CHEN Li-Zhen ZHANG Lin REN Fu-De②CAO Dun-Lin REN Jun

a (College of Chemical Engineering and Environment,North University of China, Taiyuan 030051, China)b (Department of Chemistry, College of Science, North University of China, Taiyuan 030051, China)

1 INTRODUCTION

The intermolecular hydrogen-bonding interaction has an underestimated function in the supramolecular assembly, packing of crystal structure and diversity and flexibility of biomolecular structure and molecular stability of explosive[1-8]. In particular,the formation of such hydrogen bonds is always the first step in the chemical reaction of electron donor and acceptor, which has a great impact on the selection of reaction, stereochemical characteristics and yield[9-10]. Therefore, in recent years, the study on the intermolecular hydrogen-bonding interaction has attracted more attention. The reaction for preparation of RDX and HMX by using nitric acid to resolve hexamethylenetetramine is a kind of typical nitrification reaction. Despite of mature technology,there is rare report of study on the intermolecular interaction between hexamethylenetetramine and nitric acid, and a common understanding has not yet been reached on the starting step that which of the hydroxyl and nitro groups from the nitric acid gets close to hexamethylenetetramine[11]. In this paper, it is planning to adopt the methods of ab initio and density functional theory to make theoretical study on the intermolecular interaction between hexamethylenetetramine and nitric acid with combination of NBO, temperature effect and solvation effect, and discover the microstructure and thermodynamic properties of the complex generated in the first step of such nitrification reaction so as to find more optimal reaction conditions for the improvement of RDX and HMX high explosive yield.

2 CALCULATION METHODS

The geometries of hexamethylenetetramine, nitric acid and their complexes are fully optimized and their vibration frequencies were calculated by the B3LYP method at the 6-311++G** and aug-ccpVTZ levels. The Natural Bond Orbital (NBO)[12],AIM (atom in molecule)[13]and temperature effect were analyzed by optimized geometry at the B3LYP/6-311++G** level. The hydrogen-bonding interaction energy De(the difference between the energy of the complex and total energy of the most stable monomer) was calculated by methods of B3LYP/6-311++G**, B3LYP/aug-cc-pVTZ,MP2(full)/6-311++G** and CCSD(T)/6-311++G**. At the level of B3LYP/aug-cc-pVTZ, the theoretical model of Onsager self-consistent reaction field (SCRF)[14]is used to discover the solvation effect of the complex.All computations were finished by Gaussian 03 program package[15].

3 RESULTS AND DISCUSSION

3.1 Geometry and stability

The geometry, hydrogen bond lengths and atomic labels of hexamethylenetetramine, nitric acid and their complexes are shown in Fig. 1, and some structural parameters are listed in Table 1. Fig. 1 shows that the hexamethylenetetramine monomer exhibits Tdsymmetry, and nitric acid shows CSsymmetry,which tallied with the experimental results[16]. Seven kinds of stable complexes (NImag = 0) were all C1symmetry. The distance of intermolecular O··H was 0.264–0.310 nm, all in the scope of hydrogen bonds,indicating that it was possible to form hydrogen bonding between hexamethylenetetramine and nitric acid.

From Fig. 1 and Table 1, we can find that the bond length of O(23)–H(27) in complex (a) was elongated by 0.0080 nm at the B3LYP/aug-cc-pVTZ level. The distance of H(27)··N(3) was 0.158 nm,longer than the sum of N–H covalent radii but shorter than that of van der Waals radius. The bond angle of ∠O(23)H(27)N(3) was 172.8°, larger than 90°. All these results show the hydrogen bond of H(27)··N(3) formed in complex (a). The bond length of C(17)–H(19) in complex (b) was elongated by 0.0036 nm. The distance between H(19) and O(23) was 0.270 nm, longer than the sum of O–H covalent radii but shorter than that of van der Waals radius. The bond angle of ∠C(17)H(19)O(23) was 154.6°. This result also indicated the formation of O(23)··H(19) hydrogen bond in complex (b).Similarly, in complexes (c), (d), (e), (f) and (g), the bond lengths of C(17)–H(19) were significantly elongated, and the angles of ∠C(17)H(19)O(23)and the distances of H(19)··O(23)/(25)/(26) met the structural standard of hydrogen bond, indicating the possible formation of hydrogen bonds between them.According to Fig. 1, the hydrogen bonds formed by hexamethylenetetramine and nitric acid are divided into three kinds. The first one is the hydrogen bond between the hydrogen atom from the nitric acid and the nitrogen atom (see (a)), the second one is that between the hydroxyl oxygen from the nitric acid and the methylene hydrogen from the hexamethylenetetramine, mainly existing in complexes (b), (c)and (d), and the third one, existing in complexes (e),(f) and (g), is that between nitroxide from the nitric acid and the methylene hydrogen from the hexamethylenetetramine.

