Theoretical study on a novel high-energy density material 4,6,10,12-tetranitro-5,11-bis(nitroimino)-2,8-dioxa-4,6,10,12-tetraaza-tricyclo[7,3,0,0^3,7]dodecane

Abstract

A novel high-energy density material (HEDM) 4,6,10,12-tetranitro-5,11-bis(nitroimino)-2,8-dioxa-4,6,10,12-tetraaza-tricyclo[7,3,0,0^3,7]dodecane was designed and studied by a density functional theory (DFT) method. The geometric structure and thermodynamic properties were investigated at the B3LYP/6-31G (d,p) level. The heat of formation (HOF) and detonation properties were predicted by isodesmic reactions and Kamlet–Jacobs equations. The bond dissociation energy (BDE) and impact sensitivity were also studied to give a better understanding of its chemical and physical properties. The calculated results indicate that 4,6,10,12-tetranitro-5,11-bis(nitroimino)-2,8-dioxa-4,6,10,12-tetraaza-tricyclo[7,3,0,0^3,7]dodecane belongs to the P1̄ space group, with cell parameters Z = 2, a = 13.554 Å, b = 8.552 Å, c = 15.575 Å, α = 70.638°, β = 29.515° and γ = 82.702°. In view of the heat of formation (HOF, 530.36 kJ mol⁻¹), detonation velocity (D, 9.72 km s⁻¹), detonation pressure (P, 45.12 GPa), bond dissociation energy (BDE, 109.85 kJ mol⁻¹) and impact sensitivity (h₅₀, 20.79 cm), it is predicted that 4,6,10,12-dinitro-5,11-bis(nitroimino)-2,8-dioxa-4,6,10,12-tetraaza-tricyclo[7,3,0,0^3,7] dodecane could be considered as a potential candidate high-energy density compound.

---

Introduction

Nitramine compounds, as an important class of high-energy density materials (HEDMs), have received significant attention both in military and civilian applications.^1–3 Unfortunately, their outstanding properties such as high density, high positive heat of formation (HOF) and excellent detonation properties, seem to be contrary to the stability and sensitivity.^4,5 For instance, 1,3,4,6-tetranitroglycouril (TNGU, Scheme 1A), whose density and detonation properties are superior to the well-known explosives hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX, Scheme 1B), and 1,3,5,7-tetranitro-1,3,5,7-tetraazacyclooctane (HMX, Scheme 1C), is moisture sensitive. This molecule has four nitro groups for improved density and detonation properties, but the carbonyl groups at either end of the molecule undergo hydrolytic reaction with water. Thus, to solve this problem, one possible approach is to replace the two –C=O groups with –C=N– groups.

Scheme 1 Structures of TNGU, RDX, HMX and the title compound.

On the other hand, oxygen balance is of great importance when HEDMs were screened. Generally speaking, the higher the oxygen balance is, the better the detonation properties of a HEDM. However, it is clear that over much oxygen is not favorable for advancing the detonation properties of HEDMs since the over much oxygen will produce much O₂ that takes away a great deal of energy. It is necessary to better keep the value of oxygen balance around zero when a HEDM was designed.⁶ Herein, to find new energetic materials with excellent detonation properties, a novel high-energy density material 4,6,10,12-tetranitro-5,11-bis(nitroimino)-2,8-dioxa-4,6,10,12-tetraaza-tricyclo[7,3,0,0^3,7]dodecane (Fig. 1D) with an oxygen balance of zero, was designed on the basis of the structure of TNGU.

Fig. 1 Molecular structure of the title compound.

Novel HEDMs with multiple nitro groups may pose great danger to humans and the environment during both their synthesis and performance testing. Computer simulation, as an effective way in screening promising explosives without these shortcomings, has been widely used to design various unknown energetic materials. In this study, the heat of formation (HOF), electronic structures and detonation properties of the title compound were investigated by the density functional theory (DFT) method. The impact sensitivity (IS) and the bond dissociation energy (BDE) values of the trigger bond were obtained to give a better understanding of its security during storage or use. Additionally, the feasible synthetic route was also proposed via retrosynthetic analysis.

