Charge density studies of energetic material: RDX

Experimental charge density study has been carried out for Cyclotrimethylenetrinitramine (space group Pbca), an explosive material from a low temperature X-ray diffraction experiment. The electron density was modeled using the Hansen-Coppens multipole model and refined to R=0.032 for 6226 unique observed reflections. The electron density, laplacian and electrostatic potential distributions are reported and discussed, especially, the properties of the bond (3,-1) critical points, which are thought to play a key role in the decomposition of the molecule. From the bond topological analysis of all the bonds, it is observed that the N–N bond is the weakest. The dominating nature of the oxygen atoms was clearly well understood from isosurface electrostatic potential of isolated and symmetrically sitting molecules in the crystal.


Introduction
Explosives, the energetic material, that was unstable either chemically or energetically and upon initiation, it produces a sudden expansion accompanied by the production of heat and large changes in pressure [1]. From the time of discovery of gun powder [2][3][4] to modern day explosives, the energetic materials has been of great practical importance. Their contributions in mining, road building and in missile propulsion system were accounted as its significant peaceful uses. Since, the performance of the explosives completely resides on the structural modeling including stable molecular confirmation, inter-intra molecular interactions and thermal vibrational parameters, it is important to understand various electronic and chemical properties at the molecular level [5]. As the conventional single crystal structure determination fails to interpret the chemical bonding nature of the molecules at electronic level, an extensive high resolution diffraction data was required to explicit the charge density distribution in the bonding region of the molecules. The series of charge density studies on propellants and explosives eg. 5-nitro-2,4-dihyro-3H-1,2,4-triazol-3-one (NTO) [6], two biguanidinium dinitramides [7], pentaerythritol tetranitrate [8], 1,3,4-trinitro-7,8-diazapentalene [9], 3,5,9,11-tetraacetyl-14-oxo-1,3,5,7,9,11-hexaazapenta-cyclo- [5.5.3.02,6.04,10.08, 12] pentadecane (CL-20) [10], 1,1diamino-2,2-dinitro ethylene (FOX-7) [10], were carried out and in these studies, the insights of electron density distribution of these molecules were summarized using high resolution experimental diffraction data. As sustain of this series, in this work, we investigate the energetic material RDX (Cyclotrimethylene-trinitramine) from X-ray diffraction experiment. The conventional methods of structural studies on RDX were carried and structure was first determined by C.S. Choi et al [11], reported the geometry of the molecule at room temperature.
Here, we do the experimental electron density investigation based on high resolution X-ray diffraction data obtained at low temperature. Using Hansen-Coppens formalism [12], the data were evaluated with a multipole refinement, in which individual atomic densities are described in terms of spherical core and valence densities together with an expression of atom-centered spherical harmonic function.
where ρc and ρv are the spherical core and valence densities, respectively, and the summation in the third term accounts for the valence deformation. Pv is the valance population parameter, which gives the estimate of the net atomic charge. Rnl = r nl exp(ζ-r) is a radial Slater-type function and the coefficients κ and '  describe the contraction-expansion for the spherical and multipolar valence densities respectively. Pl m is the multipole populations and Yl m± are the real spherical harmonics of order l. Hence the charge density is the exposing tool of the molecular structure at the electronic level, using theory of atoms in molecules [13], which allows extracting the topology of electron density and electrostatic properties of the molecules.
0.4 mm, possessing good morphology was selected for high resolution X-ray intensity data collection. The data collections were carried out using Bruker-Nonius Kappa CCD Area detector system [14]. As a feasible study for charge density analysis, a room temperature data has been collected priory at an X-ray wavelength of 0.71073 Å. For charge density, the sample was cooled to 110 K using stream of cold nitrogen gas. A whole set of X-ray intensity data has been collected up to the resolution (sinθ/λ)max = 1.2 Å -1 , of which only the data resolution range of 1.08 Å -1 , with maximum 2θ value 111.0˚ for the scan width 0.3˚, were taken for crystal structure determination and electron density analysis. All these raw data sets were reduced for Lorentz and Polarization correction using SAINT program [15].