In general, the shorter the hydrogen bond length,the stronger the strength of hydrogen bond. The strengths of hydrogen bonds have the order in accordance with the distance order of hydrogen bonds in Fig. 1 as follows: (a)＞(e)＞(d)＞(b)＞(c)＞(f)＞(g).

What we were interested in was that in the complexes, the bond lengths of N(3)–C(17) adjacent to the methylene in the formation of hydrogen bonds were 0.1621–0.1641 nm, but those of N(3)–C(17)near the methylene not involved in forming hydrogen bonds were about 0.1477 nm (at B3LYP/augcc-pVTZ level), and the former ones are longer than the latter ones. Based on the theory that the weakest bonds are easy to break, in the chemical reaction, the N(3)–C(17) bonds adjacent to the methylene in the formation of hydrogen bonds were easy to break.The experimental facts illustrated that DPT was obtained in the reaction for preparing RDX and HMX by using nitric acid to resolve hexamethylenetetramine, which indicated that the bond in the hexamethylenetetramine was broken in the C–N bond where the nitrogen atom is attacked by NO2+[16].The prediction obtained from the structures of the complexes tallied with the experimental facts.

Fig. 1. Optimized geometries of the two monomers and six complexes at the B3LYP/aug-cc-pVTZ level

Table 1. Geometry Parameters of Complexes at the B3LYP/aug-cc-pVTZ Level (nm)

3.2 Frequency analysis

In the process of the formation of complexes with hydrogen bonds from monomers, the vibration frequency of some chemical bonds may be changed,which is defined as follows:

Δν = νcomplex– νmonomer

Generally, the greater change of frequency means the formed hydrogen bond is stronger. In order to determine the comparative stability of the title complex, we analyzed the frequencies of the complexes (see Table 2). Δν1and Δν2respectively represented the changes of stretching vibration and rocking vibration of O–H (for (a)) or C–H after the complexes were formed. According to Table 2, ν1became smaller (red shift), and ν2became larger(blue shift). And the change values have the following order (a)＞＞(e)＞(d)＞(b)＞(c)＞(g).Except (f), such order is direct opposite to the order of hydrogen bond lengths, further proving that the complexes may have the following stability order of(a)＞ (e)＞ (d)＞ (b)＞ (c)＞ (g). Δν3and Δν4respectively represented the changes of asymmetrical and symmetrical stretching vibration of -NO2after the complexes were formed. ν3became smaller,and ν4became larger. As for complexes (a)–(d),there were smaller changes in ν3and ν4(smaller than 2 cm–1), because -NO2did not participate in forming hydrogen bonds in these four complexes. As for complexes (e)–(g), the maximum and minimum values of Δν3and Δν4were found in (e) and (g),respectively, showing that (e) had the strongest stability and (g) had the weakest, which was in agreement with the results of structural analyses.

Table 2. Selected Frequency Shifts of Monomers in Complexes at the B3LYP/aug-cc-pVTZ Levela

3.3 Energy and stability

The total energies, intermolecular hydrogen-bonding interaction energies and interaction energies corrected by BSSE of the complexes calculated at four levels of B3LYP/6-311++G**, B3LYP/aug-ccpVTZ, MP2(full)/6-311++G** and CCSD(T)/6-311++G** are listed in Table 3, in which except for(a), the intermolecular hydrogen-bonding interaction energies obtained by the MP2(full)/6-311++G**method were larger than those by the other three methods, which was similar to the past study results[17].