Computational method

The density functional theory (DFT), especially the B3LYP method that not only produces reliable geometries and energies, but also requires less time and computer resources, has emerged as a very reliable and economical tool to predict the chemical and physical properties of novel energetic materials.^7,8 All of the computations in the paper were performed with the Gaussian 03 package⁹ at the B3LYP/6-31G (d,p) basis set. The optimizations were performed using the default convergence criteria in the programs. Vibrational analyses at the same level of theory were also performed to confirm that all of the optimized structures correspond to be the local energy minima on the potential energy surfaces. The optimized structure of the title compound was shown in Fig. 1.

Calculation of the HOF of a novel energetic material is necessary to determine their detonation properties. To obtain the accurate HOF values, isodesmic reactions, in which the numbers of all kinds of bonds are kept invariable to decrease the calculation errors, were designed. This is because the electronic environment of atoms in the reactants and products are very similar in isodesmic reactions, the errors of electronic correction energies can be counteracted, and then the errors of the calculated HOFs can be greatly reduced. Previous studies also demonstrated this method as a feasible approach in estimation accurate HOFs of novel energetic materials.^10,11

The HOF for the title compound at 298 K was derived from the following isodesmic reaction (Scheme 2):

Scheme 2 Isodesmic reaction designed for the title compound.

For the isodesmic reaction (1), the HOF can be calculated from the following equation:

ΔH_298K = ∑ΔH_f,p − ∑ΔH_f,R (1)

where ΔH_f,p and ΔH_f,R are the HOFs of the products and reactants at 298 K, respectively. Thus, the HOF of the title compound can be obtained when the heat of reaction ΔH_298K is known. Besides, the HOF of a compound at 298 K can also be defined as follows:

ΔH_298K = ΔE_298K + Δ(PV) = ΔE₀ + ΔZPE + ΔH_T + ΔnRT (2)

where ΔE_298K and ΔE₀ are the change in total energy between the products and reactants at 298 K and 0 K, respectively; ΔZPE is the difference between the zero-point energy (ZPE) of the products and reactants; and ΔH_T is the thermal correction from 0 to 298 K. For reactions in the gas phase, Δ(PV) equals ΔnRT, and for isodesmic reactions, Δn = 0.

The experimental HOFs of the reference compounds NH₃, CH₄, NH₂NO₂ are available. As the experimental HOF of compound E is unavailable, additional calculations were carried out for the atomization reaction C₃H₇N₃ → 3C(g) + 7H(g) + 3N(g) by the G2 theory¹² to accurately predict its HOF. Then the HOF of the title compound was extracted easily while the HOFs of the reference compounds were known.

Since the phase of most energetic compounds is solid, the HOFs for such compounds requires solid-phase HOFs (ΔH_f,solid) rather than gas-phase HOFs (ΔH_f,gas). According to Hess' law,¹³ the ΔH_f,solid can be obtained from the ΔH_f,gas and heat of sublimation (ΔH_sub):

ΔH_f,solid = ΔH_f,gas − ΔH_sub (3)

where ΔH_sub denotes the heat of sublimation.

In addition, Politzer et al.^14,15 found that the ΔH_sub of energetic compounds correlates well with the molecular surface area and electrostatic interaction index (νσ_tot²). The empirical expression is shown as follows:

ΔH_sub = aA² + b(νσ_tot²)^0.5 + c (4)

where A, the surface area of the 0.001 e bohr⁻³ isosurface for the electronic density of the molecule; ν, the degree of balance between the positive and negative potentials on the isosurface; σ_tot², a measure of the variability of the electrostatic potential on the molecular surface; the coefficients a, b, and c were determined to be a = 2.670 × 10⁻⁴ kcal mol⁻¹ A⁻⁴, b = 1.650 kcal mol⁻¹, and c = 2.966 kcal mol⁻¹.¹⁶ The descriptors A, ν, andσ_tot² were calculated by using the computational procedures proposed by Bulat et al.¹⁷ This approach has been demonstrated to be a reliable way in prediction the heats of sublimation of energetic materials.^18,19

The detonation velocity (D) and detonation pressure (P), which are two important parameters in evaluating the explosive properties of energetic materials, can be estimated by the empirical Kamlet–Jacobs equations:²⁰

D = 1.01(NM̄^0.5Q^0.5)^0.5(1 + 1.3ρ) (5)

