Article pubs.acs.org/JPCA
Role of Inter- and Intramolecular Bonding on Impact Sensitivity Travis E. Jones* Molecular Theory Group, Colorado School of Mines, Golden, Colorado 80401, United States, and School of Physics, The University of Sydney, Sydney, New South Wales 2006, Australia ABSTRACT: A picture of impact sensitivity based on the bond bundles of the electron charge density is developed, allowing the role of both inter- and intramolecular bonding interactions to be investigated. Impact sensitive materials were found to have a convergent intramolecular bond bundle with a low electron count that serves as a trigger linkage, while insensitive materials do not. The shape and electron count of the intramolecular bond bundles was found to change between the gas phase and solid state due to the formation of intermolecular bond bundles. In the case of polynitrobenzenes, this change was subtle and did not affect the trigger linkages. However, the intermolecular bond bundles in crystalline RDX (hexahydro-1,3,5-trinitro-1,3,5-triazine) change from C−N trigger linkages in the gas phase to N−N trigger linkages in the solid state. This observation offers a theoretical justification of the experimentally observed differences in the decomposition behavior of gas phase and crystalline RDX.
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INTRODUCTION High energy density materials are used in a wide range of military and civilian applications. As such, there is a strong interest in developing new explosives that are both powerful and safe to handle.1 However, designing these new explosives is costly and time-consuming, making it desirable to computationally design or prescreen candidate materials.1 While theoretical models can now predict many of the performance properties of energetic materials, suitable methods of predicting an explosive's safety are lacking.1−3 Here, I show that topological and geometric properties of a materialʼs electron charge density, in particular its topological bonding volumes,4 can be used to offer insight into one aspect of safety: sensitivity to impact. Molecules that possess closed bonding volumes, as defined below, with a small electron count are found to be impact sensitive, while molecules whose bonding volumes are open are less sensitive to impact. I go on to show that these intramolecular properties can change between the gas phase and solid state due to the formation of intermolecular bonding volumes, a fact that is used to rationalize the experimentally observed differences in the gas phase and solid state decomposition behavior of one of the most widely used high explosives: RDX, hexahydro-1,3,5-trinitro-1,3,5-triazine. Impact sensitivity is a measure of a material's response to impact. It varies widely among compounds, with nitrogentriiodide being too sensitive to be of practical use and triaminonitrobenzene safe to handle. Impact sensitivity is most often measured using a drop weight impact test. While this test is qualitative, its simplicity has made it popular.5−8 The test is performed by dropping a 2.5 kg mass onto milligram quantities of explosive. The drop height of the mass is adjusted until 50% of the attempts results in a reaction of the sample. This height is referred to as h50%. A major goal in the energetic materials research community is to correlate molecular and solid state structure with the h50% value of a compound.5 Decades of theoretical and experimental work have shown that an impact sensitive materialʼs h50% value © 2012 American Chemical Society
depends on the rate of thermal decomposition occurring in the sample due to the temperature generated by the dropped mass.9,10 The rate determining step in this type of reaction is the homolytic cleavage of the weakest bond in the molecule. This bond is termed the trigger linkage.10−14 The concept of a trigger linkage has prompted researchers to seek correlations between bond dissociation energies in isolated molecules and impact sensitivity.9−11 Although this approach ignores the intermolecular bonding that will be present in the solid state, it has still been successful for some systems, such as polynitroaromatics, where the C−N bonds function as trigger linkages.11 In other systems, the trigger linkages appear to be different in the gas phase and solid state, most notably in RDX. Decades of studies on RDX suggest that the primary decomposition pathways differ in the gas phase and solid state.15−21 Experimental results show that the primary channel for gas phase decomposition of the cyclic nitramine is concerted ring fission.15,16 N−NO2 homolysis is found to be the primary pathway in the solid state.17−19 To rationalize this change in behavior, the role of both inter- and intramolecular bonding on impact sensitivity must be uncovered. In an effort to identify how inter- and intramolecular bonding affect impact sensitivity, Yau, Byrd, and Rice turned to Baderʼs topological theory of molecular structure,22 the Quantum Theory of Atoms in Molecules (QTAIM).23 In QTAIM, a type of saddle point, or bond point, of the electron charge density is used to unambiguously define both inter- and intramolecular bonding. However, Yau et al. found that the number of intermolecular bonding interactions in hexanitrobenzene was not consistent across a range of exchange and correlation potentials. They argued that these inconsistencies make traditional QTAIM studies of impact sensitivity impractical. Received: August 6, 2012 Revised: September 27, 2012 Published: October 29, 2012 11008
