Experimental Charge-Density Study of the Intra- and Intermolecular

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Experimental Charge-Density Study of the Intra- and Intermolecular Bonding in TKX-50 Jeremiah P Tidey, Vladimir V Zhurov, Christopher G Gianopoulos, Elizabeth A Zhurova, and A. Alan Pinkerton J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b09367 • Publication Date (Web): 31 Oct 2017 Downloaded from http://pubs.acs.org on November 2, 2017

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The Journal of Physical Chemistry

Experimental Charge-Density Study of the Intra- and Intermolecular Bonding in TKX-50. Jeremiah P. Tidey, Vladimir V. Zhurov, Christopher G. Gianopoulos, Elizabeth A. Zhurova, A. Alan Pinkerton*

* [email protected]; University of Toledo, 2801 West Bancroft Street, Toledo, Ohio, 43606

Abstract The intra- and intermolecular bonding in the known phase of dihydroxylammonium 5,5'-bistetrazole1,1'-diolate, TKX-50, has been analyzed based on the experimentally determined charge density distribution from high resolution X-ray diffraction data obtained at 20 K. This was compared to the charge density obtained from DFT calculations with periodic boundary conditions using both direct calculations and derived structure factors. Results of topological analysis of the electron density corroborate that TKX-50 is best described as a layered structure linked primarily by a number of hydrogen bonds as well as by a variety of other interactions. Additional bonding interactions were identified, including a pair of equivalent 1,5-type intramolecular closed-shell interactions in the dianion. Refinement of anharmonic motion was shown to be essential for obtaining an adequate model, despite the low temperature of the study. Although generally unusual, the implementation of anharmonic refinement provided a significant improvement compared to harmonic refinement of both traditional and split-core multipole models.

Introduction The ongoing efforts to obtain thermally and mechanically insensitive CHON-based energetic materials (EMs) has resulted in an increasing focus on energetic ionic salts (EISs). Ye and Koshi predicted that the inclusion of hydrogen bonding motifs, as well as double bonds or cage structures, would decrease the sensitivity of EMs.1 In addition, it has been shown that the formation of strong hydrogen bonded motifs generally results in more dense EMs.2 In the context of CHON-based EMs, the focus on EISs is well rationalized as the inclusion of conjugation and hydrogen-bond donors in such materials is common. There is currently significant focus on the EIS dihydroxylammonium 5,5'-bistetrazole-1,1'-diolate, TKX-50 (Fig. 1). Following the initial report in 2012,3 the alleged high stability and competitive performance of this compound has been well investigated,4-6 with some controversy surrounding claims of its superiority over conventional CHON-based EMs.7 TKX-50 certainly shows exceptional mechanical stability, attributed to a number of factors seen in various studies.8-10 One such factor is face-to-face π···π stacking which has been shown to decrease the formation of hotspots believed to play an important role in mechanically driven initiation.11-13 Additionally, the existence of layered motifs involving strong intraand weaker interlayer bonding interactions have been shown to aid dissipation of mechanical energy

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through interlayer sliding.12-15 However, while the hydrogen bonding in TKX-50 certainly helps to engender high mechanical stability, it is also predicted to decrease the thermal stability of the system.16 It has been established by theory that proton transfer from cation to anion in TKX-50 reduces the barrier to decomposition and likely presents an initiation step.17-18 The inclusion of numerous and strong

hydrogen bonds predisposes the system to such a process.

Figure 1 a) Ball-and-stick image of the packing motif in TKX-50, projected onto the plane perpendicular to the c axis, comprising layers formed perpendicular to the b axis; layer motif highlighted with black box. b) Image depicting the formula unit of TKX-50 as found in the experiment: the asymmetric unit is labeled in accordance with the text and thermal ellipsoids are drawn at the 90% probability level; O−H···O hydrogen bonds are highlighted with black lines. O atoms are colored red, N blue, C dark grey and H atoms light grey/white. Anharmonic motion is expected to be negligible at 20 K and is regularly disregarded even at 120 K, though this may not be entirely appropriate.19 In a previous study, we reported the significant development of anharmonic motion in the impact-sensitive nitramine energetic material, RDX, at 120 K. In contrast, the less sensitive nitramine EM, HMX, was found to lack significant anharmonicity at this temperature. Since that report, significant anharmonicity has been reported as low as 15 K,20 and in the case of the highly insensitive EM TATB, it was found that the refinement of anharmonic terms served a benefit to the fit to the data measured at 20 K.21 Limited topological analysis of the electron density (ED) distribution in TKX-50 has been previously reported from theory,2 but not correlated with direct experimental measurements. We report the experimental determination of the ED distribution using high-resolution X-ray diffraction data, supported by a corresponding model obtained from theoretically generated structure factors and also by results derived directly from theory.

Experimental TKX-50 was used as received from Prof. T. Klapötke. A colorless single crystal of dimensions 0.38 × 0.29 × 0.22 mm was mounted using a mixture of Parabar 10312 and mineral oil (1:1 v/v) on a glass capillary