P = 1.558ρ²NM̄^0.5Q^0.5 (6)

where ρ, the loaded density of the explosive (g cm⁻³); D, the detonation velocity (km s⁻¹); P, the detonation pressure (GPa); N, the number of moles of detonation gases per-gram explosive (mol g⁻¹); M̄, the average molecular weight of these gases (g mol⁻¹); and Q, the heat of detonation (cal g⁻¹). The variables N, M̄, and Q were calculated according to ref. 20. The theoretical density was obtained from the molecular weight divided by the average molecular volume. The volume was defined as the space inside an electronic isodensity contour of 0.001 electron bohr⁻³ evaluated using a Monte-Carlo integrator.⁸

However, the results for ρ obtained using this method may have some errors for some systems in which there are strong hydrogen bonds. Thus, Politzer et al.²¹ proposed that the ρ of CHNO energetic materials should be corrected using the following equation to give an accurate results:

where ν, the degree of balance between the positive and negative potentials on the isosurface; σ_tot², a measure of the variability of the electrostatic potential on the molecular surface; and the coefficients β₁, β₂, and β₃ are of 0.9183, 0.0028, and 0.0443, respectively. This method has been successfully applied to various energetic materials.

The strength of bonding, which can be evaluated using bond dissociation energy (BDE), plays an important role in predicting the thermal stability of an energetic material. Usually, the energy required for bond homolysis at 298 K and 1 atm corresponds to the enthalpy of reaction:

A–B(g) → A˙(g) + B˙(g) (8)

ΔH₂₉₈(A–B) = [Δ_fH₂₉₈(A˙) + Δ_fH₂₉₈(B˙)] − Δ_fH₂₉₈(A–B) (9)

where A–B, the neutral molecule, A˙ and B˙, the corresponding product radicals after bond dissociation; ΔH₂₉₈(A–B), the bond dissociation enthalpy of A–B; Δ_fH₂₉₈(A˙), Δ_fH₂₉₈(B˙), and Δ_fH₂₉₈ (A–B), the enthalpies of formation for the free radicals and the parent molecule at 298 K, respectively.²²

For many organic compounds, the BDE(A–B) and ΔH₂₉₈(A–B) are usually interchangeably in the literature.²³ Therefore, the homolytic bond dissociation energy can be extracted by the following expression:

BDE₀(A–B) → E₀(A˙) + E₀(B˙) − E₀(A–B) (10)

The BDE corrected for the ZPE can be calculated using eqn (11):

BDE(A–B)_ZPE = BDE₀(A–B) + ΔE_ZPE (11)

where ΔE_ZPE is the difference between the ZPEs of the products and reactants.

Since the high-energy density compounds are usually in solid phases, the possible polymorphs and crystal structure of the title compound were predicted using polymorph module of Materials Studio. The Compass force field capable of predicting the condensed phase properties by searching the possible molecular packing among the most probable seven space groups (P2₁/c, P1̄, P2₁2₁2₁, Pbca, C2/c, P2₁ and Pna2₁).^24,25

Results and discussion

Molecular geometry and electronic structure

It is useful to examine the geometric structure of the title compound since the structure is closely related to the physical and chemical properties. Table 1 lists the selected geometry parameters of the title compound at the B3LYP/6-31G (d,p) level. From the table, the length of the C–C bond (1.5614 Å) in the title compound is much longer than the normal C–C single bond (1.54 Å) which is due to the cage strain in the system; The C–N bond lengths of the title compound are found to be shorter than the normal C–N single bond (1.49 Å) though the difference is not significant; the bond lengths of N–N bonds in N–NO₂ groups are longer than the usual N–N bond lengths due to the electron with-drawing inductive effect of the nitro groups.