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been shown that such a ridge faithfully recovers the occurrence of chemical bonds, including weak interactions.27−29 The existence of such a ridge is guaranteed by the presence of a (3, −1) CP between the two nuclei. This CP is often referred to as a bond CP. The other two types of CPs have also been correlated with features of molecular structure. A (3, +1) CP is found at the center of ring structures and is designated a ring CP. Cage structures must enclose a single (3, +3) CP,30 which is referred to as a cage CP. Bader was also able to show that a molecule or solid can be partitioned into space filling regions, called Bader atoms, in which each region contains a single nucleus bounded by a surface of zero flux in the gradient of the charge density, referred to as a zero flux surface. By virtue of being bounded by a zero flux surface, the properties of these unique regions are well-defined and additive.23,25,31,32 That is, molecular properties, e.g., energy and electron count, can be expressed as the sum of Bader atom energies. Jones and Eberhart4,24 went on to note that the topology of ρ(r)⃗ can be more fully characterized through the inclusion of the charge density ridges. In 2 dimensions, a ridge is a familiar topographic feature, the 1D-gradient path connecting mountain passes to neighboring peaks, for example. There is only one such gradient path. It is a path of locally least steep ascent terminating at the local maximum. Consequently, it is an extremum with respect to all neighboring paths.33 Similarly, a valley is the gradient path connecting a saddle point to a local minimum, and because valleys and ridges differ only by the sign of the curvature along the path, they can both be denoted generically as ridges. Because ρ(r)⃗ is a 3-dimensional field, ridges are both the gradient paths and surfaces that are extrema with respect to all neighboring gradient paths and surfaces. They are denoted by an index, n−d, where n is the dimensionality of the space and d is the number of principal directions in which the charge density is extremal.34 Explicitly including ridges in the description of the topology of ρ(r)⃗ recovers bond paths and Bader atoms. The bond path is a 1-ridge connecting bound nuclear CPs, and the surface of a Bader atom is composed of 2-ridges.4,24 Charge density ridges also provide a much richer picture of molecular structure by endowing space with a simplicial complex topology, analogous to how, in 2D, ridges partition landscapes into Maxwellʼs hillsides.35 As an example, consider once more the relief plot of the charge density in ethene at the bottom of Figure 1. A set of ridge lines terminating at one carbon atom are shown by way of black lines in this 2D slice, and the Maxwell hillside between them is shaded red. However, this relief plot is only one slice of the charge density and there are infinitely more above and below this plane. If we were to look at all of these planes together, we would find that the ridges trace out the structure shown in the top of the figure, a 3D simplex referred to as an irreducible bundle (IB). Because IBs are bounded by 2-ridges, they have well-defined and additive properties.4,24,32 They can be glued together to form chemically meaningful structures, two of which are shown in Figure 2. The structure on the left of the figure is the carbon Bader atom in ethene. It is the union of IBs around a common (3, −3) carbon CP and is the type of structure that has received the most attention, owing to the fact that it was part of the original formulation of QTAIM, but it is the union of IBs sharing a common bond CP, or the bond bundle, that decomposes a material into its constituent interand intramolecular bonds, an example of which is shown for the
The problems encountered by Yau et al. can be overcome by extending QTAIM to include bonding volumes, referred to as bond bundles.4,24 Bond bundles are less sensitive to differences in exchange and correlation potential than bond points because they are defined using global features of the charge density, as opposed to isolated points.
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TOPOLOGY OF THE CHARGE DENSITY QTAIM and its extensions derive molecular structure from a quantum mechanical observable, ρ(r)⃗ . The theory capitalizes on the fact that, as a 3-dimensional scalar field, ρ(r)⃗ possesses a topology that is partially characterized by its rank 3 critical points (CP). The CPs are the places where the charge density achieves extreme values in all three principal directions. In three-dimensional space, there are four kinds of nondegenerate rank 3 CP; local minima, local maxima, and two types of saddle points. In QTAIM, these CPs are referred to by the (rank, signature) notation, where the signature is the number of positive curvatures minus the number of negative curvatures. For example, a minimum CP has positive curvature in three orthogonal directions; therefore, it is called a (3, +3) CP. A maximum is denoted by (3, −3) because all three curvatures are negative. A saddle point with two of the three curvatures negative is denoted (3, −1), while the other saddle point is a (3, +1) CP. Bader showed that it was possible to correlate the topological properties of ρ(r)⃗ with elements of molecular structure and bonding.23,25,26 Nuclear sites were found to coincide with maxima, and the (3, −3) CP was denoted an atom, or nuclear, CP, which can be seen by way of the example in the relief plot of the charge density in ethene at the bottom of Figure 1. Here, the two large truncated maxima near the center of the plane correspond to the carbon atoms, while the 4 smaller maxima correspond to the hydrogen atoms. Bound atoms can be seen to be linked by a ridge of maximum charge density, and it has
Figure 1. Charge density relief plot in the molecular plane of ethene with a set of ridges terminating at a carbon nuclear site shown as black lines (bottom). These ridges trace the intersection of an IB with the molecular plane. The IB bundle corresponding to the red shaded area in the relief plot is shown above. 11009
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As a first example, consider the C−C bond bundle in an isolated benzene molecule. The 2-ridges bounding one such bond bundle are shown by way of gray shading in the upper left pane of Figure 4, and though the bond bundle has infinite
Figure 2. Carbon Bader atom (left) and the C−C bond bundle in ethene (right).
