A Theoretical Investigation of the Ring Strain Energy, Destabilization Energy, and Heat of Formation of CL-20

The cage compound CL-20 (a.k.a., 2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane, HNIW, or 2,4,6,8,10,12-hexanitro2,4,6,8,10,12-hexaazatetracyclo[5.5.0.03,11.05,9]dodecane) is a well-studied high-energy-density material (HEDM). The high positive gas(Δ f H◦ g ) and solid(Δ f H ◦ s ) phase heat of formation values for CL-20 conformers have often been attributed to the strain energy of this cage compound and, by implication, to the conventional ring strain energy (CRSE) inherent in isowurtzitane which may be viewed as a “parent compound” (although not the synthetic precursor) of CL-20. Δ f H◦ g values and destabilization energies (DSEs), which include the contribution from CRSE, were determined by computation using a relatively new multilevel ab intio model chemistry. Compared to cubane, isowurtzitane does not have an exceptionally high CRSE. It is about the same as that of cyclopropane and cyclobutane. These investigations demonstrate that instead of the CRSE inherent in the isowurtzitane parent compound, the relatively high Δ f H◦ g and DSE values of CL-20 conformers must be due, primarily, to torsional strain (Pitzer strain), transannular strain (Prelog strain), and van der Waals interactions that occur due to the presence of the six >N–NO2 substituents that replace the six methylene (–CH2–) groups in the isowurtzitane parent compound. These conclusions are even more pronounced when 2,4,6,8,10,12-hexaazaisowurtzitane is viewed as the “parent compound.”

In addition to its use as a high explosive compound, [3] CL-20 has potential use as a propellant [6].
CL-20 is often compared to octanitrocubane (ONC) which, like CL-20, is a polynitro cage compound.Although both have many properties that recommend them for use as high explosives [7][8][9][10][11][12], economic considerations appear to limit the large scale production and usefulness of ONC [11,12].On the other hand such problems for largescale production of CL-20 appear to have been successfully addressed, although cost reduction is still an issue.CL-20 is produced commercially by ATK-Thiokol Propulsion (Brigham City, UT, USA) [13].
The relatively high heat of combustion and heat of detonation values of many HEDMs are due, in part, to their high positive heat of formation values.Octanitrocubane (ONC) is a case in point (see Scheme 3).
Estimates of gas-phase (Δ f H • g ) and solid-phase (Δ f H • s ) heat of formation values of this compound have been calculated to be ∼726 and ∼594 kJ/mol, respectively [8,9], and it is reasonable to conclude that such high heat of formation values are due, in large measure, to the considerable conventional ring strain energy (CRSE) inherent in the parent compound, cubane.
At first glance, it may appear that, like cubane, isowurtzitane and/or 2,4,6,8,10,12-hexaazaisowurtzitane may also have very high CRSEs that contribute to the high heat of formation of CL-20 (see Scheme 4).
In this study it is shown that this is not the case.Using gas-phase calculations, it was demonstrated that the CRSE inherent in isowurtzitane is relatively minor (compared to cubane, e.g., which is clearly highly strained) and the CRSEs of 2,4,6,8,10,12-hexaazaisowurtzitane conformers are exceptionally small.Thus the modestly high (compared to ONC) destabilization energy (DSE) and heat of formation values of CL-20 must be due to factors other than the CRSE inherent in the parent compound(s).

Computational Approach
2.1.Heat of Formation.Gas-phase heat of formation values were calculated using a recently described [15] multilevel ab initio model chemistry (known as T1) as implemented in the Spartan 10 (Wavefunction, Inc., Irvine, CA, USA) suite of programs.The T1 program has been described in substantial detail by Ohlinger et al. [15].Briefly this program is based on the G3MP2 model chemistry.The major differences between T1 and G3MP2 model chemistries are those in the T1 program; the MP2/6-31G(d) equilibrium geometry is substituted with an HF/6-31G(d) equilibrium geometry.The HF/6-31G(d) frequency and QCISD(T)/6-31G(d) energy steps are removed and the MP2/G3MP2 large energy step is approximated using a dual basis set RI-MP2 technique [15].
Comparing computed results with experimental values from 1805 structurally diverse compounds from the NIST database, Ohlinger et al. [15] reported this procedure to have a mean absolute error of 8.5 kJ/mol and a root mean square error of 11.5 kJ/mol.Thus it is reasonable to suggest that the values computed in this investigation have similar accuracy.