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[internal diameter =0.1 mm] and cooled to 20.0(1) K using an open-flow helium cryostat.22-23 The X-ray diffraction data were collected on a Rigaku R-axis RAPID-II diffractometer equipped with a Mo Kα rotating anode, SHINE graphite monochromator, UltraX-18 generator operating at 50 kV and 300 mA, and a cylindrical image plate detector. To obtain sufficiently redundant data, runs collecting 30 × 6 ° ωscans commencing at ω = 20 ° with an exposure time of 90 s were performed at χ = 0 °, φ = 0 and 180 °, and at χ = 40 °, φ = 0, 90, 180 and 270 °. These were complemented by runs collecting 29 × 6 ° ω-scans beginning at ω = 23 ° for the aforementioned positions in χ and φ. Thus, frames were overlapped by a half frame width, i.e., by 3 °, to improve scaling and allow for the omission of partial and overlapping reflections. Data were indexed and the unit cell refined using the HKL2000 software suit.24 Data were then integrated with the program VIIPP with background and reflection profiles averaged over the full dataset as previously described.25-27 A floodfield correction was applied and partial and overlapped reflections were rejected during the integration process. The effects of absorption [μ = 0.175 mm−1] and thermal diffuse scattering were considered negligible. Data were merged and scaled using SORTAV28-30 in monoclinic space group P21/c with a subsequent correction for λ/2 contamination.31-32 Outliers were flagged both using SORTAV and further manually through equivalence comparison to minimize contamination by multiple scattering and to exclude partial reflections not otherwise rejected by the software. This amounted to 3.0% of the observed, symmetry-allowed reflections and the resulting dataset comprised a total of 72,294 observations yielding 7,716 unique data. The final, merged dataset included 7,072 unique data with I/σ(I) > 3. The structure was solved and a spherical-atom model obtained using the SHELXTL program suit.33 All atomic positions were determined from difference Fourier peaks. At this stage, thermal motion was considered to be isotropic for hydrogen atoms and anisotropic for all others. The resulting model formed the starting point for refinement of the ED using the Hansen-Coppens multipole formalism34 as implemented in XD2006.35 This allows for modification of spherical pseudo-atoms to model the valence ED using atom-centered multipole functions: = + +

± ± /

Where Pc and Pv are core and valence populations, respectively; Rl are normalized Slater-type radial functions; Plm± are the mth multipole populations of order l; ylm± are real angular spherical harmonics of order m, l; and κs and κl are coefficients describing the expansion/contraction of the spherical and multipolar valence density, respectively. The standard description given presumes an unperturbed, spherical core. This can, however, be replaced by treatment akin to that of the valence part.36 Refinement was performed against F over all merged data with I/σ(I)>3 and using the VM databank.35 The molecular electroneutrality constraint was applied throughout. All multipoles were refined up to and including the hexadecapole level for non-H atoms and up to and including the quadrupole level for hydrogen atoms. Initial X−H bond lengths were constrained to neutron-diffraction averages while Uiso were freely refined for H atoms at this stage. Anharmonic refinement of thermal parameters proceeded



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with inclusion of all third and fourth order terms of the Gram-Charlier expansion for all non-hydrogen atoms.37 A total of seven sets of expansion-contraction coefficients (κs, κ1, κ2, κ3 and κ4) were used to describe the non-hydrogen atoms, with one set per unique atom site excepting N(2) and N(3) for which one common set sufficed. At this stage of the refinement, κ1-4 were constrained to be equal within each set. One κ set was used to describe all H atoms for which all κ were fixed to equal 1.2. Starting from this model, X−H bond lengths were calculated by geometry optimization of only hydrogen atom positions in CRYSTAL0938-39 as described below, and initial hydrogen anisotropic displacement parameters (ADPs) were estimated using the SHADE2 algorithm.40 X−H bond lengths and hydrogen atom ADPs were then refined with use of the rigid bond constraint implemented in XDLSM and κ1-4 were allowed to refine freely for all non-hydrogen κ sets. The result of this multipole refinement (MPR) is designated MPRanh. A similar approach was implemented using theoretically generated structure factors with atomic coordinates fixed to the values obtained from MPRanh. Refinement was carried out to a resolution of 1.35 Å−1 to be comparable with the experiment. All multipoles were refined up to and including the hexadecapole level for non-hydrogen atoms, and up to and including quadrupoles for atoms of hydrogen. The same sets of expansion-contraction coefficients as those of MPRanh were used to describe the valence ED. To adequately model the remaining residual ED, the frozen spherical core approximation was lifted for all non-H atoms, and core multipoles were refined up to and including the quadrupole level. The according seven spherical expansion-contraction coefficients, κs, were refined, but refinement of the corresponding κ parameters for the multipole terms was not possible and these were set to 1.0. The resulting model is designated MPRtheor [R1 = 0.0022; Δρmin/max = −0.092/0.120 e Å−3]. The final quality of each MPR was confirmed by low discrepancy indices, residual density features being within ±0.12 e Å−3 and assessment of statistical measures. Plots of averaged ratios (0.05 Å−1 bins) of Fobs/Fcalc and the normal probability plot for MPRanh indicate good model fitting across the full sinθ/λ range and are deposited (Fig. S1-S2). Calculation of the total ED using 0.001 Å3 grid-spacing was also performed using WinXPRO41-42 to ascertain that electron density is positive everywhere for each model. Table 1 provides the experimental crystallographic details and refinement summary.

Table 1 Details for experimental crystallographic data collection and refinements. Chemical formula

C2H8N10O4

Space group

P21/c

a (Å)

5.49040(10)

b (Å)

11.4912(3)

c (Å)

6.45560(10)

β (°)

95.5710(16)

−3

V(Å )

405.368(14) 2

Z −3

Density (g cm )

1.935

Crystal size (mm)

0.38 × 0.29 × 0.22


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T (K)

20.0(1)

λ (Å)

0.71073 −1

sin(θ/λ)max (Å )

1.33

Reflections integrated

74492

Rint, average data multiplicity

0.014, 9.4

Completeness: all data (%)

96.6

Independent reflections

7716

Observed reflections [I> 3σ(I)]

7072

Spherical atom refinement Total number of parameters 2

R1,wR2(F ), GOF

75 0.0219, 0.0706, 1.121

−3

Δρmin/max (e Å )

