Stability of Carbon-Nitrogen Cages in Fourfold Symmetry

Abstract

Molecules consisting entirely of nitrogen have been studied extensively for their potential as high energy density materials (HEDM). Many nitrogen molecules previously studied have low-energy dissociation routes and are therefore too unstable to serve as practical HEDM. However, the incorporation of heteroatoms into a nitrogen structure can have stabilizing effects. Theoretical calculations are carried out on a sequence of high-energy cages with carbon and nitrogen. Density functional theory (B3LYP), perturbation theory (MP2 and MP4), and coupled-cluster theory (CCSD(T)) are used in conjunction with the correlation-consistent basis sets of Dunning. Stability trends as a function of molecule size are calculated and discussed.

Introduction

Nitrogen molecules have been the subjects of many recent studies because of their potential as high energy density materials (HEDM). An all-nitrogen molecule N_x can undergo the reaction N_x → (x/2) N₂, a reaction that can be exothermic by 50 kcal/mol or more per nitrogen atom^1,2. To be a practical energy source, however, a molecule N_x would have to resist dissociation well enough to be a stable fuel. Theoretical studies^3–7 have shown that numerous N_x molecules are not sufficiently stable to be practical HEDM, including cyclic and acyclic isomers with eight to twelve atoms. Cage isomers of N₈ and N₁₂ have also been shown^7–10 by theoretical calculations to be unstable. Experimental progress in the synthesis of nitrogen molecules has been very encouraging, with the N₅⁺ and N₅⁻ ions having been recently produced^11,12 in the laboratory. More recently, a network polymer of nitrogen has been produced¹³ under very high pressure conditions. Experimental successes have sparked theoretical studies^1,14,15 on other potential all-nitrogen molecules. More recent developments include the experimental synthesis of high energy molecules consisting predominantly of nitrogen, including azides^16,17 of various heteroatoms and polyazido isomers¹⁸ of compounds such as 1,3,5-triazine. Future developments in experiment and theory will further broaden the horizons of high energy nitrogen research.

The stability properties of N_x molecules have also been extensively studied in a computational survey¹⁹ of various structural forms with up to 20 atoms. Cyclic, acyclic, and cage isomers have been examined to determine the bonding properties and energetics over a wide range of molecules. A more recent computational study²⁰ of cage isomers of N₁₂ examined the specific structural features that lead to the most stable molecules among the three-coordinate nitrogen cages. Those results showed that molecules with the most pentagons in the nitrogen network tend to be the most stable, with a secondary stabilizing effect due to triangles in the cage structure. A recent study²¹ of larger nitrogen molecules N₂₄, N₃₀, and N₃₆ showed significant deviations from the pentagon-favoring trend. Each of these molecule sizes has fullerene-like cages consisting solely of pentagons and hexagons, but a large stability advantage was found for molecules with fewer pentagons, more triangles, and an overall structure more cylindrical than spheroidal. Studies^22,23 of intermediate-sized molecules N₁₄, N₁₆, and N₁₈ also showed that the cage isomer with the most pentagons was not the most stable cage, even when compared to isomer(s) containing triangles (which have 60° angles that should have significant angle strain). For each of these molecule sizes, spheroidally-shaped molecules proved to be less stable than elongated, cylindrical ones.

However, while it is possible to identify in relative terms which nitrogen cages are the most stable, it has been shown⁷ in the case of N₁₂ that even the most stable N₁₂ cage is unstable with respect to dissociation. The number of studies demonstrating the instability of various all-nitrogen molecules has resulted in considerable attention toward compounds that are predominantly nitrogen but contain heteroatoms that stabilize the structure. In addition to the experimental studies^16–18 cited above, theoretical studies have been carried out that show, for example, that nitrogen cages can be stabilized by oxygen insertion^24,25 or phosphorus substitution²⁶.

