Research Article  Open Access
Carrie Sanders, Douglas L. Strout, "Carbon Substitution on N_{24} Cages: Crossover between Triangular and Hexagonal Structures", Journal of Chemistry, vol. 2013, Article ID 960156, 6 pages, 2013. https://doi.org/10.1155/2013/960156
Carbon Substitution on N_{24} Cages: Crossover between Triangular and Hexagonal Structures
Abstract
Complex forms of nitrogen are of interest for their potential as highenergy materials, but many allnitrogen systems lack the stability for practical highenergy applications. Inclusion of carbon atoms in an otherwise allnitrogen structure can increase stability. Nitrogen cages are known for energetically preferring cylindrical structures with triangular endcaps, but carbon cages prefer the pentagonhexagon structure of the fullerenes. Previous calculations on N_{22}C_{2} have shown that carbon inclusion narrows the gap between triangular and fullerenelike structures. In the current study, three isomers of N_{24} are used as frameworks for carbon substitution. Theoretical calculations are carried out on isomers of N_{20}C_{4}, N_{18}C_{6}, and N_{16}C_{8}, with the goal of determining what level of carbon substitution causes the carbon fullerenelike structures to become energetically preferred.
1. Introduction
Complex nitrogen molecules are of interest for their potential as highenergy materials. Synthetic successes [1–4] such as the and ions, as well as various azido compounds [5–10] and even a network polymer of nitrogen [11], demonstrate the potential for novel highenergy molecules. Theoretical studies of highenergy nitrogen include cyclic and acyclic compounds [12–19], as well as nitrogen cages [20–26]. A theoretical study [27] of N_{24} cages predicted that N_{24} prefers a tightly curved, cylindrical structure with triangular endcaps. Many allnitrogen molecules dissociate with low barriers, which limits the utility of these molecules in energetic applications. Incorporation of heteroatoms such as carbon into an otherwise allnitrogen molecule can increase stability, but the resulting molecule would still be highly energetic. If carbon atoms are incorporated into a nitrogen cage structure, would the structure still energetically prefer a cylindrical structure?
The behavior of nitrogen stands in contrast to the wellknown behavior of carbon, whose most stable cages are spheroidal in shape and consist of pentagons and hexagons. A previous study [28] on N_{22}C_{2} cages illustrated this difference between carbon and nitrogen. The triangular, cylindrical form of N_{22}C_{2} is the most stable isomer, but the energy difference between the cylinder and the spheroid is less than that for the same isomers of N_{24}. Carbon substitution stabilizes the spheroidal isomer relative to the others. Since C_{24} prefers a spheroidal structure, additional incremental substitution of additional carbon on N_{24} must necessarily lead to an energetic crossover from favoring the cylinder to favoring the spheroid. In the current study, the N_{22}C_{2} results are extended by theoretical calculations to N_{20}C_{4}, N_{18}C_{6}, and so forth, to determine the cage composition at which the structural crossover occurs. Triangular, square, and hexagonal isomers from the N_{24} study are used as the basis for carbon substitution.
2. Computational Methods
Geometries are optimized with the HartreeFock method. Singleenergy points are calculated with the PBE1PBE density functional method [29–31] and with coupledcluster theory [32, 33] (CCSD(T)). HartreeFock is used for geometries for the following two reasons. (1) The previous study on N_{24} showed that the isomer energies do not depend strongly on the choice of geometry. (2) Some of the PBE1PBE geometry optimizations are dissociative. However, PBE1PBE optimizations have been carried out successfully for N_{16}C_{8}. All molecules in this study have been confirmed as local minima by HartreeFock vibrational frequencies. All calculations in this study are carried out with the Dunning ccpVDZ atomic orbital basis set [34]. The Gaussian09 computational chemistry software [35], along with its Windows counterpart Gaussian09W, is used for all calculations in this study.
3. Results and Discussion
The three N_{24} frameworks in this study are shown in Figure 1. They include the triangular (T) cylinder, the hexagonal (H) fullerenelike spheroid, and a square (S) isomer with fourfold symmetry. Carbon atoms are substituted on these structures in C_{2} pairs sharing a C=C double bond, whose strong bond enthalpy should lend stability to the molecule. Additionally, structures with isolated carbon atoms necessarily have either strong formal charges or openshell electrons. Carbon substitution isomers are selected for study based on criteria established by the N_{22}C_{2} study. The T isomer energetically prefers carbon substitution parallel to the long axis of the molecule. The H isomer prefers carbon substitution in the hexagons themselves, and the S isomer prefers substitution at the molecule’s equator, parallel to the C_{4} axis. Additionally, the C_{2} pairs are isolated from each other, because increasing the number of C–C bonds also increases the number of N–N bonds, which have very low bond enthalpy.
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(b)
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N_{20}C_{4}. The above criteria generate eight isomers of N_{20}C_{4}, which are shown in Figure 2. Relative energies of the eight molecules are tabulated in Table 1. Several trends appear in the data. For each structural framework, the lowest energy isomer is one in which the two C_{2} pairs are far apart. This may be due to the polarization of the C–N bonds around the C_{2} pairs; each bond would polarize the nitrogen negatively, and negatively charged nitrogens in close proximity to each other would be energetically unfavorable. Also, the lowest energy hexagonal isomer H4 is only (with CCSD(T) theory) about 40 kcal/mol higher in energy than T1, compared with an energy gap of about 70 kcal/mol for N_{22}C_{2} and 100 kcal/mol for N_{24}. The progressive favoring of the hexagonal isomer with increasing carbon is evident. Additionally, square isomer S2 is less than 20 kcal/mol above T1.