Spherical and Aspherical model refinement
The structure was solved by Direct methods using SHELXS97 [16] and refined by means of full-matrix least squares procedure using SHELXL97 [17]. All the H-atoms were located using difference fourier map, and these parameters were refined isotropically. The Multipole model charge density refinement was performed with XDLSM routine incorporated to XD [18] program suite. The multipole refinement was carried out on |F 2 | using only reflections with I > 3(I). As a first step, the scale factor is refined using the whole data set and keeping the scale factor fixed, the positional and anisotropic displacement parameters for the non-H atoms were refined using high angle data (sin/ > 0.8 Å -1 ). At this point, all H atom positions were adjusted to neutron distance values [19] [C-H: 1.092 Å]. Since the molecule consists of the same functional groups with identical local chemical environments, the chemical constraints were used extensively in the multipole refinement. The multipole populations of all oxygen atoms of nitrate groups were constrained to O1, those of nitrogen atoms of same to N4, those of N2 and N3 to N1, those of C2, and C3 to C1 and those of all hydrogen atoms to H1. The monopole population, κ, multipole populations and scale were refined with the constraints. At this point, the κ values for H atoms were fixed to theoretical values [20] at 1.2. The charge neutrality was applied throught the refinement. The whole process was repeated until convergence. Using the same chemical constraints, the monopole populations with κ were refined together, followed by the multipole populations, followed by the positional and displacement parameters, followed by the scale factor alone. At this point, reported κ' values [20] were fixed for the all non-H atoms and then refined in the subsequent cycles. In the final refinement the group of parameters Pv, κ, κ', s and Pl m, x, y, z respectively were refined separately until all the parameters were converge. The final residual values of multipole refinements details were given in Table 1. Figure 2 presents the residual map after the multipole refinement in the molecular plane, confirms the correctness of the modeling. The total electron density ρbcp(r), Laplacian  2 ρbcp(r), the bond, ellipticity ε at the bond critical points (BCP's) and eigen values (λ1, λ2, λ3) were calculated by using XDPROP routine. The deformation density Δρ and Laplacian electron density  2 ρ maps were plotted using XDGRAPH routine incorporated to XD program suite.

Structural Aspects
The ORTEP [21] plot of RDX molecule was depicted in Figure 3 showing the thermal ellipsoid atoms and the atom numbering scheme. The parallel bond distances in the six membered ring were almost equal with the maximum difference of 0.006(1) Å for C3-N3 [1.494(1) Å] and C2-N1[1.500(1) Å] bonds respectively. The trend was found to be similar in the reported 11 distances at room temperature, with the maximum difference of 0.008(4) Å for the same bonds. The C-N bond distances were ranges from 1.433(1) to 1.529(1) Å with the average distance 1.486(1) Å, which was 0.032 Å longer than that of reported C-N bonds. The N3-N6 bond distance [1.286(1) Å] was ~0.115(1) Å shorter than the other two parallel N-N bonds N2-N5 [1.419(1) Å] and N1-N4 [1.383(1) Å], while C.S. Choi et al reported that the decrement of N3-N6 bond distance from that of parallel N-N bonds by ~0.044 Å. This unique orientation of N3-N6 bond may be attributed from the effect of repulsive non-bonded interactions between adjacent nitro groups. The average N=O distance of unique nitrate group was ~1.284(1) Å, which was 0.070(1) Å longer than that of parallel nitrate groups [~1.214(1) Å], the similar trend appears in reported values. The average C-H bond distances from both low temperature and reported room temperature experiments were ~1.092(1) and ~1.080(8) Å respectively. On the whole it was found that the bond distances from the low temperature measurement were longer than that of reported room temperature measurement. The parallel nature of C1-N1 and C3-N2 bonds was reflected from the identical angles at N1 and N2 of the bonds C2-N1-C1 were found to be widen on compared with angles around N3, which makes N3-N6 bond flatter compared with other parallel N-N bonds. The angle at N6 atom [130.7(3)˚] in -NO2 group was significantly larger than at N4 and N5 of other two -NO2 groups and the angles were 126.6(4) and 124.0(4)˚ respectively. The six membered ring of RDX molecule was not planar, but adopts the chair confirmation which reveals from the gauche orientation of C1-N1 and C3-N2, bonds from the torsion angles -46.0 (4) The molecules in the unit cell were predominantly stabilized by C-H···O type of hydrogen bonding interaction. Figure 4 shows the dominant nature of O-atoms in the crystal packing having the density of 1.857 mg/m 3 calculated from cell parameter.