Conventional Ring Strain Energy (CRSE) and Destabilization Energy (DSE).
Conventional ring strain energies (CRSE) as described by Benson and associates [16,17] were calculated by difference using gas-phase heat of formation (Δ f H • (grp.add.)g ) values determined by group additivity theory (without consideration of ring strain energy, etc.) and the gas-phase heat of formation (Δ f H • g ) of the molecule determined by experiment or by computation, using theory (such as T1 or G3MP2) that is sufficiently robust to account for and include ring strain and other contributing factors.Thus, for gas-phase reactions, CRSE is calculated as follows: Leroy [18] makes the point that for unsubstituted cyclic compounds, destabilization energy (Leroy uses the term negative stabilization energy) is equivalent to CRSE.Thus in this study the term CRSE is used to describe strain inherent in the unsubstituted cyclic and cage compounds under investigation.In contrast to CRSE, the term destabilization energy (DSE) is used here as a more inclusive term and is reserved for characterization of substituted cyclic and cage compounds although it is calculated in precisely the same way as CRSE: Although the distinction between CRSE and DSE is somewhat arbitrary, it is warranted as it should be appreciated that for substituted cyclic and cage compounds DSE includes not only the energy contribution from ring strain but also the effects that substituents impose on the structure.For example, substituents, such as nitro groups, may increase or decrease bond angles and bond lengths (depending on placement).Furthermore van der Waals interactions between adjacent or nearby substituents will affect DSE.For nitro groups, close interaction leads to an increase in DSE.Other factors such as torsional strain (Pitzer strain) and transannular strain (Prelog strain) also contribute to DSE.
It should also be appreciated that DSE may be calculated for acyclic compounds in which CRSE, by definition, is not a factor.
The ASTM CHETAH 8.0 software program (CHETAH (The Computer Program for Chemical Thermodynamics and Energy Release Evaluation) University of South Alabama, Mobile Alabama 36688-0002 (http://www.southalabama.edu/engineering/chemical/chetah/index.html)and ASTM International (http://www.astm.org/)) was used to calculate strainless gas-phase heat of formation values (Δ f H • (grp.add.)g ) that, in turn, were used to calculate CRSE and DSE, as described above.This software uses the Benson group additivity approach.Thus the Benson group values as well as other group values provided by the software manufacturer were used in these calculations [16,17,19].

Contribution of Ring Nitrogen and Nitro Group Substituents to the DSE, (Δ f H •
(grp.add.)g ), and Δ f H • g Values of CL-20.The contributions of ring nitrogen and nitro group substituents to the DSE and Δ f H • g values of CL-20 were determined using the T1 multilevel ab initio model chemistry [15].To do this, the Δ f H • g value for CL-20 conformer HNIW-III (one of four known conformers of CL-20 See [14]) was calculated first.The Δ f H • g value for 2,4,6,8,10pentanitro-2,4,6,8,10,12-hexaazaisowurtzitane was then calculated following computational removal of one of the nitro groups from the equilibrium conformation of HNIW-III.

Δ f H •
g values for the remaining nitrohexaazaisowurtzitanes were calculated in a similar manner.The same approach was used to assess the effect of ring nitrogen substitution on Δ f H • g .Nitro groups or ring nitrogens were computationally removed in the following order N-12, N-10, N-8, N-6, N-4, and N-2.Δ f H • (grp.add.)g values were also calculated using the group additivity approach described above and DSE values were calculated using (2).All Δ f H