0.75/−0.65

Multipole refinement Total number of parameters, Nref/Nv 2

R1, wR2(F ), GOF, wGOF −3

Δρmin/max, RMS (e Å ) a

Weighting scheme : a, b a

573, 12.34 0.0068, 0.0104, 1.333, 1.2268 −0.071/0.103, 0.018 0.0015, 0.0015

- w2=1/[σ2(F2)+(ap)2+bp], p=0.3333Fobs2 + 0.6667Fcalc2

Periodic-boundary density functional theory (DFT) calculations were performed with CRYSTAL0938-39 using B3LYP functionals. The basis sets used were (8s)-(411sp)-(1d1d) for oxygen atoms, (6s)-(311sp)(1d1d) for carbon,43 and 6-311G** for atoms of nitrogen and hydrogen. The first such calculation employed coordinates from a preliminary multipole refinement (see above) with a view to obtaining predicted O−H and N−H bond lengths in the absence of neutron data. A further calculation was performed using the experimentally obtained coordinates from MPRanh to generate the theoretical wavefunction. This served two purposes: theoretical structure factors (Ftheor) were generated to obtain a corresponding static, noise-free, theoretical MPR (MPRtheor); and topological analysis of the ED was obtained directly from the calculated wavefunction using TOPOND.44 In the case of the MPRs, topological analysis of the ED and its derivatives was performed using XDPROP in the XD2006 software suit35 and WinXPRO.41-42 Additional gas phase DFT calculations were carried out with Gaussian09.45 The geometry optimized DFT electronic structure was computed for the dianion and for the formula unit as described in Fig. 1b as the starting point; further calculations were performed employing the solid state conformation of only the dianion with 90° rotation about the C−C bond as the starting point. These calculations were performed using the B3LYP functional46-47 and analogous calculations were carried out with the M06-2X functional for comparison.48 Calculations with different basis sets were in good agreement and discussion is made with reference to those of B3LYP. The 6-311+G(2d,p) basis set was used for all atomic basis functions. Vibrational analysis was carried out for geometry optimized structures; zero imaginary frequencies were found for true minima and one imaginary frequency for transition state structures. The topology of the



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electron density was analyzed in terms of the QTAIM as implemented in the program MultiWfn.49 The NBO-3.1 program50 was used to investigate the influence of orbital interactions for the short 1,5-type intramolecular N···O interaction.

Results and Discussion Modeling and anharmonic motion Despite the low temperature, it was found that harmonic treatment of thermal motion in the experimental data did not give a satisfactory model, with all other parameters refined as described for MPRanh. It was found that structured features in the residual ED maps remained around several heavy atoms after harmonic refinement, and regions of slight negativity in the total ED were present at the origin of the unit cell [ρ = −0.002 e Å−3]. Refinement of both the 3rd and 4th order terms of the GramCharlier anharmonic expansion resulted in the elimination of all discernable features, while additionally removing the negative density regions and further reducing the R1 from 0.76% to 0.68%. This resulted in a significantly improved deformation density almost identical to that of MPRtheor (Fig. 2). It also allowed for sensible and stable hydrogen ADPs to be refined with use of the rigid bond constraint. Despite the magnitude of the refined anharmonic terms being small, statistical significance of the dominant terms is of the order of 6 to 12 sigma (Table S1-S2). Given the low temperature of the experiment and the expectation that the harmonic approximation should be adequate, a model incorporating an aspherical core, as determined from theoretical structure factors, was investigated but found to offer negligible improvement to the spherical core, harmonic model. Moreover, anharmonic refinement in the presence of a revised description of the core resulted in little change to the parameter values and without any statistical improvement vs. MPRanh.


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Figure 2 Static deformation density maps for TKX-50 dianion (left) and cation (right) in MPRanh (top) and MPRtheor (middle) with scheme provided for atom assignment (bottom). Contours drawn at 0.05 e Å−3 intervals; positive deformation density in solid red, negative in dotted blue, and the zero contour in dashed black; atomic positions marked with crosses and bond vectors with solid black lines; symmetry code _p = x, y, 1+z. Note that MPRtheor incorporates significant deformation to the core electron density, unresolved in the experiment.

Anisotropic displacement parameters show atomic motion to be primarily perpendicular to the plane of the dianion, while the secondary motion appears to correspond to an in-plane libration of the whole molecule about the molecular two-fold axis through the centre of the C−C bond. Visualization of the total probability density functions for the dianion shows anharmonicity to be most pronounced at N(2), N(3) and N(4), while the more highly connected C(1) and N-oxide moiety appear less perturbed. Moreover, the anharmonicity appears to affect most atomic motions corresponding to the aforementioned libration (Fig. S3).

Topological analysis of the electron density TKX-50 crystallizes in monoclinic spacegroup P21/c as previously reported3 and the unit cell comprises two formula units, packing to form layers perpendicular to the b axis (Fig. 1a). The shortest and indeed strongest bonding motif between cation and anion is an O−H···O hydrogen bond and the asymmetric unit is chosen to reflect this. The crystal packing of TKX-50 is dominated by cation-cation and cationanion hydrogen bonds as well as face-to-face π···π interactions.10, 16 Herein, we discuss the intra- and intermolecular bonding on the basis of the total electron density and its derivatives with reference to the values obtained from experiment. Covalent bonding interactions. The charge concentrations associated with covalent bonds and lone pairs are clearly shown by static deformation maps depicted in Fig. 2. The topology of the total electron density was analyzed using WinXPRO. All (3,-1) bond critical points have been characterized and the relevant data and derived properties for intramolecular covalent bonds are reported in Table 2.