According to Table 3, except for (f), the total energies of complexes obtained at four levels had the following order of (a)＜(e)＜(b)＜(c)＜(d)＜(g),indicating the stability of complexes had the order of(a)＞(e)＞(b)＞(c)＞(d)＞(g). At the CCSD(T)/6-311++G** level, the interaction energies of complexes (a)–(g) after being corrected by BSSE were 63.13, 8.23, 8.35, 6.24, 13.98, 4.99 and 2.97 kJ/mol,respectively. It was found by Fang G. Y. et al. after study that in the complexes formed by 3-nitro-1,2,4-triazol-5-one and H2O, the hydrogen bond formed between nitroxide atom and hydrogen was the weakest one, having energy of 34.66 kJ/mol after BSSE correction[18]. At four levels, the intermolecular interaction energies of the complexes had the following order of (a)＞＞(e)＞(b)＞(c)＞(d)＞(f)＞(g). Except for (d), such order was the same to the structural analysis results. Therefore, it indicated that(a) had the highest stability and biggest hydrogenbonding strength and thus it was the main complex formed by hexamethylenetetramine and nitric acid.As the hydrogen bonds were formed by the hydrogen atoms from nitric acid and the nitrogen atoms from hexamethylenetetramine in complex (a),it could be predicted that the starting step of the reaction might be that hydrogen atoms from nitric acid approached the nitrogen atoms from hexamethylenetetramine.

According to the literature data[19], the hydrogenbonding energy and BSSE correction energy were in the same order of magnitude, with relative error between 10% and 40%; therefore it was necessary to make BSSE correction to the interaction energies of complexes. It was found in Table 3 that in the four methods of B3LYP/6-311++G**, B3LYP/aug-ccpVTZ, MP2(full)/6-311++G** and CCSD(T)/6-311++G**, the maximum proportions of the interaction BSSE correction energies of complexes to non-corrected energies reached 20.70%, 48.48%,56.80% and 50.42%, respectively, showing that for the interaction of hydrogen bond, BSSE correction could not be ignored, which was consistent with our previous study results[20].

Table 3. Total Energies (Etotal(a.u.)) and Binding Energies (–De (kJ/mol))

3.4 NBO analysis

In recent years, NBO analysis method has been extensively applied in the study on discovering the nature of hydrogen bond. Stabilization energy E(2)can give a quantitative description on the strength of electron donor/acceptor interaction: the higher E(2)is,the stronger interaction E(2)between electron donor orbital i and acceptor orbital j will be, and conesquently, the electron delocalization degree seems larger[12]. In order to further demonstrate the nature of the hydrogen-bonding formation, we had made NBO analysis on the complexes, and listed part of the analysis results in Table 4.

Judging from Table 4, we can find that the hydroxyl oxygen and nitroxide from the nitric acid mainly exhibited sp0.66and p1.00hybrid, respectively,and the nitrogen atoms from hexamethylenetetramine mainly exhibited sp4.16hybrid. For (a), the essence of intermolecular hydrogen-bond interaction was mainly sp4.16hybrid electrons of nitrogen atoms from hexamethylenetetramine transferred to the σ(O(23)–H(27))*anti-orbitals. For (b), (c) and (d), their essence was mainly sp0.66hybrid electrons of hydroxyl oxygen transferred to the σ(C(17)–H(19))*anti-orbitals. But for (e), (f) and (g), their essence was mainly the lone pair electrons of nitroxide transferred to the σ(C(17)–H(19))*anti-orbitals. For (a),the interorbital interaction energy E(2)reached 208.22 kJ/mol; however, in the rest six complexes,the E(2)did not exceed 12 kJ/mol. From Table 4, we can also find that for complexes (a) and (d), the molecules of nitric acid had negative electric charges,indicating that in the process of forming complexes(a) and (d), the electrons were transferred from hexamethylenetetramine to the nitric acid. And the other complexes had positive electric charges, which indicated that the electrons were transferred from nitric acid to hexamethylenetetramine in their formation process. The maximum values of both interorbital interaction energy E(2)and electron transfer were found in complex (a), which suggested that complex (a) had the strongest intermolecular hydrogen-bonding interaction, so it was the most stable,which was consistent with the above analysis results.

Table 4. Parts of the Calculated NBO Results of Complexes at the B3LYP/6-311++G** Level

3.5 AIM analysis

As proposed by Bader[13], the existence of bond saddle point suggests the bonding interaction between two atoms, and the topology size of the bond saddle point is closely relative to the nature of the chemical bonds. Generally, the larger ρ is, the stronger the interaction will be; in reverse, it is weaker. ρ was in the range of 0.002–0.04 a.u, and▽2ρ＞0, which was the sign of the formation of weak intermolecular interaction[13]. If ▽2ρ＜0,there are dense charges at the critical point, and the covalence of chemical bond is greater if it is a larger negative value.