A study²⁷ of carbon-nitrogen cages showed that carbon substitution into an N₁₂ cage results in a stable N₆C₆H₆, but larger, nitrogen-richer molecules were predicted to be less stable than N₆C₆H₆. Replacement of the nitrogen triangles in N₁₂ by carbon triangles led to the stable N₆C₆H₆, but it is possible that angle strain in the triangles still influenced the stability of the molecules. In the current study, carbon-nitrogen cages are examined in fourfold symmetry rather than threefold, with carbon squares rather than triangles. Starting with a cage N₈C₈H₈, a fourfold-symmetric counterpart to N₆C₆H₆, a sequence of molecules will be tested to determine if this further relief of ring strain enhances the stability of the molecules. The stability of each carbon-nitrogen cage is determined by theoretical calculations of the energies of various dissociation pathways.

Computational Details

Geometries are optimized with density functional theory^28,29 (B3LYP) and second-order perturbation theory³⁰ (MP2). Single energy points are calculated with fourth-order perturbation theory³⁰ (MP4(SDQ)) and coupled-cluster theory³¹ (CCSD(T)). Molecules are optimized in the singlet state, and dissociation intermediates are optimized in the triplet state, which is the ground state for all dissociations in this study. (Open-shell calculations have been carried out using UHF. Spin contamination is not a significant problem. For example, for the MP2/cc-pVDZ calculations on the three intermediates of N₈C₈H₈, the S² values are all between 2.03 and 2.06.) Vibrational frequencies have been calculated at the MP2/cc-pVDZ level of theory for N₈C₈H₈ and its dissociation intermediates. B3LYP/cc-pVDZ frequencies have been calculated for all intact molecules in this study. The basis sets are the double-zeta (cc-pVDZ), augmented double-zeta (aug-cc-pVDZ), and triple-zeta (cc-pVTZ) sets of Dunning³². The Gaussian03 computational chemistry software³³ has been used for all calculations in this study.

Results and Discussion

N₈C₈H₈

The smallest molecule in this study is the N₈C₈H₈ molecule shown in Figure 1. The molecule has D_4d point group symmetry and three symmetry-independent bonds. The bond dissociation energies for these bonds have been tabulated in Table 1. As with the previously-studied N₆C₆H₆, the NN bond is the weakest, but its dissociation energy is over 30 kcal/mol at the CCSD(T)/cc-pVDZ level of theory, which should be considered the most reliable calculation in Table 1. Basis set effects, calculated with MP2 theory, indicate that larger basis sets increase the bond-breaking energies slightly. Inclusion of zero-point energy decreases the bond energies, but the decrease is less than the increasing effect of the larger basis sets for the NN bond. Therefore, the actual dissociation energy for the NN bond is most likely even higher than the best cc-pVDZ calculations would indicate. The other bonds have even higher energies, so the N₈C₈H₈ molecule should resist dissociation well enough to be a stable high energy density material.

Figure 1.

N₈C₈H₈ molecule, with three symmetry-independent bonds labeled. The molecule has D_4d point group symmetry. Nitrogen atoms are shown in white, carbon atoms in gray, and hydrogen atoms are in white on the ends of the molecule.

TABLE 1.

Bond dissociation energies for the N₈C₈H₈ cage (energies in kcal/mol).

		Bonds (see Figure 1)
Energy	Geometry	CC	CN	NN
B3LYP/cc-pVDZ	B3LYP/cc-pVDZ	+65.8	+72.9	+25.0
MP2/cc-pVDZ	MP2/cc-pVDZ	+78.1	+92.3	+44.4
MP2(+ZPE)/cc-pVDZ	MP2/cc-pVDZ	+75.5	+89.7	+43.7
MP4/cc-pVDZ	MP2/cc-pVDZ	+72.3	+83.6	+35.5
CCSD(T)/cc-pVDZ	MP2/cc-pVDZ	+71.0	+80.3	+34.2
MP2/aug-cc-pVDZ	MP2/aug-cc-pVDZ	+78.2	+93.5	+46.8
MP2/cc-pVTZ	MP2/cc-pVTZ	+80.0	+95.5	+46.8
MP4/aug-cc-pVDZ	MP2/aug-cc-pVDZ	+72.3	+84.4	+37.4