Table 2 Characteristics of the bond critical points for the intramolecular covalent bonding interactions in TKX-50.b Bond

rij, Å

d1, Å

d2, Å

O(1)−N(1)

1.322

0.674

0.648

ρ, −3 eÅ 2.605

∇2ρ, −5 eÅ −4.03

−5

−5

−5

λ1, e Å

λ2, e Å

λ3, e Å

−21.650

−20.772

38.397


ε

ntopo

0.042

1.42


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N(1)−N(2)

N(2)−N(3)

N(3)−N(4)

N(4)−C(1)

N(1)−C(1)

C(1)−C(1)

m

O(2)−H(2)

O(2)−N(5)

N(5)−H(5A)

N(5)−H(5B)

N(5)−H(5C)

1.322 1.321 1.335 1.335 1.336 1.310 1.310 1.313 1.343 1.343 1.346 1.333 1.333 1.334 1.346 1.346 1.346 1.440 1.440 1.440 0.935 0.935 0.910 1.410 1.410 1.410 1.000 1.000 0.977 1.007 1.007 0.986 1.015 1.015 0.994

0.676 0.675 0.689 0.687 0.693 0.662 0.663 0.665 0.678 0.674 0.675 0.798 0.775 0.790 0.834 0.820 0.849 0.720 0.720 0.720 0.747 0.745 0.772 0.727 0.738 0.737 0.776 0.755 0.767 0.789 0.760 0.769 0.791 0.771 0.781

0.645 0.646 0.646 0.648 0.643 0.648 0.648 0.648 0.666 0.670 0.670 0.535 0.558 0.544 0.513 0.527 0.497 0.720 0.720 0.720 0.188 0.190 0.138 0.683 0.672 0.673 0.224 0.245 0.210 0.219 0.248 0.217 0.225 0.244 0.213

2.499 2.558 2.638 2.558 2.598 2.824 2.731 2.787 2.545 2.497 2.544 2.455 2.393 2.423 2.282 2.21 2.234 1.954 1.904 1.917 2.339 2.550 2.564 2.121 2.057 2.078 2.161 2.355 2.396 2.143 2.341 2.369 2.118 2.285 2.308

−2.80 −10.27 −14.70 −12.61 −18.10 −18.31 −15.74 −21.62 −13.61 −11.76 −17.11 −28.64 −23.37 −27.42 −24.26 −20.42 −22.41 −17.26 −15.28 −17.50 −43.19 −54.79 −66.75 −3.10 −4.35 −7.25 −35.22 −40.01 −52.34 −37.28 −39.87 −50.20 −37.00 −39.63 −49.31

−20.300 −21.978 −23.823 −22.293 −23.231 −26.301 −24.213 −25.039 −21.679 −20.793 −21.665 −20.821 −19.480 −20.629 −19.135 −17.713 −18.580 −14.737 −14.492 −14.628 −43.600 −47.692 −53.258 −17.605 −16.330 −17.303 −31.720 −33.579 −36.317 −32.143 −33.266 −35.401 −31.913 −32.943 −34.678

−18.623 −20.701 −20.122 −18.622 −19.303 −22.600 −20.998 −21.352 −19.559 −18.629 −19.255 −17.084 −15.793 −16.580 −15.226 −13.652 −14.194 −12.914 −11.623 −12.604 −41.308 −45.523 −51.692 −16.596 −15.406 −16.532 −30.859 −33.121 −35.690 −31.272 −32.526 −34.702 −30.737 −32.220 −34.052

36.120 32.413 29.247 28.300 24.436 30.590 29.471 24.774 27.633 27.657 23.810 9.268 11.899 9.784 10.097 10.942 10.362 10.388 10.836 9.760 41.717 38.429 38.197 31.102 27.383 26.581 27.360 26.688 19.665 26.138 25.918 19.906 25.653 25.531 19.448

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0.090 0.063 0.184 0.197 0.204 0.164 0.153 0.173 0.108 0.116 0.126 0.219 0.233 0.245 0.257 0.297 0.308 0.141 0.247 0.161 0.056 0.048 0.030 0.061 0.060 0.048 0.028 0.014 0.017 0.028 0.023 0.020 0.038 0.022 0.018

1.36 1.26 1.39 1.49 1.35 1.37 1.49 1.40 1.40 1.48 1.36 1.22 1.39 1.35 1.12 1.29 1.27 1.12 1.18 1.05 0.42 0.63 0.59 1.05 0.96 0.92 0.63 0.57 0.60 0.59 0.58 0.60 0.58 0.55 0.58

b

First line corresponds to MPRanh, second to MPRtheor and the third to data extracted directly from TOPOND calculations: rij is the bond path length; d1 and d2 are the distances of the critical point from the first and second atoms, respectively; ρ is the electron density; ∇2ρ the Laplacian; λ1, λ2 and λ3 are the

Hessian eigenvalues; ε is the bond ellipticity = 1 − ; and ntopo is the topological bond order (see

main text). Symmetry operator m = 1−x, 1−y, 2−z.

The properties of the (3,−1) bond critical points (BCPs) for all covalent bonds appear unexceptional and there is good agreement between experiment and theory. From the data obtained, the topological bond order, ntopo, can be estimated for covalent interactions: !"! = # + #$ %$ + %& + #& % + # '()