Electron density ρ(r) and the corresponding Laplacian ▽2ρ at each bond saddle points of six complexes calculated at the aug-cc-pVTZ level with B3LYP method are listed in Table 5. As shown in Table 5, the electron density ρ value at the bond saddle point between H(27) and N(3) of complex (a)was 0.0189 a.u, and that at the bond saddle point between H(19) and O(23)/(25)/(26) of the rest six complexes fell in the range of 0.0051–0.0160 a.u,and the ▽2ρ are all positive values, indicating that the complex system is under the closed shell interaction. All these characteristics also illustrated the presence of intermolecular hydrogen bonds. The order of ρBCPwas (a)＞(e)＞(d)＞(b)＞(c)＞(f)＞(g);except for (d), such order was consistent with that of hydrogen bonding energy.

Besides, we also find that the ρBCP(N(3)–C(17))of N(3)–C(17) adjacent to the methylene involving hydrogen bonds was smaller than the ρBCP(N(7)–C(13))of C–N bond close to the methylene not involved in hydrogen bonds. It indicated the strength of C–N bond in the former one was weaker than that of the latter, which tallied with the results of structural analysis. And it also illustrated that in the chemical reaction the C–N bond near the methylene involving hydrogen bonds was easy to break.

Table 5. Selected Bond Critical Point Properties (in a.u.) at the B3LYP/aug-cc-pVTZ Level

3.6 Temperature effects

According to the calculation methods of Xiao H.M et al.[18], we had given the thermodynamic properties of complexes formed by hexamethylenetetramine and nitric acid at different temperature,including heat capacity, heat capacity at constant pressure, standard entropy and standard enthalpy of monomers and changes of standard entropy, enthalpy and Gibbs’ energy for the formation of complexes by hexamethylenetetramine and nitric acid(see Table 6). According to this table, except for the circumstance of (a) at low temperature, the process of hydrogen bond formation was an exothermic reaction. And with the increase of temperature, the standard entropy, heat capacity at constant pressure and enthalpy change all increased, indicating that the heat release in the reaction became stronger and stronger with the increase of temperature. Therefore,with consideration of the safety in explosive synthesis, it was best to prepare it at low temperature.Judging from the table, we can also see that Gibbs’free energy is positive, so it was not easy to have a spontaneous formation of stable complexes by hexamethylenetetramine and nitric acid at ambient temperature, which was consistent with the experimental results. The Gibbs’ free energy increased with the rise of temperature, showing the weakening of spontaneous formation of the complexes. In fact,the chemical reaction was also influenced by dynamics, i.e. the reaction speed will accelerate as the temperature increases.

3.7 Solvation effect

As the preparation of RDX and HMX by hexamethylenetetramine and nitric acid is always made in the concentrated nitric acid solution and concentrated sulphurinc acid solution, and the permittivity of nitric acid and sulphurinc acid is 50.0 and 84.5,respectively[21], the theoretical model of Onsager Self-Consistent Reaction Field (SCRF)[20]is utilized to study the intermolecular interaction with electric constants in the range of 50.0–85.0 in this paper (see Fig. 2).

As shown in Fig. 2, except for (a), the interaction energies of all complexes increased with the rise of permittivity, which indicated that in order to obtain stable complex (a) with OˉH···N hydrogen bond(first kind), the solvent with smaller permittivity shall be selected; for complexes with CˉH···OˉH(the second kind) or OˉH···OˉN (the third kind)hydrogen bond, however, the permittivity of the solvent shall be increased. It is worth noting that the factors that affect intermolecular interactions are more complicated, especially the temperature which has significant impact, so we have to consider it comprehensively in the specific experiments.

Table 6. Thermodynamics Parameters at the B3LYP/6-311++G**a Level

To be continued

Fig. 2. Intermolecular interaction as a function of dielectric constant

4 CONCLUSION

A stable complex with hydrogen bond can be formed by hexamethylenetetramine and nitric acid molecules. The order of interaction energies are as follows: (a)＞＞(e)＞(b)＞(c)＞(d)＞(f)＞(g). As the process to form hydrogen bonds is an exothermic reaction, it is helpful to the formation of hydrogen bonds at low temperature. So it can be predicted that in the chemical reaction the C–N bond adjacent to the methylene involving the hydrogen-bonds is easy to break.

(1) Desiraju, G. R.; Steiner, T. The Weak Hydrogen Bond in Structural Chemistry and Biology. International Union of Crystallography, Oxford University Press, Oxford 2001.

(2) Mons, M.; Dimicoli, L.; Tardivel, B.; Piuzzi, F.; Brenner, V.; Millié, P. Site dependence of the binding energy of water to indole: microscopic approach to the side chain hydration of tryptophan. J. Phys. Chem. A 1999, 103, 9958ˉ9965.