Larger molecules

Since it is the nitrogen content of the molecules that provides the energy release, it is favorable to study molecules richer in nitrogen than the N₈C₈H₈, which is only 52% nitrogen by mass. The basic design of the N₈C₈H₈ has been extended to the larger molecules N₁₆C₁₂H₈ and N₂₄C₁₆H₈. These larger molecules are shown in Figures 2 and 3 and are composed of 60% and 63% nitrogen by mass, respectively. However, in the threefold symmetry study, lengthening the molecule resulted in decreasing stability. Are these larger fourfold-symmetric molecules as stable as the smaller N₈C₈H₈? Bond-breaking energies for symmetry-independent bonds (five in N₁₆C₁₂H₈ and seven in N₂₄C₁₆H₈) are tabulated in Tables 2 and 3. For these molecules, as with N₈C₈H₈, the weakest bonds are the N-N bonds. However, the bond-breaking energies are about the same as for N₈C₈H₈. The stability of these fourfold-symmetric molecules is not dependent on molecule size, which stands in contrast with the previously-studied threefold-symmetric molecules. The molecules in the current study are all stable enough to serve as high energy density materials (HEDM).

Figure 2.

N₁₆C₁₂H₈ molecule, with five symmetry-independent bonds labeled. The molecule has D_4h point group symmetry. Nitrogen atoms are shown in white, carbon atoms in gray, and hydrogen atoms are in white on the ends of the molecule.

Figure 3.

N₂₄C₁₆H₈ molecule, with seven symmetry-independent bonds labeled. The molecule has D_4d point group symmetry. Nitrogen atoms are shown in white, carbon atoms in gray, and hydrogen atoms are in white on the ends of the molecule.

TABLE 2.

Bond dissociation energies for the N₁₆C₁₂H₈ cage (energies in kcal/mol).

		Bonds (see Figure 5)
Energy	Geometry	CC1	CN1	NN	CN2	CC2
B3LYP/cc-pVDZ	B3LYP/cc-pVDZ	a	a	+25.5	a	+72.8
MP2/cc-pVDZ	MP2/cc-pVDZ	+79.2	+96.6	+45.3	+109.8	+92.3
MP4/cc-pVDZ	MP2/cc-pVDZ	+73.2	+87.1	b	+101.1	+84.7

^aGeometry optimization not successful

^bCalculation exceeds resources, due to C₁ symmetry of intermediate

TABLE 3.

Bond dissociation energies for the N₂₄C₁₆H₈ (energies in kcal/mol)

Bonds (see Figure 6)	B3LYP/cc-pVDZ	MP2/cc-pVDZ
CC1	a	+79.2
CN1	a	+96.7
NN1	+25.6	+45.1
CN2	a	+108.2
CC2	+72.6	+92.5
CN3	a	+114.7
NN2	+25.1	+45.1

^aGeometry optimization not successful

Comparison to azido compounds

Although these results indicate the possibility of an entire class of stable high-energy molecules, the general stoichiometry of these molecules in the limit of large sizes is N₂C. This means the class of fourfold-symmetric molecules has a theoretical upper limit of 70% nitrogen by mass. As stated previously, much research effort is focused on the development of high-energy azido or polyazido compounds, some of which have nitrogen composition well above 70%. The azido functionality is a straightforward way to enrich a molecular structure with nitrogen. It is therefore reasonable to ask how the molecules in Figures 1–3 compare with azido compounds in terms of energy release. Table 4 shows the energy release data for unimolecular dissociation of the three molecules in this study along with an appropriate azido compound for reference, namely triazidomethane (N₉CH). (Note: For unimolecular dissociation, it is assumed that the carbon becomes graphitic in nature. Graphitic compounds, namely benzene (C₆H₆) and coronene (C₂₄H₁₂) are chosen as products.) Triazidomethane is 91% nitrogen by mass, far richer than any molecule in this study, but it is no more energetic than N₁₆C₁₂H₈ or N₂₄C₁₆H₈, which are both less than 65% nitrogen. The reason for this is a straightforward comparison between the N-N single bonds in the molecules in the current study and the N=N double bonds in the N=N=N azido bonding group, which release less energy³⁴ upon conversion to the triple bonds in molecular N₂. Therefore, the molecules in this study have energy release properties comparable even to other high-energy molecules that are richer in nitrogen.