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Where λ1, λ2 and λ3 are the Hessian eigenvalues; ρBCP the ED at the BCP; and a0, a1, a2 and a3 are coefficients taken from the literature as appropriate.51-52 Tetrazolium N−N bonds yield values for ntopo of approximately 1.4 and are reasonably consistent between models, while this is slightly lower for bonds to carbon for which ellipticity at the bond critical point is in fact higher. Notably, C(1)−C(1)m which links the two tetrazolium moieties (symmetry operator m = 1−x, 1−y, 2−z) is calculated as having a value of 1.12 for ntopo and 0.14 for ε, indicating a non-negligible degree of conjugation between the two atoms, consistent with the exceptional planarity of the system [torsion N(1)−C(1)−C(1)m−N(4)m = 0.3 °]. The topological bond order of 1.42 for the N-oxide bond is suggestive of multiple bond character for this interaction. This is in stark contrast to the ellipticity of 0.04 and the inability of the oxygen to engage in classical π-delocalization in this system. Moreover, the deformation density for TKX-50 reveals the occurrence of a σ-hole at the oxygen, as expected for a singularly bonded sp3 center (Fig. 3; comparison with Fig. 2 shows the importance of considering the full 3D ED distribution, rather than a 2D section). This value of ntopo is, nevertheless, within the range calculated by Lukomska et al. for amine and imine Noxides.53 It was found that ntopo was consistently greater than 1 in the case of aryl imines and electron deficient amines due to LP→π* and LP→σ* interactions, respectively. Similarly, gas-phase calculations reveal a number of LP→σ* hyperconjugation interactions between O(1) and the tetrazolium ring that might be expected to increase the N−O bond order as suggested by Lukomska. Values for the Laplacian at the BCPs suggest a lower degree of covalency, as expected, for both of the strongly polar N-oxide and

hydroxylammonium N−O bonds than for bonds within the bis-tetrazolium moiety.

Figure 3 Image of the 3D deformation density showing the 'doughnut' formation at O(1), typical of a σ-hole type charge distribution. Mesh iso-surfaces drawn at the ±0.30 e Å−3 level; charge accumulation in blue mesh, charge depletion in orange; O atoms colored red, N atoms blue and C atoms dark grey.

Closed shell interactions All but one critical point in the total electron density corresponding to closed shell interactions were confirmed by a virial path search for both MPRs. The remaining critical point, otherwise forming part of the π···π stacking interaction, is mentioned in the text but otherwise omitted.



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Hydrogen bonding The crystal structure of TKX-50 includes several varied hydrogen bonding interactions which have been previously theoretically analyzed with respect to impact sensitivity of the system.16 The authors discussed the formation of hydrogen bonded layer motifs within the crystal structure. Hydrogen bonds designated as intralayer are more numerous and generally stronger than those designated interlayer, of which only two such unique interactions are reported. We employ the Espinosa et al. relationship54-55 for estimation of the bond dissociation energy (De) and, therefore, the strength of these interactions. With the exception of one intralayer interaction, we find good agreement with the previous report16 regarding the relative strengths within this set of interactions (Table 3). We also note that for two of the hydrogen bonds previously reported we find bond paths that terminate at the hydroxylammonium nitrogen, being deflected by rather than terminating at the corresponding hydrogen; one further such interaction not previously discussed is also found. These are clearly not typical hydrogen bonds, but are nevertheless included in this section for the sake of comparison. Beyond this, the previously reported bond dissociation energies tend to be around 30% lower on average, as compared to those obtained in this study. A similar discrepancy between the values calculated therein for TATB and those determined from experimental data is also observed.21 These differences may be a result of the calculations in the aforementioned study being based on geometry optimized structures rather than those at experimental geometry. Within the present work, experiment and theory match exceptionally well with the exception of the strongest hydrogen bonding interaction, O(2)−H(2)···O(1), for which experiment and theory differ by 16.9 kJ mol−1.

Table 3 Characteristics of the (3,−1) cri`cal points corresponding to the unique hydrogen bonding interactions and interactions typically designated hydrogen bonding in the related literature but where bond paths are deflected by an ammonium hydrogen, connecting the dianion instead to the ammonium nitrogen atom.c Bond

rij, Å

d1, Å

d2, Å

O(1)···H(2) (intralayer)

1.663 1.663 1.689 1.714 1.821 1.821 1.844 1.960 2.036 2.036 2.062 2.184 2.078 2.078 2.103 2.359 2.920

1.091 1.112 1.124 1.187 1.197 1.200 1.286 1.293 1.304 1.311 1.314 1.319 1.440

0.571 0.550 0.565 0.636 0.624 0.644 0.751 0.744 0.758 0.768 0.765 0.785 1.524

n

O(1)···H(5C) (intralayer)

O(1)···H(5A) (intralayer)

o

p

O(2)···H(5B) (interlayer)

N(3)···N(5)

q

ρ, −3 eÅ 0.433 0.356 0.344 0.315 0.263 0.256 0.243 0.180 0.154 0.149 0.148 0.109 0.128 0.128 0.121 0.007 0.090

∇2ρ, −5 eÅ 1.94 2.96 3.57 2.96 2.00 2.05 2.58 2.16 1.72 1.64 1.83 1.35 1.61 1.54 1.69 1.03 1.24

g, au

v, au

h, au

0.0429 0.0418 0.0267 0.0265 0.0171 0.0163 0.0150 0.0145 0.0107

−0.0657 −0.0528 −0.0327 −0.0317 −0.0165 −0.0157 −0.0133 −0.0130 −0.0086

−0.0228 −0.0111 −0.0060 −0.0052 0.0007 0.0006 0.0017 0.0015 0.0021


De, −1 kJ mol 86.2 69.3 59.1 42.9 41.6 27.7 21.6 20.6 13.9 17.5 17.1 8.2 11.3

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(intralayer) [N(3)··H(5B)] r N(4)···H(5A) (intralayer)

s

N(2)···N(5) (interlayer)

[N(2)··H(5B)] m N(4)···N(5) (intralayer)

2.920 2.689 2.435 2.405 2.405 2.483 2.393 2.944 2.944 3.179 2.497 3.099 3.099 3.338 -

1.460 1.482 1.458 1.471 1.487 1.470 1.484 1.501 1.544 1.575 1.587 -

1.499 1.208 0.962 0.946 0.996 1.512 1.502 1.678 1.597 1.543 1.751 -

0.079 0.088 0.084 0.089 0.075 0.081 0.083 0.076 0.070 0.074 0.070 0.064 0.052 0.054 -

