6-31G(d, p)) geometry optimized molecules to calculate the gas phase heat of formations. The density of each compound was predicted from the molecular volume divided by molecular weight, while the molecular volume of each molecule was obtained from the statistical average of 100 single-point molar volume calculations for each optimized structure. The molar volume was defined as inside a contour of 0.001 electrons/Bohr3 density that was evaluated using a Monte Carlo integration implemented in the Gaussian 03 software package.20 This method of calculation for densities was used extensively in the literature.21

The relative amount of oxygen with respect to the oxygen required to oxidize the material itself completely is expressed as the oxygen balance (Ω). When an explosive is exactly oxygen balanced, neither rich nor poor, it produces the maximum energy output per unit weight of that explosive. When Table 4 is considered, it is obvious that compounds 1 and 3 are underoxidized like TNT, RDX, and HMX. However, compounds 2, 48 are overoxidized like nitroglycerine, C3H5N3O9 (3.52 %).26

The calculated density and detonation properties of parabanic acid derivatives are listed in Table 4. It also includes experimental (in parenthesis) and theoretical performance values of TNT,27 RDX,22,2830 and HMX22,2830 obtained from the literature.

Table 4. Predicted densities and detonation properties of PA and its derivatives at the theoretical level of B3LYP/6-31G(d, p).
CompoundΩ / %ΔHfo /kJ·mol–1Q /kJ·g–1N / %V /cm3·mol–1ρ /g·cm–3D /km·s–1P /GPa)
HMX–21.61270.41 1633.3837.8157.931.88(1.90)9.28(9.10)39.21(39.00)

When the detonation velocity and pressure values in Table 4 are considered, it is obvious that all the compounds 18 are strong candidates for high explosives. Their explosive character follows the order 7 > HMX > 8 > 5 > 6 > RDX > 3 > 4 > 2 > 1 > TNT. Compounds 58 seem to be as effective as RDX and HMX. Others should be better than a well-known explosive, TNT.

Although Kamlet-Jacobs equations do not explicitly relate the weight percent of nitrogen ( % N) of an explosive with “D” and “P” apparently, it is an additional significant parameter that affects the ballistic properties. The order of % N value of presently considered explosives is same as the order of detonation velocity. As the values of % N increases, detonation velocity also increases. For instance, compound 7 has the greatest % N (43.3 %) and detonation velocity (9.48 km/s); whereas, compound 1 has the lowest % N (26.4 %) and detonation velocity (8.04) of all.

Density of PA was calculated as 1.753 g·cm–3. As seen from Table 4, the density increases from compound 1 to 8. Further nitration and further imination followed by nitration (from compound 1 to 8) creates compounds with greater density, accordingly superior explosives considering Kamlet-Jacobs equations. These molecules shall easily be employed in munitions requiring limited volume.

Further nitration of lactam nitrogen of compound 1 yields a better explosive (compound-2). Similarly, the imination of compound gives an enhanced explosive character (compound 3) increasing the detonation velocity value from 8.38 to 8.88 km·s–1. However, nitration of the imino group of compound 3 yields compound 4 with lower detonation velocity. Additional imination of the carbonyl group of compound 4 gives compound 5 with superior detonation velocity. Conversely, nitration of that imine group produces compound 6 lessening the detonation velocity. Conversion of the last carbonyl group of compound 6 to imino derivative gives compound 7, which has the best explosive properties of all. Nitration of compound 7 decreases the ballistic properties (as in the previous cases). Computationally, it has been shown that nitration of parabanic acid is a useful method in the enhancement of ballistic properties. On the other hand, imination of carbonyl group (at least in the present case) is not a convenient method in the improvement of explosive properties; whereas nitration of the formed imine group is an effective way of increasing both the detonation velocity and pressure. All the compounds in the present article are potential candidates for high explosives.

Explosive Power and Power Index

Heat and gases are the products of an explosive reaction. The volume of gas formed delivers information on the amount of work done by the explosive. Standard conditions must be set up so as to measure the volume of produced gas, since the volume of gas varies according to the temperature. The standard conditions (273 K, 1 atm) enable one to make assessments on numerous explosives. Division of the value of total volume of gas produced upon detonation by the molecular weight gives information on how much gas is released per gram of explosive.

The heat of explosion Q can be calculated as stated in the previous section. The volume V and Q values can be combined to give the value for the explosive power31 as shown in the following equation:

Explosive power = QV

The value for the explosive power is then compared with the explosive power of a standard explosive (picric acid, PAc) to obtain power index, as shown in the following equation:

Power index = [QV / Q(PAc)V(PAc)] × 100

In order to clarify the quantity and identity of the decomposition products, a set of rules developed by Kistiakowsky and Wilson was used.31 Table 5 shows the decomposition products of compounds 18. For instance, complete decomposition of compound 1 produces 1.5 mol of N2, 0.5 mol of H2O, 1.5 mol of CO, and 1.5 mol of CO2. Table 5 shows the decomposition products of the compounds 18. Compound 8 gives the most amount of hot gas upon detonation. The total moles of decomposition products data are inputs for the calculation of power index values.

Table 5. The identity and the quantity of the decomposition products of the compounds 18.

Table 6 shows the power index values of the compounds 18 and picric acid. The power index values of the considered compounds vary between 57 and 92 % and in the following manner: 7 > 5 > 3 > 8 > 6 > 1 > 4 > 2. Compound 7 seems to be the best of all. The power index values of some renowned explosives are given for comparison: hexanitrostilbene (HNS) (109 %), trinitrotoluene (TNT) (110 %), triamino trinitro benzene (TATB) (99 %), 5-nitro-2, 4-dihydro-3H-1, 24-triazol-3-one (NTO) (87 %), RDX (168 %), HMX (166 %).31 The results show that compounds 7, 5, and 3 are as effective as TATB and NTO, but not as good as RDX and HMX in terms of power index concept.

Table 6. The power index values of compounds 18 and picric acid.
CompoundQ /kJ·g–1V /dm3·g–1Q·VPower index / %
Picric acid1379.070.8311146.09100


  1. Top of page
  2. Abstract
  3. Introduction
  4. Computational Methods
  5. Results and Discussion
  6. Conclusions

Parabanic acid was chosen as a starting frame due to its high nitrogen content and high density value. DFT studies were performed on eight parabanic acid derivatives. The corrected absolute and relative total energies of the geometry optimized structures were calculated at the theoretical level of B3LYP/6-31G(d, p). The density data of compounds 18 were calculated and found to be much more than RDX and HMX. These molecules shall easily be employed in munitions requiring small volume. Detonation velocity and pressure values were calculated employing Kamlet-Jacobs equations. The results showed that the explosive character follows the order 7 > HMX > 8 > 5 > 6 > RDX > 3 > 4 > 2 > 1 > TNT. Compounds 58 are found as effective as RDX and HMX, others were found superior than a well-recognized explosive, TNT. The identity and quantity of the decomposition products were enlightened. Power index values have indicated that some of our explosives are as effective as TATB and NTO in terms of amount of work done by the explosive. It was shown that nitration of parabanic acid is a useful method in the enhancement of ballistic properties. Whereas, imination of the carbonyl group is not a convenient method in the improvement of explosive properties but nitration of the formed imine group is an effective way of increasing both the detonation velocity and pressure. All the compounds in the presented article are potential candidates for high explosives.

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