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N_{18}C_{6}. Four isomers of N_{18}C_{6} are shown in Figure 3, and their energies are shown in Table 2. The only T isomer meeting the previous criteria of carbon substitution parallel to the C_{3} axis while also avoiding C_{4} chains has three C_{2} pairs on the same end of the molecule. As the number of carbon atom pairs increases, the options for a stable triangular cage decrease rapidly. The S and H isomers of N_{18}C_{6} are much more stable than the T isomer. With three carbon pairs, the triangular isomer is no longer the most stable, and any additional carbon would further penalize the triangular framework energetically. Interestingly, the S isomer is the most stable for N_{18}C_{6}, but additional carbon substitution is still expected to favor the hexagonal isomer, which in the limit of 100% carbon would be the wellknown C_{24} fullerene.

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N_{16}C_{8}. Since the T isomer of N_{18}C_{6} is so much less stable than the others, only S and H energies are shown in Table 3. Isomer H1 is the most stable, and therefore N_{16}C_{8} is the crossover composition for the 24atom hexagonal framework. The theory methods in this study disagree as to whether isomer H2 is more stable than S for N_{16}C_{8}, but the stability of H1 is sufficient to demonstrate the crossover to favoring hexagonal structure. Table 3 also shows that geometry effects are small. PBE1PBE optimizations on all three N_{16}C_{8} isomers have been carried out, and all theory methods agree within a few kcal/mol regardless of the choice of optimization method. Isomer H1 is the most stable with all theory methods. Any further carbon substitution to N_{14}C_{10}, N_{12}C_{12}, and so on would only increase the hexagonal structure’s energetic advantage.

Heat of Formation. The energetic properties of the molecules in this study are shown in Table 4 as heat of formation calculated using CCSD(T)//HF energies. Heat of formation is calculated using the following isodesmic equations: Heat of formation for NH_{3}, C_{2}H_{4}, and N_{2}H_{4} is taken from the Computational Chemistry Comparison and Benchmark Database, http://cccbdb.nist.gov/. Since the energy release from the molecules derives from the decomposition of the nitrogen, the heat of formation of these molecules would be expected to decrease with increasing the carbon content. The energetic trend is shown in Table 4, but even with eightcarbon atoms, the molecules have a very high heat of formation. Any of the molecules in this study would be a highenergy material that releases large amounts of energy on decomposition.

4. Conclusion
Following previous trends established for N_{24} and N_{22}C_{2}, carbon substitution on nitrogen cages progressively favors the fullerenelike structures favored by allcarbon systems. With eightcarbon atoms, the hexagonal isomer crosses over all other isomers and becomes the energetically preferred form. Even with a composition of twothirds of nitrogen and onethird of carbon, the N_{16}C_{8} hexagonal isomer should be highly energetic and, if synthesized, have potential as a highenergy material.
Acknowledgments
The Alabama Supercomputer Authority is gratefully acknowledged for a grant of computer time on the SGI Altix in Huntsville, AL, USA. This work was supported by the National Science Foundation (NSF/HBCUUP Grant 0505872). Carrie Sanders is supported by NSF/HBCUUP as an undergraduate STEM Scholar. This work was also supported by the National Institutes of Health (NIH/NCMHD 1P20MD00054701) and the Petroleum Research Fund, administered by the American Chemical Society (PRF 43798B6). The taxpayers of the state of Alabama in particular and the United States in general are gratefully acknowledged.
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Copyright
Copyright © 2013 Carrie Sanders and Douglas L. Strout. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.