1.29 1.16 1.12 1.16 1.20 1.01 1.05 1.11 1.13 1.01 1.01 0.83 0.83 0.72 -

0.0107 0.0102 0.0099 0.0093 0.0092 0.0069 0.0066 -

−0.0079 −0.0082 −0.0073 −0.0071 −0.0067 −0.0053 −0.0046 -

0.0027 0.0019 0.0026 0.0022 0.0025 0.0016 0.0020 -

10.4 10.1 10.8 9.6 9.7 9.3 8.8 8.3 7.0 6.0 -

c

First line corresponds to MPRanh, second to MPRtheor, third to data extracted directly from TOPOND calculations and fourth area data taken from the literature.16 rij is the bond path length; d1 and d2 are the distances of the critical point from the first and second atoms, respectively; ρ is the electron density; ∇2ρ the Laplacian of the electron density; g, v and h are the local kinetic, potential and total electronic energy densities, respectively; De is the bond dissociation energy, estimated using the Espinosa et al. relationship.54-55 Symmetry operators: m = 1−x, 1−y, 2−z; n = 1−x, 1−y, 1−z; o = −1+x, y, z; p = x, y, 1+z; q = x, 0.5−y, 0.5+z; r = −1+x, y, 1+z; s = −1+x, 0.5−y, 0.5+z.

The three strongest hydrogen bonds are calculated as being those between hydroxylammonium protons and the N-oxide oxygen. The fourth strongest hydrogen bond as assessed in this study appears both significantly underestimated and 0.281 Å longer in the previous report, in our case forming the strongest interlayer interaction between O(2) and H(5B)p of two cations (symmetry code p = x, y, 1+z). Gatti showed that the ratio of |vb|/gb (where vb and gb are the local potential and kinetic energy densities at the BCP, respectively), together with the sign of the total electronic energy density at the BCP, hb, allows for the assignment of bonding interactions as either purely closed shell (|vb|/gb < 1, hb > 0, ∇2ρb > 0) or shared-shell, i.e., covalent, interactions (|vb|/gb > 2, hb < 0, ∇2ρb < 0).56 Intermediate values of this proportionality (1 > |vb|/gb < 2, hb < 0, ∇2ρb > 0) represent a so-called transit region of increasing covalency. In the case of interactions O(2)−H(2)···O(1) and N(5)−H(5C)···O(1), the experimental values are found to be 1.53 and 1.22, respectively, indicating partially covalent character. All remaining interactions yield values less than 1 and are designated purely closed-shell interactions. Nevertheless, with the exception of N(4)···N(5), all interactions described in this section are stronger than the strongest intermolecular interactions in the more sensitive EMs RDX,19 HMX57 and PETN.58 Moreover, the summation of these interactions alone exceeds the intermolecular bonding in the aforementioned cases, as well as in the case of the less sensitive EM, TATB,21 in agreement with the work of Meng et al.16 In the high-pressure crystallographic study of TKX-50, Dreger et al. describe two hydrogen bond interactions to the nitrogen of the N-oxide moiety.10 Where all other prescribed hydrogen bond interactions are significantly compressed, the authors report negligible contraction in those at the N-



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oxide nitrogen with pressures up to 10.3 GPa. They conclude that the strength of these two interactions be either unaffected or made weaker by the application of pressure. To this end, we find no corresponding bond paths for these supposed hydrogen bonding interactions to the N-oxide nitrogen (Fig. 4), while bond paths for all other contacts identified therein as interactions are found.

Figure 4 Molecular graphs depicting the bond paths (thinner, curved lines) and (3,−1) cri`cal points (gold spheres) for all intralayer (left) and interlayer (right) bonding interactions at the asymmetric unit. One (3,+1) critical point associated with the intramolecular ring formed including a 1,5-type closed-shell interaction is included as a blue diamond, and that of the (3,+3) critical point for the intermolecular cage as a purple cube (see also Fig. 5). Oxygen atoms are colored red, nitrogen in blue, carbon in dark gray and hydrogen in green; bonds and bond paths reflect the color of the atom types associated.

pi-pi interactions As mentioned earlier, face-to-face π···π stacking is also observed in TKX-50 and forms within the layered motifs that comprise the extended packing. Topological analysis reveals two unique bond paths and (3,−1) critical points of comparable properties in the total ED associated with this interaction, describing interactions N(1)···N(3)t, and N(2)···C(1)t (symmetry operator t = −x, 1 − y, 2 − z) and their symmetry equivalents. Of these, only the interaction between N(1) and N(3)t was confirmed by a virial path search for both MPRs and consequently the latter is not designated as bonding and so omitted from discussion. Thus, only two bonding interactions exist between the face-to-face interacting rings (Table 4; Fig. 4), and considering this interaction as a whole yields a total estimated De of 11.0 kJ mol−1. There also occurs two inequivalent interlayer interactions between dianions, each approximately half as strong as the individual components of the π···π stack. These form a zig-zag arrangement of interactions O(1)···N(3)t, N(2)···N(3)t and their symmetry equivalents, bonding each dianion to its two nearest neighbors in each adjacent layer.