Electron density
The topological analysis of the electron density has been performed for RDX molecule. The electron density of all the bonds with (3,-1) critical points which characterize the covalent bonds in RDX crystal were given in Table 2. The bond density ρbcp(r) at C-N bonds in the six membered ring ranges from 1.62(3) to 1.86(1) eÅ -3 , with the maximum ρbcp(r) of 1.86(1) and 1.85(1) eÅ -3 for the parallel bonds C1-N1 and C3-N2 respectively. This parallel heteronuclear bonds, which forms the mean plane, exhibits the maximum polarizability of about ~8.0% towards the carbon atoms due to the perturbations caused by other C-N bonds lies above and below mean plane atoms. The maximum deviation of BCP from the internulear axis was found for C2-N2 bond [0.042 Å] among the other bonds in the molecule. The N-N bonds appear to be of particular interest. All the N-N bonds in the RDX molecule were carrying markedly different densities, among these the N3-N6 bond density at bond critical point was 2.56(1) eÅ -3 , which was much higher than that of other N-N bonds, N1-N4 [2.22(1) eÅ -3 ] and N2-N5 [2.07(1) eÅ -3 ] respectively, however, the large electron density values ranges 1.98 to 2.31 eÅ -3 at bond critical point on N-N bonds was found for the explosive CL-20 10 . The electron density at the critical points on the N=O bonds were ranges 2.99 to 3.49 eÅ -3 , which were the highest electron density values in RDX molecule and thus was the best candidate for the bond to be considered as a double bond. The large charge accumulation was found for N5-O3  Figure 5(a-c) shows the deformation density of N-NO2 groups in the RDX molecule. The average electron density in C-H bond regions of the six membered ring was ~1.83 eÅ -3 , with the polarity values close to 17.5% towards hydrogen.

Bond Topological Analysis
Bond topological analysis [22] was clearly predicted from Laplacian of charge distribution  2 ρbcp(r) at the bond critical points. As expected, the parallel bonds C1-N1 and C3-N2, having high electron density values, exhibit the most negative Laplacian -16.3(1) and -16.1(1) eÅ -5 attributes the maximum depletion of charges among the C-N bonds of the molecule at the bond critical points. The Laplacian of electron density in the plane of three nitro groups were shown in figure 6(a-c). The solid contours show the negative value of the laplacian i.e. they represent the accumulation of electron density in the crystal. For the RDX molecule, this accumulation was mostly around the atoms and along the chemical bonds. For the oxygen atoms, the electron density concentrates mainly in the non-bonding directions, which emphasize the lone pair region. The  2 ρbcp(r) values for N=O bonds ranges -5.5(1) eÅ -5 to -14.9(1) eÅ -5 . Notably, the N6-O5 and N6-O6 bonds possess maximum electron density, has less Laplacian of -5.5(1) and -7.4(1) eÅ -5 at its critical points on compare with other N-O bonds. The topological analysis in p-nitroaniline [23], lithium bis(tetramethylammonium) hexanitro-cobaltate(III) [24] and transtetra-aminedinitronickel(II) [25]  , indicating that the charge depletion in the bond direction was significantly higher than that of the other bonds. The same feature was also observed in trinitrodiazapentalene (TNDP) [9]. As per above results, it was found that the N-N bonds should be weak, in particular N1-N4 and N2-N5 be the first to break during the chemical decomposition. The ellipticities were smaller for the ring bonds C-N [~0.09] than for N-N [~0.23] and N=O [~0.12] bonds. These values were similar to those observed in CL-20.