Table 1 Selected bond lengths of the title compound at B3LYP/6-31G (d,p) level

Bond	Bond length	Bond	Bond length	Bond	Bond length
C1–O16	1.4165	N2–N34	1.4383	N20–O19	1.2208
C5–O15	1.4112	N4–N28	1.4439	N20–O21	1.2099
C1–C5	1.5614	C3–N17	1.2697	N28–O29	1.2121
C1–N2	1.4355	N17–N20	1.4454	N28–O30	1.2154
C5–N4	1.4502	N34–O35	1.2198	C3–N4	1.4199
C3–N2	1.4107	N34–O36	1.2072

---

Molecular orbital is an important parameter which can provide useful information on electronic structures. It was proposed that the larger energy gap (ΔE) of the molecule, the lower reactivity in the chemical. The calculated energy gap value of the title compound is 4.89 eV, indicating the title compound may have a lower reactivity. Fig. 2 illustrates the 3D plots of the highest occupied molecular orbital (HOMO), lowest unoccupied molecular orbital (LUMO) and the molecular electrostatic potentials (MEP) of the title compound at the B3LYP/6-31G (d,p) level. Obviously, most of the HOMO and LUMO levels are 2-fold degenerate which indicates that the removal of an electron from the HOMO level or addition of an electron to the LUMO level could weaken the skeleton framework. In view of the MEP of the title compound (colors range from −0.03 to 0.06 Hartree, with red denoting the most negative potential and blue denoting the most positive potential), the negative potentials appear to be distributed mostly on the oxygen atoms of the –NO₂ groups while the positive potentials appear to be at the center of the skeleton. This may attribute to the stabilization of the molecular structure.

Fig. 2 HOMO, LUMO, and MEP of the title compound.

Heat of formation and thermodynamic properties

It is of great importance to obtain the accurate heats of formation (HOFs) of an energetic material since the HOF is usually taken as the indicator of the “energy content”. It has been reported that DFT is accurate enough to compute the HOF through isodesmic reactions.²⁶ With the calculated enthalpies of all relative species, it is easy to obtain the HOF of the target compound. Table 2 summarized the total energies (E₀), thermal corrections (H_T), zero-point energies (ZPE), and HOFs for the reference compounds being enlisted in the isodesmic reaction. The evaluated ΔH_f,solid value of 530.36 kJ mol⁻¹ was extracted using the Politzer's approach. It is seen that the condensed-phase heat of formation (ΔH_f,solid) is larger than that of the well-known energetic material HMX (263.70 kJ mol⁻¹) and benefits the heat release during the detonation.⁸ Therefore, the high energy content of the title compound satisfies the necessary characteristic of energetic materials.

Table 2 Calculated total energies (E₀, au), thermal corrections (H_T, kJ mol⁻¹), zero-point energies (ZPE, kJ mol⁻¹), and heats of formation (HOFs, kJ mol⁻¹) for the reference compounds

Compound	E0	HT	ZPE	ΔHf,gas	ΔHsub	ΔHf,solid
a Experimental values taken from ref. 27.b Values calculated at the G2 level.c Experimental values taken from ref. 28.
NH3	−56.5577769	0.034442	0.003807	−45.9^a
CH4	−40.524020	0.045026	0.00381	−74.6^a
CH3OCH3	−155.032965	0.079912	0.005248	−184.1^a
C3H7N3	−282.790266	0.112373	0.006223	102.5^b
NH2NO2	−261.037824	0.038304	0.004439	6.69^c
D	−1940.354676	0.027418	0.201846	585.03	54.67	530.36

---

Fig. 3 presents the simulated IR spectrum of the title compound. The modes in 3000–3250 cm⁻¹ are associated with the C–H stretch vibration; the rage of 1600–1800 cm⁻¹ belongs to the N=O asymmetric stretch; band at 1100–1400 cm⁻¹ is composed of the N–N asymmetric stretch together with C–H twisting out of plane; The bands less than 900 cm⁻¹ which belong to the fingerprint spectrum, are mainly caused by the deformation of heterocyclic skeleton and the bending vibration of C–H and C–C bonds.

Fig. 3 Simulated IR spectra of the title compound at B3LYP/6-31G (d,p) level.

To give a better understanding of the thermodynamic properties of the title compound, the standard molar heat capacity C⁰_p,m, standard molar entropy S⁰_m and standard molar enthalpy H⁰_m from 200 to 800 K were evaluated. Fig. 4 presents the temperature-dependent relations for C⁰_p,m, S⁰_m and H⁰_m in the range of 200–800 K, and the correlation equations between the thermodynamic functions and different temperatures were also calculated (where R² is the correlation coefficients).

Fig. 4 Relationships between the thermodynamic functions and temperature (T) for the title compound.