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Table 4 Details of the (3,−1) cri`cal points for each unique non-hydrogen bonding closed-shell interaction.d Bond t

N(1)···N(3) (intralayer)

u

O(1)···N(3) (interlayer)

u

N(2)···N(3) (interlayer)

m

O(1)···N(4) (intramolecular) v

O(1)···N(4) (intralayer)

u

O(2)···C(1) (interlayer)

rij, Å

d1, Å

d2, Å

3.102 3.102 3.121 3.398 3.398 3.438 3.401 3.401 3.424 2.943 2.943 2.961 3.116 3.116 3.159 3.191 3.191 3.213

1.549 1.540 1.545 1.692 1.701 1.698 1.693 1.679 1.694 1.467 1.483 1.488 1.503 1.518 1.515 1.535 1.572 1.567

1.584 1.589 1.576 1.740 1.709 1.739 1.711 1.726 1.730 1.477 1.462 1.474 1.627 1.613 1.644 1.682 1.626 1.646

ρ, −3 eÅ 0.053 0.050 0.047 0.032 0.034 0.034 0.032 0.031 0.034 0.078 0.081 0.074 0.046 0.041 0.040 0.049 0.047 0.040

∇2ρ, −5 eÅ 0.700 0.690 0.627 0.380 0.370 0.386 0.390 0.390 0.386 0.940 0.870 0.964 0.590 0.550 0.578 0.560 0.470 0.554

g, au

v, au

h, au

0.0057 0.0056

−0.0042 −0.0040

0.0015 0.0016

De, −1 kJ mol 5.5 5.3

0.0031 0.0030

−0.0021 −0.0021

0.0009 0.0009

2.8 2.8

0.0031 0.0031

−0.0021 −0.0021

0.0010 0.0010

2.8 2.7

0.0082 0.0079

−0.0066 −0.0066

0.0016 0.0012

8.7 8.7

0.0048 0.0044

−0.0034 −0.0031

0.0013 0.0013

4.5 4.0

0.0047 0.0040

−0.0035 −0.0031

0.0012 0.0009

4.6 4.1

d

First line corresponds to MPRanh, second to MPRtheor, and the third line to data extracted from TOPOND calculations: rij is the bond path length; d1 and d2 are the distances of the critical point from the first and second atoms, respectively; ρ is the electron density; ∇2ρ the Laplacian of the electron density; g, v and h are the local kinetic, potential and total electronic energy densities, respectively; De is the bond dissociation energy, estimated using the Espinosa et al. relationship.54-55 Symmetry operators: m = 1−x, 1−y, 2−z; t = −x, 1−y, 2−z; u = x, 0.5 − y, −0.5+z; z = x, y, −1+z.

Other closed shell interactions An intramolecular 1,5-type closed-shell interaction is found between O(1) of the N-oxide and N(4)m of the adjoined tetrazolium moiety (Fig.5, Table 4) which is significantly within the sum of the relevant van der Waals radii [rij = 2.943 Å; ΣvdW = 3.07 Å].59 This interaction forms a five membered ring of O(1), N(1), C(1), C(1)m and N(4)m and is by necessity present on the other side of the molecule by symmetry. The De is estimated to be 8.7 kJ mol−1, comparable to the weaker hydrogen bonds found in the crystal structure. The bond path and its characteristic (3,−1) cri`cal point are also iden`ﬁed in Figs. 4-5. The corresponding (3,+1) critical point is found to reside typically close to the (3,−1) BCP in ques`on and its presence satisfies the Poincaré-Hopf rule.60



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Figure 5 Trajectory plot for the gradient of the total electron density in the plane of the anion showing (3,−1) and (3,+1) cri`cal points associated with the 1,5-type intramolecular closed-shell interaction in blue and red, respectively; (3,−1) and (3,+3) cri`cal points associated with the intermolecular cage formation are shown with red and purple circles, respectively. Atomic positions are highlighted with black circles, bond paths in black, zero-flux surfaces in blue and gradient lines in red.

Intramolecular 1,5-type closed-shell interactions such as this do not appear uncommon and, for example, have already been observed in the dinitramide anion61 and 2,6-dinitrophenol.62 Additionally, such interactions were also discussed in the context of β-keto carboxylic esters.63 The authors established that the expected electrostatic repulsion of the lone pairs is counteracted by negative hyperconjugation, i.e., the donation of lone pair (LP) electron density into neighboring antibonding orbitals (specifically, p → σ*), employing the delocalization index (di) as part of their rationale.64 The di corresponds to the average number of electrons which are delocalized across the interacting atoms. In this context, we calculate di to be 0.065 e− for the gas-phase dianion at the experimental geometry, directly comparable to those of the aforementioned study (di = 0.0607). By extension, it might seem reasonable to conclude that intramolecular negative hyperconjugation stabilizes this close contact between O(1) and N(4)m. In this instance, it would be expected that the oxygen donates electron density into nearby antibonding orbitals. However, the stabilization due to such interactions was found to be small on the basis of NBO calculations and insufficient to stabilize the solid-state conformation in the gas-phase. Indeed, the planar structure for the gas-phase dianion was found to be a transition state on the basis of frequency analysis, while the true global minimum geometry in the gas phase was twisted by 95.7 ° about the C−C bond. Furthermore, while a number of other stabilizing interactions were found, their energies were found to be insensitive to torsion about the C−C bond. Inclusion of two cations, so as to build a full molecular unit as described by Fig. 1b, recovers the planar conformation seen in the solid-


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state, and the most significant stabilizing interaction calculated for the described formula unit fragment was for donation from lone pairs at O(1) into the σ* orbital of O(2)−H(2), i.e., for the hydrogen bond O(2)−H(2)···O(1) [ΣE = −33.5 kJ mol−1]. This is in corroboration with the earlier assessment of this particular hydrogen bond as being partially covalent in nature. Another closed-shell interaction is formed by N-oxide O(1) with N(4)v of the in-plane neighboring dianion (symmetry operator v = x, y, −1+z), slightly beyond the sum of the relevant van der Waals radii [rij = 3.116 Å] (Table 4; Fig. 4). De is estimated at 4.5 kJ mol−1, slightly weaker than the weakest hydrogen bond and comparable to the individual interactions comprising the π-stacking motif. Thus, the fourmembered intermolecular ring O(1), N(4)m, O(1)n, N(4)v is formed entirely of closed-shell interactions. These form a cage about the center of the unit cell along with hydrogen bonds from the cations at x, y, z and 1−x, 1−y, 1−z to the N-oxide oxygen atoms. The required (3,+3) cage critical point was found in satisfaction of the Poincaré-Hopf rule,60 located precisely at the inversion centre. The final bonding interaction observed in this study is between a lone pair of O(2) directed towards the highly electron deficient C(1)u (symmetry operator u = x, 0.5−y, −0.5+z), providing an additional interlayer bonding interaction with De estimated at 4.6 kJ mol−1.