Atomic Charges and Electrostatic Potential
The atomic charges were calculated from the monopole population (Pv) of the final refinement, (i.e) q = N -Pv, where N is the number of valence electrons for the neutral atoms [26]. Further, the AIM charges [27,28] were also calculated for all atoms from the charge integration of electron density distribution (EDD) within the atomic basin using TOPXD [23] routine incorporated to XD program. These results were summarized in Table 3. Both the definition agrees on the broad picture of positive nitrogen and negative oxygen atoms of nitrate groups, though the actual values vary significantly within this. The monopole charges of the carbon atoms in the six membered ring are highly negative [-0.27(1) e], reflecting the fact that it attracts the large amount of electron density from its two hydrogen atoms. However, the CH2 moiety remains positive when the hydrogen atomic charges are included [CH2: +0.15 e]. On the other hand, the AIM charges of the carbon atoms are highly positive [+0.24 e], due to electronegative nitrogen atoms [-0.50 e] bonded to these carbon atoms, though have almost equal actual values as their monopole charges. The monopole charges for -NO2 fragments attached at N1, N2 and N3 atoms, having the monopole charges of 0.07(1) e, are -0.22(1) e which attributes the hyperconjugation effect and make the N-NO2 bonds be highly polarized. This confirms the weakness of N-N bonds in the RDX molecule. The monopole and AIM charges of H-atoms were nearly equal and they were closed to 0.20 e.
The molecular electrostatic potential (MEP) was calculated from the multipole refinement, having the ability to derive MEP for the isolated molecule in the crystalline environment. Further it also helps to evaluate the Murray et al's [29] hypothesis that a key factor in determining the impact sensitivity of the compound may be extent to which the stabilizing the effect of charge delocalization has been concentrated. The calculated MEP, according to the method by su and coppens [30], were visualized in XDGRAPH and displayed in figure 7(a). As expected, the negative regions (red) around oxygen atoms of the three nitro groups and positive (blue) resides on the rest of the molecule were observed. These potentials represent the sites of electrophilic and electrophobic attacks. The shape of the electronegative surface over the oxygen atoms was interesting, as it shows the slight difference between O(5), which is involved in intermolecular hydrogen bond, and remaining oxygen atoms. The hydrogen bond interaction deconvolutes the electronegative character of O(5) and preventing it from attracting the external positive charge. Since the nitro groups and CH2 groups pointing in the opposite directions, the either side of the ring exhibit complementary electrostatic potential regions. This was in accord with the large molecular dipole moment 6.8(2) Debye, which indicates the large separation of positive and negative charges. The polarization of N-NO2 bonds was clearly exhibited from positive and negative potential around N and -NO2 regions, which again reveals the weakness of N-N bonds. The shape of ESP between two symmetrically sitting molecules in the crystal field environment was shown in the figure 7(b). . Isosurface representation of Electrostatic potential of (a) isolated molecule and (b) symmetrically sitting two molecules in the crystal. Blue (+0.5 eÅ -1 ) and red (-0.2 eÅ -1 ) regions are positive and negative ESP respectively. Grey grid indicate the zero ESP.

Conclusion
The geometrical and bond topological properties of RDX molecule were determined from low temperature X-ray diffraction data. The significant differences were observed in bond distances when compared with that obtained from reported room temperature measurement. The bond topological analysis has been carried out from multipole refinement. From the position of the critical points, significant polarization of C-N and C-H bonds may be concluded, however the N-O and N-N bonds were less polarized. The present results obtained from bond topological analysis reveals the strength of the entire bonds in the molecule. Among all other bonds in the RDX molecule, the N-N bonds were found to be weak, which was predicted from small negative Laplacian values. Specifically, N3-N6 bonds, having shorter bond length, has large charge accumulation and concentrated charges [-4.4(1) eÅ -5 ] at the bond critical point. On the other hand, the longer N1-N4 and N2-N5 bonds has low electron density and the charges were depleted, as their  2 ρbcp(r) values were -1.8(1) and -0.4(1) eÅ -5 respectively. Based on these results, it was cleared that the bond properties of N-N bonds strongly depends upon the equilibrium bond length. It is concluded from the above results, on decomposition, the N-N bonds were expected to break first. The molecular electrostatic potential of the RDX molecule clearly indicates the possible reactive surface in the molecule from electro positive and electro negative regions. In particular, the high negative electro potential resides on one face of the molecule and