C−C bond in ethene on the right of Figure 2, and both the C− C and C−H bond bundles in Figure 3. Notice that no 2-ridges terminate at the H atom in the C−H bond bundle. Thus, the C−H bond bundle contains the entire Bader H atom as has been observed before.24
Figure 4. C−C (top) and C−H (bottom) bond bundles in benzene.
extent, the 2-ridges have been truncated at approximately ∼0.01 electrons/Å3. Despite this truncation, the ridges from neighboring carbon atoms can be seen to converge as they move away from the bond path in the molecular plane, making the bond bundle convergent in directions parallel to this plane. Contrast this to the behavior of the ridges in the direction normal to the ring, which can be seen in the charge density cut plane containing the 2 C atoms and a cross-section of the C−C bond bundle in the direction normal to the molecular plane, upper right pane of Figure 4. The C−C bond bundle is shaded red in this pane, and the positions of the C atoms are indicated by way of filled black circles. The ridges bounding the bond bundle in this plane clearly move apart as they move away from the nuclei. Hence, the bond bundle is divergent in the direction normal to the plane of the ring, and because the divergent/ convergent behavior can be seen at relatively large values of ρ(r)⃗ , all of the bond bundles in this study have been truncated at ∼0.01 electrons/Å3. Unlike the C−C bond bundle in benzene, the C−H bond bundle is bound only by 2-ridges terminating at the C atom, Figure 4. This topology leads to two obvious differences from a C−C bond: (i) an entire Bader atom is contained within the bond bundle (the H atom); (ii) the bond bundle is divergent in all directions because the 2-ridges terminating at the C atom do not fold over on themselves. The latter observation is typical of bond bundles that contain a Bader atom. It is also typical of nonbonding bundles because they have a similar topology. Nonbonding bundles are the irreducible bundles that are not associated with any of the bond points in a molecule. By definition, they are bound by 2-ridges that terminate at a single nuclear site. An example of an O nonbonding bundle in t-butyl mesylate is shown in the cut plane on the right of Figure 5 by
Figure 3. C−C and C−H bond bundles in ethene.
One of the advantages of investigating impact sensitivity with bond bundles is that they recover many of the properties that underly our concept of a bond. Bond order has been found to correlate with the number of electrons in a bond bundle, or bond bundle occupancy, and nonbonding or lone pair volumes also emerge.4,24 More significantly, the shape of a moleculeʼs bond bundles and nonbonding volumes have been shown to mediate functionality and stability.36,37
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BOND BUNDLE EXAMPLES Bond bundle shape can be classified into two categories: (i) divergent and (ii) convergent. The 2-ridges bounding a divergent bond bundle move apart as they move away from the bond path, while the 2-ridges bounding a convergent bond bundle come together as they move away from the bond path. To make these definitions manifest, we will now turn our attention to examples of the two types of bond bundles. 11010
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eralized gradient approximation (PBE),47 and the Becke 3parameter Lee−Yang−Parr hybrid functional by Stephens et al. (B3LYP).48 VASP calculations were performed with the VWN and PBE potentials. However, the B3LYP hybrid functional is not available in VASP version 4.6; the Perdew−Wang 91 generalized gradient approximation (PW91)49 was used as a third Vxc. Differences were observed in the number of internuclear bond points found using the different exchange and correlation potentials. The bond bundles associated with these spurious bond points were, however, infinitely thin, i.e., the bond bundle occupancy was zero. These small local differences in ρ(r)⃗ did not alter the shape or electron count of the bond bundles with a nonzero occupancy. Thus, these spurious points and paths were ignored in this study.
way of green shading. The ridges bounding the bundle clearly diverge as they move away from the O nuclear site (filled red circle).