From the data, it is found that C⁰_p,m, S⁰_m and H⁰_m increase evidently with the temperature increasing. The main contributions to the thermodynamic functions are from the translation and rotation of molecules when the temperature is low; however, at higher temperature, the vibrations are intensified and therefore make more contributions to the thermodynamic properties and lead to the increase in the thermodynamic functions.²⁹ The correlation equations between the thermodynamic functions and temperature in the range of 200–800 K can be expressed as follows:

C^θ_p,m = 56.516 + 1.372T − 0.000706T², R² = 0.9999

S^θ_m = 333.115 + 1.640T − 0.000495T², R² = 0.9999

H^θ_m = −20.878 + 0.218T + 0.000197T², R² = 0.9998

Crystal structure

Compass force field, as an effective way in producing the gas-phase and condensed-phase properties of a broad range of systems including nitramines, was employed to predict the crystal structure of the title compound in this study. The approach is based on the generation of possible packing arrangements in all reasonable space groups to search for the low-lying minima in the lattice energy surface.³⁰ The geometry that optimized at the B3LYP/6-31G (d,p) level is considered as the input structure for the polymorph search.

Table 3 summarized the unit cell parameters of the packing with the lowest energy in seven most possible space groups. It is obvious that the energies are in the range from −137.48 to −134.96 kJ mol⁻¹ cell⁻¹ and the structure with P1̄ symmetry has the lowest energy. Therefore, the title compound probably belongs to the P1̄ space group (Fig. 5) since the stable polymorph usually possesses lower Gibbs free energy (or total energy at 0 K). The corresponding cell parameters are Z = 2, a = 13.554 Å, b = 8.552 Å, c = 15.575 Å, α = 70.638°, β = 29.515° and γ = 82.702°, respectively.

Table 3 Unit cell parameters of the possible molecular packing of the title compound

Space groups	P1̄	P21	P212121	P21/c	Pna21	Pbca	C2/c
Z	2	2	4	4	4	8	8
E (kJ mol^−1 cell^−1)	−137.488	−135.770	−134.966	−136.862	−135.937	−135.719	−135.435
a (Å)	13.554	13.866	8.363	25.137	13.636	30.878	14.398
b (Å)	8.552	7.713	15.981	8.571	7.490	7.622	17.984
c (Å)	15.575	7.636	11.964	15.434	15.825	13.607	12.568
α (°)	70.638	90.000	90.000	90.000	90.000	90.000	90.000
β (°)	29.515	91.172	90.000	150.538	90.000	90.000	93.697
γ (°)	82.702	90.000	90.000	90.000	90.000	90.000	90.000

---

Fig. 5 Simulated crystal structure of the title compound.

Detonation properties

Detonation velocity (D) and pressure (P) are the most important targets when an energetic material was designed. Together with the density of 1.99 g cm⁻³ obtained by Monte-Carlo method, the detonation properties were computed by Kamlet–Jacobs empirical equations. Table 4 collected the predicted crystal densities (ρ), detonation velocities (D), and detonation pressure (P) of the title compound. For a comparison, the ρ, D and P of the well-known explosives RDX and HMX were also listed in the Table. It could be found that the ρ, D and P of the title compound were larger than those of RDX and HMX which illustrated that the title compound has better detonation properties than RDX and HMX. Generally speaking, the closer to zero of the oxygen balance is, the larger the D and P values are, and the better the performance of an energetic compound. Obviously, the oxygen balance of the title compound is equal to zero and is superior to that of the RDX and HMX. According to the energy criterion for HEDMs (i.e., ρ > 1.9 g cm⁻³, D > 9.0 km s⁻¹, P > 40.0 GPa), the title compound meets the requirements and can be considered as a novel high-energy density material.

Table 4 Detonation properties of the title compound, RDX and HMX

Compound	ρ (g cm^−3)	D (km s^−1)	P (GPa)	OB^b (%)
a Experimental values taken from ref. 31.b Oxygen balance(OB, %) for CaHbOcNd: 1600 × (c − 2a − b/2)/MW; MW = molecular weight of the title compound.
Title compound	1.99	9.72	45.12	0
RDX^a	1.82	8.7	34.0	−21.6
HMX^a	1.91	9.1	39.0	−21.6

---

Thermal stability and impact sensitivity

Thermal stability and impact sensitivity are two fundamental parameters of an energetic material since they can provide important information on the safety property during usage or storage. They can be deduced on the basis of bond dissociation energies (BDEs) and h₅₀ that proposed by Keshavarz et al.:³²where a, b, c, and d stand for the number of C, H, N, and O atoms in the explosive molecule, respectively; n_–CNC– and n_–CNNC– stand for the number of –CNC– and –CNNC– in the molecule, respectively; Mw stands for the molecular weight.