Conventional Ring Strain Energy (CRSE) and Heat of Formation.
Computed values for gas-phase heat of formation (Δ f H • g ), strainless heat of formation (Δ f H • (grp.add.)g ), and destabilization energy (DSE) for four CL-20 conformations as well as several other compounds directly relevant to this investigation are presented in Table 1.
The computed gas-phase heat of formation values of the four CL-20 conformations (HNIW-I, HNIW-II, HNIW-III, and HNIW-IV) range between 548.0 and 571.6 kJ/mol.Subtracting the heat of sublimation value (168.7 kJ/mol) for CL-20 calculated by Zeman and Krupka [27] yields solid phase heat of formation values for these conformations ranging from 379.3 to 402.9 kJ/mol.These values are clearly consistent with the experimentally determined solid phase heat of formation values (377.4 ± 13 and 431.0 ± 13 kJ/mol) reported for two of the crystalline polymorphs [5].
Isowurtzitane and 2,4,6,8,10,12-hexaazaisowurtzitane may be thought of as the parent compounds (although not the synthetic precursors) of CL-20.Similarly cubane may be thought of as the parent compound for ONC.Thus it was informative to compute the Δ f H The values in parentheses for octanitrocubane are the heat of formation value calculated by Zhang and Xiao [8] and values calculated using this heat of formation.
Other values in parentheses are those reported in, or calculated using, those referenced in the NIST Chemistry WebBook (http://webbook.nist.gov/chemistry/)or in the CRC's Standard Thermodynamic Properties of Chemical Substances.HAIW refers to 2,4,6,8,10,12-hexaazaisowurtzitane.compounds may contribute to the Δ f H • g values of CL-20 and ONC.These values are also presented in Table 1.

HNIW I HNIW II HNIW III HNIW IV
One characteristic of ONC that makes it a high-energy compound is the fact that the cubane cage imposes tremendous ring strain on the compound and it is the ring strain that is inherent in the cubane cage that imparts a very substantial contribution to the Δ f H • g and DSE of ONC.Several experimental and computed values for the CRSE (destabilization energy) of cubane have been reported (see [28] and references therein).These values range between 656.9 and 707.6 kJ/mol and are consistent with the value (685.8 kJ/mol) calculated in this investigation (Table 1).It should also be appreciated that substitution of the eight hydrogens in cubane by eight nitro groups to form ONC leads to a more negative Δ f H • (grp.add.)g , and this contributes substantially to the exceptionally high DSE of ONC.
Because ONC and CL-20 are both polynitro cage compounds, it is tempting to assume that the high heat of formation values characteristic of both compounds are due, in large measure, to ring strain inherent in the parent cage compounds (i.e., their CRSE).This is clearly true for ONC.However, this is not the case for CL-20.Data presented in Table 1 shows that the calculated CRSE (destabilization energy) of isowurtzitane is only 108.0 kJ/mol.Although this value is not inconsequential (it is about the same as that observed for cyclopropane and cyclobutane), it is much less than the CRSE of cubane (CRSE = 685.8kJ/mol), a compound that clearly deserves to be called "highly strained."This comparison is even more striking when calculated CRSEs are expressed on a per carbon basis.When analyzed in this manner, the CRSE for isowurtzitane per carbon is even less than that observed for cyclopropane and cyclobutane and almost ten times less than that observed for cubane (Table 1).
An even more appropriate comparison involves 2,4,6,8,10,12-hexaazaisowurtzitane.When CRSEs (destabilization energies) for four conformers of 2,4,6,8,10,12hexaazaisowurtzitane (derived from HNIW-I, HNIW-II, HNIW-III, and HNIW-IV) were calculated, values were found to range from −34.8 to −2.2 kJ/mol.Negative CRSE or DSE values are more properly known as stabilization energies (SEs) and are clearly not responsible for the high Δ f H • g and DSE of the CL-20 conformers.The major point of comparison between Figures 2(a) and 2(b) involves the effect of substituting -NO 2 groups for hydrogens on nitrogens in 2,4,6,8,10,12hexaazaisowurtzitane.In Figure 2(a), such substitutions result in a decrease in Δ f H • (grp.add.)g (closed triangles), whereas in Figure 2(b) this substitution results, initially, in a decrease of Δ f H • g (closed triangles), but as more -NO 2 groups are added, a substantial increase is observed due to a combination of torsional strain (Pitzer strain), transannular strain (Prelog strain), and van der Waals interactions between the six >N-NO 2 substituents.