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Figure 5. C−O bond bundle in t-butyl mesylate (left) and a crosssection of the C−O bond bundle and O nonbonding bundle (right) with the bond bundle shaded red and the nonbonding bundle shaded green.
RESULTS
To develop a correlation between impact sensitivity and bond bundle properties, we can begin by examining the relatively simple gas phase bond bundles of polynitroaromatics. It is widely believed that the C−N bonds serve as the trigger linkages in these systems, and the good correlation between gas phase C−N bond dissociation energy and impact sensitivity suggests that intermolecular bonding does not play a large role in determining their impact sensitivity. Take, for example, 1,3,5-trinitrobenzene (TNB) and hexanitrobenzene (HNB). The h50% values of these two molecules differ by nearly an order of magnitude, with HNB having a h50% of 10 cm and TNB 70 cm.5 This difference is reflected only in the shapes of their C−N bond bundles. Figure 6 shows a C−N and C−C bond bundle in HNB and TNB in the top pane and a cross-section of the C−N bond
As a final example, consider the C−O bond bundle in t-butyl mesylate, Figure 5. Inspection of the 2-ridges on the left side of the figure reveals that the bond bundle appears to be closed because the 2-ridges bounding the bundle are convergent. This behavior can clearly be seen in the cut plane on the right of the figure where the C−O bond bundle is shaded red. As the ridges move away from the bond path, they come together forming a convergent bond bundle. The two types of bond bundles have different properties. Divergent bond bundles and nonbonding volumes are susceptible to the addition of a new atom or group. Convergent bond bundles are not.36 However, unlike a divergent bond bundle, a convergent bond bundle will collapse onto its bond path under a small perturbation, reducing the occupancy of the bond bundle to zero and breaking the bond.37 This ability to relate properties with the shapes of bond bundles allows us to garner powerful qualitative insights into the behavior of both gas phase and solid state systems, much like the shapes of orbitals in frontier orbital theory offer insight into reactivity.
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METHODS The electron charge densities needed to search for possible relationships between bond bundle properties and impact sensitivity were calculated using two different packages, one for gas phase and another for solid state calculations. The Amsterdam Density Functional Package (ADF) version 2012 with a triple-ζ single polarized basis set was used to calculate the charge density of the isolated molecules.38 Solid state charge densities were calculated using the Vienna ab initio Simulation Package (VASP) version 4.6 with Projected Augmented Wave potentials.39−41 The coordinates of the atoms in the ADF calculations were allowed to relax, while the coordinates and lattice vectors in the VASP calculations were held fixed at their experimentally determined values.42−44 In all cases, the analysis of the charge densities was performed using the Tecplot software package on charge density grids with 20 points per Ångstrom.45 Calculations were performed using three different exchange and correlation potentials to examine the role of spurious bond points like those observed by Yau et al. ADF calculations were performed with the Vosko−Wilk−Nusair local density approximation (VWN),46 the Perdew−Burke−Ernzerhof gen-
Figure 6. C−N and C−C bond bundle in TNB (left) and C−N bond bundle in HNB (right). A cross-section of the C−N bond bundle in HNB is also shown (bottom). 11011
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bundle in HNB in the lower pane. Inspection of the figure reveals that the C−C bond bundles in both molecules are convergent in the plane of the ring and divergent in the direction normal to the plane of the ring. These bond bundles are nearly identical to those seen in an unsubstituted benzene molecule, Figure 4, and are expected to behave in a similar fashion. Contrast this to the C−N bond bundles. These trigger linkages are quite different in TNB and HNB. The TNB C−N bond bundle is divergent in the direction normal to the ring, albeit to a lesser extent than the C−C bond bundle, and is convergent in the plane of the ring. The HNB bond bundle is convergent in all directions. Its behavior in the direction normal to the plane of the ring can be seen in the cut plane shown in the lower half of the figure. Here, the C−N bond bundle is shaded red, and the ridges bounding it are shown as thick black lines. Notice that, as these ridges move away from the C−N bond path, they converge. The trigger linkage bond bundles in HNB and TNB are the most convergent bond bundles in these two molecules, suggesting that a trigger linkage may be associated with a convergent bond bundle. Furthermore, the C−N bond bundle in HNB is more convergent than it is in TNB because of the difference in bond bundle occupancy. Integration of the charge in a TNB C−N bond bundle yields 5 electrons, while only 3 electrons are found in a HNB C−N bond bundle. These observations are consistent with the fact that convergent bond bundles with a low electron count are associated with weak bonds.37 It is then reasonable to hypothesize that intramolecular trigger linkages in unstable