(3) Guo, F.; Guo, W. S.; Toda, F. Supramolecular stereoisomer – the conformational isomer of 1,1,6,6-tetraphenylhexa-2,4-diyne-1,6-diol in the different inclusion compounds. Cryst. Eng. Comm. 2003, 5, 45ˉ47.

(4) Guo, W. S.; Guo, F.; Xu, H. N.; Yuan, L.; Wang, Z. H.; Tong, J. Host channel framework determined by C–H··π interaction in the inclusion crystal of 2,5-bis(diphenylmethyl)hydroquinone and benzaldehyde. J. Mol. Struct. 2005, 733, 143ˉ149.

(5) Evans, D. J.; Juck, P. C.; Smith, M. K. Intramolecular C–H··π interactions influence the conformation of N,N?-dibenzyl-4,13-diaza-18-crown-6 molecules. New J. Chem. 2002, 26, 1043ˉ1048.

(6) Wang, G. X.; Gong, X. D.; Xiao, H. M. A theoretical investigation on pyrolysis mechanism and impact sensitivity of nitro derivatives of benzene and aminobenzenes. Acta Chim. Sinica 2008, 66, 711ˉ716.

(7) Xu, X. J.; Xiao, H. M.; Gong, X. D.; Ju, X. H. Computational studies on the nitration of adamantane with NO2. Acta Chim. Sinica 2006, 64,306ˉ312.

(8) Chen, T. N.; Tang, Y. P.; Song, H. J. Theoretical study on intermolecular interaction of furoxan dimers. Chin. J. Energ. Mater. 2007, 15, 641ˉ645.

(9) Ammal, S. S. C.; Venuvanalingam, P. π-systems as lithium/hydrogen bond acceptors: some theoretical observations. J. Chem. Phys. 1998, 109,9820ˉ9830.

(10) Tsuzuki, S.; Uchimaru, T.; Matsumura, K.; Mikami, M.; Tanabe, K. Effects of the higher electron correlation correction on the calculated intermolecular interaction energies of benzene and naphthalene dimers: comparison between MP2 and CCSD(T) calculations. Chem. Phys. Lett. 2000,319, 547ˉ554.

(11) Lv, C. X. Nitrate Theory. Jiangsu Science and Technology Press, Jiangsu 1993.

(12) Reed, A. E.; Curtis, L. A.; Weinhold, F. A. Intermolecular interactions from a natural bond orbital, donor-acceptor viewpoint. Chem. Rev. 1988, 88,899ˉ926.

(13) Bader, R. F. W. Atoms in Molecules, A Quantum Theory. Oxford University Press, New York 1990.

(14) Tapia, O.; Goseinski, O. Self-consistent reaction field theory of solvent effects. Mol. Phys. 1975, 29, 1653ˉ1661.

(15) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B. Gaussian 03, Revision E.01, Gaussian, Inc., Pittsburgh PA 2003.

(16) Yi, W. B.; Cai, C. Synthesis of RDX by nitrolysis of hexamethylenetetramine in fluorous media. J. Hazard. Mater. 2008, 150, 839ˉ842.

(17) Li, R. Y.; Li, Z. R.; Wu, D.; Li, Y.; Chen, W.; Sun, C. C. Study of π halogen bonds in complexes C2H(4-n)Fn-ClF (n = 0ˉ2). J. Phys. Chem. A 2005,109, 2608ˉ2613.

(18) Fang, G. Y.; Xu, L. N.; Xiao, H. M.; Ju, X. H. Theoretical study on intermolecular interactions of 3-nitro-1,2,4-triazol-5-one with NH3and H2O. Acta Chim. Sinica 2005, 63, 1055ˉ1061 (in Chinese).

(19) Lu, Y. L.; Xiao, H. M.; Gong, X. D.; Ju, X. H. Density functional theory study on intermolecular interactions of 1H-ANTA dimer. Acta Chim. Sinica 2006, 64, 1954ˉ1960 (in Chinese).

(20) Ren, F. D.; Cao, D. L.; Wang, W. L.; Wang, J. L.; Li, Y. X.; Hu, Z. Y.; Chen, S. S. Can B≡B triple bond be as potential proton acceptor: An ab initio study on unusual intermolecular T-shaped X–H··π interactions between OCB≡BCO and HF, HCl, HCN or H2C2. Chem. Phys. Lett. 2008, 455,32ˉ37.

(21) Dean, J. A. Lange’s Handbook of Chemistry. 13th Edition. Beijing: Science press 1991, 6, 31ˉ32.