TABLE 4.

Free energies of unimolecular dissociation of the compounds in this study, with triazidomethane (N₉CH) included for comparison. Energies calculated using B3LYP/cc-pVDZ method. Mass percentages of nitrogen are shown for each molecule. Benzene (C₆H₆) and coronene (C₂₄H₁₂) are graphitic products that are chosen to account for carbon and hydrogen in the decomposition.

Molecule	% N	Reaction	kcal/mol	kcal/g
N8C8H8	52	N8C8H8 →4 N2+ (4/3) C6H6	−339.6	−1.6
N16C12H8	60	N16C12H8 →8 N2+ (2/3) C6H6+ (1/3) C24H12	−683.0	−1.8
N24C16H8	63	N24C16H8 →12 N2+ (2/3) C24H12	−1028.6	−1.9
N9CH	91	N9CH →(9/2) N2+ (1/6) C6H6	−243.3	−1.8

Table 5 shows the results of a similar energetic comparison, the difference being the assumption of an oxygen atmosphere. Such an atmosphere would permit not only the decomposition of the nitrogen into N₂ but also combustion of the hydrocarbon content. The energies in Table 5, therefore, include the energies from Table 4 and an additional contribution from the carbon. Not surprisingly, the data in Table 5 vary strongly by the carbon content of each molecule. The triazidomethane had the smallest hydrocarbon contribution to the energy because it has the smallest percentage of hydrocarbon content. The energies of the fourfold-symmetric molecules in this study decrease with increasing size because of decreasing hydrocarbon content. In an oxygen atmosphere, the hydrocarbon content of the molecules in this study provide an even greater energy release relative to azido compounds that are richer in nitrogen.

TABLE 5.

Free energies of dissociation of the compounds in this study, with triazidomethane (N₉CH) included for comparison. The presence of an oxygen atmosphere is assumed. Energies calculated using B3LYP/cc-pVDZ method. Mass percentages of nitrogen are shown for each molecule.

Molecule	% N	Reaction	kcal/mol	kcal/g
N8C8H8	52	N8C8H8+ 10 O2 →4 N2+ 8 CO2+ 4 H2O	−1644.2	−7.6
N16C12H8	60	N16C12H8+ 14 O2 →8 N2+ 12 CO2+ 4 H2O	−2514.1	−6.7
N24C16H8	63	N24C16H8+ 18 O2 →12 N2+ 16 CO2+ 4 H2O	−3386.3	−6.3
N9CH	91	N9CH + (5/4) O2 →(9/2) N2+ CO2+ (1/2) H2O	−406.4	−2.9

Conclusion

These fourfold-symmetric molecules represent an entire class of high-energy materials with no significant variations in stability with respect to molecule size. Successive stacking of eight-membered rings of nitrogen with four-membered rings of carbon results in molecules of arbitrary size, as well as substantial energy release properties. Also, the conversion of N-N single bonds to triple bonds is sufficiently energetic to overcome the limitations of the N₂C stoichiometry of the molecules in the current study. N₈C₈H₈, N₁₆C₁₂H₈, and N₂₄C₁₆H₈, as well as their larger analogues, all have the ability to serve as high energy density materials (HEDM).