Atomic charges Integration of the total electron density over the atomic basins as defined by the zero-flux surfaces yielded reasonable atomic charges, q, for all atoms in all models. The total charge in all models was necessarily close to zero while the summation of all atomic volumes, Ω, in the asymmetric unit equated that of V/Z within an error of 0.1% for the MPRs and 0.2% direct from theory. The accuracy is further confirmed by low values for the integration of the Laplacian over the atomic basins, L, and the data from experiment and theory showed good agreement (Table 5).

Table 5 Atomic charges (q) and volumes (Ω), integrated over the atomic basins for each atom. Atom O(1) O(2) N(1) N(2) N(3) N(4) N(5) C(1) H(2) H(5A) H(5B) H(5C)

MPRanh −0.661 −0.657 −0.171 −0.115 −0.091 −0.637 −0.727 0.870 0.590 0.504 0.549 0.548

q, e MPRtheor −0.670 −0.768 −0.127 −0.131 −0.111 −0.524 −0.542 0.760 0.630 0.489 0.482 0.512

3

TOPOND −0.685 −0.782 −0.175 −0.121 −0.121 −0.571 −0.548 0.849 0.659 0.499 0.489 0.510

MPRanh 13.703 14.598 8.214 12.310 12.448 13.044 11.368 7.297 1.518 2.397 2.303 2.063

Ω, Å MPRtheor 14.118 15.264 8.185 12.414 12.592 12.848 10.365 7.241 1.286 2.356 2.492 2.128

TOPOND 13.968 15.153 8.167 12.449 12.580 13.057 10.275 7.256 1.223 2.320 2.470 2.252



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The total charges for the individual components of the salt were found to be +0.807 e for each cation and −1.610 e for the dianion, significantly higher in magnitude than those calculated for one molecular unit in the gas phase.18 While these values agree closely with those of the individual moieties reported by An et al.,8 charges for each individual atom vary significantly with respect to that study. Ring nitrogen atoms were found to have only low negative charges on the order of −0.1 e, with the exception of N(4) for which the charge was significantly greater [q = −0.637 e], comparable to the anticipated high charge on O(1) [q = −0.661 e]. In contrast, the carbon of the tetrazolium moiety was found to be comparably positive [q = +0.870 e]. Thus, TKX-50 shows significant charge partitioning within the dianion with a high degree of positive charge at its center. Such extreme charge partitioning might initially be taken to suggest a predisposition of the dianion towards shock sensitivity, but this does not translate to significantly positive regions on the electrostatic potential surfaces (EPSs), as shown in Fig. 6. While it is expected that less sensitive energetic materials should have lesser featured EPSs,65 these are very much featureless in the case of TKX-50, with only a marginally less negative potential over the C−C bond as compared to the majority of the dianion surface, with the exception of the region around and between O(1) and N(4)m which has a potential approximately up to −0.15 e Å−1 more negative. Integrated atomic charges for the hydrogen atoms were unexceptional [q = +0.5-0.6 e], with ammonium hydrogen atoms being marginally more positive than the hydroxyl hydrogen. Accordingly, the negative charge on the hydroxylammonium oxygen was slightly higher than for the nitrogen

[q = −0.65 and −0.71 e, respectively].

Figure 6 Color-map images for MPRanh of the electrostatic potential drawn on the 0.001 au isosurface for the anion, cation and complete molecular fragment as considered in this study, generated using WinXPRO.

Conclusions Accurate experimental determination of the charge-density of the energetic ionic salt, TKX-50, was undertaken with subsequent topological analysis of the electron density. The results are in qualitative agreement with the preceding theoretical studies of this compound, though absolute values differ


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between studies. Refinement of anharmonicity was required to obtain an adequate model, most prominently at the lesser bound N(2), N(3) and N(4) atoms of the dianion and O(2) of the cation. We experimentally confirm and quantify the significantly stronger and more numerous bonds within the previously described layer motifs as compared to between layers, formally describing the π···π stacking and other previously unreported interactions. Most notably, an additional intramolecular 1,5-type closed-shell interaction was identified between O(1) of the N-oxide and N(4) of the adjoined tetrazolium moiety. In summation, the calculated ratio of total intra- and interlayer intermolecular bond dissociation energies is approximately 5:1, marginally lower than the theoretical assessment of hydrogen bonding alone (6:1).16 This further supports the description of TKX-50 as containing stronger intra- than interlayer bonding with respect to the layer motifs forming in the ac plane. While significant charge partitioning was calculated in the dianion, this is not reflected on the electrostatic potential surfaces for the dianion nor formula unit. These findings are consistent with the observed mechanical stability of the phase and the current understanding of mechanically sensitizing properties.

Acknowledgements We thank Prof. T. Klapötke for generously supplying the crystalline sample used in this study, and Dr. Xiche Hu for providing access to Gaussian09 and high-performance CPU time. We also thank the Office of Naval Research for financial support (grant number N00014-16-1-2058).

Supplementary information available Crystallographic information files; experimental and theoretical structure factor files; scale factor and normal probability plots, table of refined experimental anharmonic parameter populations, figure showing probability distribution functions, extended tables of critical point characteristics.

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