Nowadays, people have reached a consensus that nitro groups in the energetic material often represent the primary cause of initiation reactivity when heated or assaulted. Therefore, the weakest N–N bonds in the N–NO₂ was selected as the breaking bond to calculate the BDE at B3LYP/6-31G (d,p) level. Considering the practical requirements, a quantitative criteria-associated stability (BDE of the trigger bond) requirements, i.e., BDE ≈ 80–120 kJ mol⁻¹, is proposed and employed to filtrate and recommend potential HEDMs by Chung et al.³³ The BDE_ZPE value of the title compound (109.85 kJ mol⁻¹) essentially satisfies this requirement. Additionally, the calculated values of h₅₀ (20.79 cm) also demonstrated that the title compound has an acceptable impact sensitivity. Based on the above-described reason, the title compound has the potential to be a HEDM.

Synthetic routes

When a novel energetic material was designed, the following important task is to synthesize it. Thus, the feasible synthetic route for the title compound was proposed via retrosynthetic analysis (Scheme 3). From the scheme, it is clear that the synthetic rote is simple enough and all of the crude materials can be easily obtained with commercial use.

Scheme 3 Synthetic route of the title compound.

Conclusions

In this paper, the B3LYP/6-31G (d,p) basis set of density functional theory (DFT) has been employed to investigate the geometry and electronic structure, IR spectrum, thermodynamic functions, heat of formation, detonation properties, bond dissociation energy and impact sensitivity of a novel high-energy density material 4,6,10,12-tetranitro-5,11-bis(nitroimino)-2,8-dioxa-4,6,10,12-tetraaza-tricyclo[7,3,0,0^3,7]dodecane. The calculated results show that the most possible packing structure of the title compound belongs to the P-1 space group with the cell parameters Z = 2, a = 13.554 Å, b = 8.552 Å, c = 15.575 Å, α = 70.638°, β = 29.515° and γ = 82.702°, respectively. The calculated values of density (1.99 g cm⁻³), detonation velocity (D, 9.72 km s⁻¹) and detonation pressure (P, 45.12 GPa) indicate that the designed compound has superior detonation properties to those of RDX and HMX. The bond dissociation energy (109.85 kJ mol⁻¹) and impact sensitivity (20.79 cm) also demonstrate that the title compound essentially satisfies the quantitative criteria for the energy and can be considered as a novel candidate high-energy density material.

Acknowledgements

This study was supported by the National Natural Science Foundation of China and the China Academy of Engineering Physics (Grant no. 11076017) and the National Defence Advanced Research Projects (Grant no. J-KY-2012-1317)