molecules will have convergent bond bundles with a low occupancy. The advantage of this picture of impact sensitivity is that it can be extended to the solid state by observing how intermolecular bonding alters the shape and occupancy of trigger linkage bond bundles. In the solid state, both HNB and TNB form O···O and C···O intermolecular bond paths. These bond paths form inside the C−C intramolecular bond bundles and the O nonbonding volumes because they are the most divergent bundles in the molecules. A prototypical C···O bond path in TNB is shown by way of a dashed line in Figure 7. The 2-ridges bounding the C− N, and a C−C, bond bundle on the C atom are also shown, all of which have been truncated at ∼0.01 electrons/Å3. Figure 7 illustrates that the formation of intermolecular bond paths in TNB does not alter the shape of the intramolecular C− C or C−N bond bundles. Integration of the charge in these bundles reveals that the bond bundle occupancy is not
appreciably reduced by intermolecular bond path formation. The same observations hold true for HNB, suggesting that intermolecular bonding does not play a large role in the impact sensitivity of the polynitroaromatics because it does not alter the gas phase trigger linkages. We can now use the bond bundle picture of impact sensitivity to rationalize the experimentally observed differences between the decomposition of gas phase and solid state RDX. When the bond bundles of an isolated RDX molecule are identified, only those associated with the C−N bond path are totally convergent, Figure 8. The N−N bond bundles are
Figure 8. Two-ridges bounding a N−N bond bundle in RDX (top left) with the cross-section of the bond bundle and charge density contour lines in the indicated cut plane shown in the lower center. The 2-ridges bounding a C−N bond bundle are shown on the upper right.
convergent in the plane of the molecule but are divergent in one direction normal to that plane. The later feature can be seen most easily by way of the charge density contour plot in Figure 8, which shows the cross-section of the N−N bond bundle in the plane normal to the ring. The ridges bounding the bond bundle, thick black lines, converge as they move away from the bond path below the ring. However, they are nearly parallel as they move away from the bond path in the direction above the ring. These features indicate that, in the gas phase, the C−N bond bundle is more prone to collapse than the N−N bond bundle. The integrated charges in the gas phase RDX bond bundles also suggest that the C−N bond bundle is less stable than the N−N bundle. The convergent C−N bond bundle was found to contain approximately 3.5 electrons. The partially divergent N− N bond bundle contains four electrons. Together, these observations suggest that the primary decomposition channel in gas phase RDX will be C−N bond rupture, in agreement with experimental results.15,16 In the solid state, RDX forms intermolecular bond paths inside the O nonbonding volumes and N−N bond bundles. The C−N bond bundles are left relatively unperturbed by these intermolecular bond paths. The intramolecular N−N bond bundles, however, donate electrons to the N···N intermolecular bond bundles and become convergent as shown in Figure 9.
Figure 7. C−N bond bundle in crystalline TNB near an intermolecular C···O bond path (left). The same C−N, and a C−C, bond bundle viewed from the top (right). The intermolecular bond path is shown by way of a black dashed line. 11012
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Figure 9. Two-ridges bounding a N−N bond bundle in α-RDX (top right). Cut planes showing the electron charge density and the crosssection of the N−N bond bundle (bottom). The intermolecular bond path is shown by way of a black dashed line.
The top frame of Figure 9 shows two RDX molecules in αRDX. A single N···N intermolecular bond bundle is shown by way of a dashed line along with an intramolecular N−N bond bundle. Cross-sections of the N−N bond bundle are shown in the bottom of the figure. Comparing Figure 9 to Figure 8 reveals that the intramolecular N−N bond bundle closes in response to the formation of the intermolecular N···N bond path. When the bond bundle changes shape, it also loses charge to the intermolecular bond bundle, reducing its electron count to 3. Thus, the N−N bond bundle in α-RDX has the characteristics one would expect of a trigger linkage, in agreement with experiment.17−19
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CONCLUSIONS In summary, the shape of a materialʼs bond bundles and their occupancy may aid in our understanding of the origins of its impact sensitivity. Impact sensitive materials were found to have convergent bond bundles with low electron counts, while the bond bundles in less sensitive materials are divergent and have higher electron counts. It was also shown that these properties may change between the gas phase and solid state. This fact was used to rationalize the experimentally observed differences between the gas phase and solid state decomposition behavior of RDX.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS I gratefully acknowledge Betsy Rice and Mark Eberhart for their helpful discussions and support of this work by ARO under 421-20-18 and ONR under Grant No. N00014-10-1-0838. 11013
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