Effect of -NH-and -NO
It should be pointed out that such strain and interactions result because, in contrast to noncage or acyclic compound, the parent cage compounds presents a rigid scaffold that substantially limits bond rotation to relieve or minimize strain, and van der Waals interactions.
Finally, the effect on DSE and Δ f H • g of substituting -NO 2 groups for hydrogens in >C-H groups in cubane is compared with the effect of substituting -NO 2 groups for hydrogens in >N-H groups in 2,4,6,8,10,12-hexaazaisowurtizane (Figure 3).Also presented and compared (Figure 3) is the effect on DSE and Δ f H • g caused by substituting -CH 2 -groups in isowurtzitane with >N-NO 2 groups.In all cases, these substitutions increase the DSE relative to the parent compounds and the preceding compound in these substitution series.Figure 3 also nicely demonstrates that, relative to cubane, the CRSE inherent in isowurtzitane and 2,4,6,8,10,12hexaazaisowurtzitane have a comparatively minor effect on the DSE (and therefore on the Δ f H • g ) of CL-20.

Conclusions
It is known that the high Δ f H • g and DSE values characteristic of octanitrocubane are due, in large measure, to the high Δ f H • g and CRSE values inherent in and characteristic of cubane, its highly strained parent compound.
The situation for CL-20, however, is different.Isowurtzitane and 2,4,6,8,10,12-hexaazaisowurtzitane can be viewed as parent compounds (but not synthetic precursors) of CL-20, but neither of these compounds have exceptionally high CRSE values.This is due to the fact that the bond angles in these compounds are not as highly strained as the 90 • CCC bond angles in cubane and ONC.
Thus the high Δ f H • g and modestly high DSE values characteristic of CL-20 conformers are not due to high CRSE values of the parent compound(s).Instead, the high Δ f H • g and modestly high DSE values of CL-20 conformers must be due, in large measure, to torsional strain (Pitzer strain), transannular strain (Prelog strain), and van der Waals interactions that occur due to the presence of the six >N-NO 2 substituents that are present in this HEDM.Such strain and interactions result or are enhanced because the parent cage compounds presents a rigid scaffold that substantially limits bond rotation that would otherwise relieve or minimize strain and van der Waals interactions.It should be appreciated that the group contribution energies characteristic of the >N-NO 2 groups provide the greatest contribution to the Δ f H • g and DSE of CL-20.

Table 1 :
Comparison of the strainless gas-phase heat of formation, destabilization energy, and gas-phase heat of formation of CL-20, ONC, and other relevant compounds of interest.
• g values, Δ f H • (grp.add.)g values, and CRSE values for these compounds to determine and compare how the cage structures of the parent Figure 3: The effect on DSE and Δ f H • g of substituting -NO 2 groups for hydrogens in >C-H groups in cubane compared with (1) the effect of substituting -NO 2 groups for hydrogens in >N-H groups in 2,4,6,8,10,12-hexaazaisowurtizane and (2) the effect of substituting -CH 2 -groups in isowurtzitane with >N-NO 2 groups.Note: for compounds having no −NO 2 substituents, CRSE = DSE.Open circles: CRSE and DSE values for cubane and nitrocubanes, open triangles: CRSE and DSE values for 2,4,6,8,10,12-hexaazaisowurtzitane and -NO 2 substituted 2,4,6,8,10,12-hexaazaisowurtzitanes, open squares: CRSE and DSE values for isowurtzitane and >N-NO 2 substituted isowurtzitane (i.e., nitroazaisowurtzitanes). Closed circles: Δ f H • g of cubane and nitrocubanes, closed triangles: Δ f H • 2 Substitutents on CRSE, DSE and Heat of Formation.Figures 2(a) and 2(b) present the relative effects of successive -NH-, -NO 2 and >N-NO 2 group substitutions on the heat of formation of isowurtzitane.In Figure2(a), only the strainless group contribution to gas phase heat of formation (Δ f H • (grp.add.)g ) values is