References

1. Y. H. Joo, B. Twamley and J. M. Shreeve, Chem.–Eur. J., 2009, 15, 9097.
2. M. Rahm, S. V. Dvinskikh, I. Furo and T. Brinck, Angew. Chem., Int. Ed., 2011, 50, 1145.
3. Y. Q. Wu, F. L. Huang and Z. Y. Zhang, RSC Adv., 2012, 2, 4152.
4. M. H. Keshavarz, H. Motamedoshariati, R. Moghayadnia, H. R. Nazari and J. Azarniamehraban, J. Hazard. Mater., 2009, 172, 1218.
5. R. H. Wang, Y. Gao, R. J. Sa and J. M. Shreeve, Chem.–Eur. J., 2010, 16, 8522.
6. Q. Wu, Y. Pan, X. L. Xia, Y. L. Shao, W. H. Zhu and H. M. Xiao, Struct. Chem., 2013, 24, 1579.
7. L. M. Yang, P. Ravindran, P. Vajeeston and M. Tilset, RSC Adv., 2012, 2, 1618.
8. F. Wang, G. X. Wang, H. C. Du, J. Y. Zhang and X. D. Gong, J. Phys. Chem. A, 2011, 115, 13858.
9. M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, J. A. Montgomery, T. Vreven, K. N. Kudin, J. C. Burant, J. M. Millam, S. S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N. Rega, G. A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J. E. Knox, H. P. Hratchian, J. B. Cross, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, P. Y. Ayala, K. Morokuma, G. A. Voth, P. Salvador, J. J. Dannenberg, V. G. Zakrzewski, S. Dapprich, A. D. Daniels, M. C. Strain, O. Farkas, D. K. Malick, A. D. Rabuck, K. Raghavachari, J. B. Foresman, J. V. Ortiz, Q. Cui, A. G. Baboul, S. Clifford, J. Cioslowski, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. Nanayakkara, M. Challacombe, P. M. W. Gill, B. Johnson, W. Chen, M. W. Wong, C. Gonzalez and J. A. Pople, Gaussian 03, Gaussian Inc., Pittsburgh, PA, 2003.
10. M. Jaidann, S. Roy, H. Abou-Rachid and L.-S. Lussier, J. Hazard. Mater., 2010, 176, 165.
11. V. D. Ghule, S. Radhakrishnan and P. M. Jadhav, Struct. Chem., 2011, 22, 775.
12. L. A. Curtiss, K. Raghavachari, P. C. Redfern and J. A. Pople, J. Chem. Phys., 1997, 106, 1063.
13. P. W. Atkins, Physical chemistry, Oxford University Press, Oxford, 1982.
14. P. Politzer, P. Lane and J. S. Murray, Cent. Eur. J. Energ. Mater., 2011, 8, 39.
15. P. Politzer, J. S. Murray, M. E. Grice, M. DeSalvo and E. Miller, Mol. Phys., 1997, 91, 923.
16. E. F. C. Byrd and B. M. Rice, J. Phys. Chem. A, 2006, 110, 1005.
17. F. A. Bulat, A. Toro-Labbe, T. Brinck, J. S. Murray and P. Politzer, J. Mol. Model., 2010, 16, 1679.
18. M. Jaidann, S. Roy, H. Abou-Rachid and L. S. Lussier, J. Hazard. Mater., 2010, 176, 165.
19. G. Z. Zhao and M. Lu, J. Phys. Org. Chem., 2013, 26, 211.
20. M. J. Kamlet and S. T. Jacobs, J. Chem. Phys., 1968, 48, 23.
21. P. Politzer, J. Martinez, J. S. Murray, M. C. Concha and A. Toro-Labbé, Mol. Phys., 2009, 107, 2095.
22. I. Mills, T. Cvitas, K. Homann, N. Kallay and K. Kuchitsu, Quantities, units, and symbols in physical chemistry, Black well, Oxford, 1988.
23. S. J. Blanksby and G. B. Ellison, Acc. Chem. Res., 2003, 36, 255.
24. R. Srinivasan, Acta Crystallogr., Sect. A: Found. Crystallogr., 1992, 48, 917.
25. N. Y. Chernikova, V. K. Belsky and P. M. Zorkii, J. Struct. Chem., 1990, 31, 661.
26. L. Türker, S. Gümüş and T. Atalar, J. Energ. Mater., 2010, 28, 139.
27. J. A. Dean, LANGE'S handbook of chemistry, McGraw-Hill, 15th edn, New York, 1999.
28. X. W. Fan, X. H. Ju and H. M. Xiao, J. Hazard. Mater., 2008, 156, 342.
29. J. Y. Zhang, H. C. Du, F. Wang, X. D. Gong and Y. S. Huang, J. Phys. Chem. A, 2011, 115, 6617.
30. G. Z. Zhao and M. Lu, J. Mol. Model., 2013, 19, 57.
31. M. B. Talawar, R. Sivabalan, T. Mukundan, H. Muthurajan, A. K. Sikder, B. R. Gandhe and A. S. Rao, J. Hazard. Mater., 2009, 161, 589.
32. M. H. Keshavarz, H. R. Pouretedal and A. Semnani, J. Hazard. Mater., 2007, 141, 803.
33. G. Chung, M. W. Schmidt and M. S. Gordon, J. Phys. Chem. A, 2000, 104, 5647.

---