Carbon Substitution on N 24 Cages : Crossover between Triangular and Hexagonal Structures

Complex forms of nitrogen are of interest for their potential as high-energy materials, but many all-nitrogen systems lack the stability for practical high-energy applications. Inclusion of carbon atoms in an otherwise all-nitrogen structure can increase stability. Nitrogen cages are known for energetically preferring cylindrical structures with triangular endcaps, but carbon cages prefer the pentagon-hexagon structure of the fullerenes. Previous calculations on N 22 C 2 have shown that carbon inclusion narrows the gap between triangular and fullerene-like 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 fullerene-like structures to become energetically preferred.

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.

Computational Methods
Geometries are optimized with the Hartree-Fock method.Single-energy points are calculated with the PBE1PBE density functional method [29][30][31] and with coupled-cluster theory [32,33] (CCSD(T)).Hartree-Fock 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 Hartree-Fock vibrational frequencies.All calculations in this study are carried out with the Dunning cc-pVDZ 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.

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)   with increasing carbon is evident.Additionally, square isomer S2 is less than 20 kcal/mol above T1.
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 well-known C 24 fullerene.
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 24-atom 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.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.

Conclusion
Following previous trends established for N 24 and N 22 C 2 , carbon substitution on nitrogen cages progressively favors the fullerene-like structures favored by all-carbon systems.With eight-carbon atoms, the hexagonal isomer crosses over all other isomers and becomes the energetically preferred form.
Even with a composition of two-thirds of nitrogen and onethird of carbon, the N 16 C 8 hexagonal isomer should be highly energetic and, if synthesized, have potential as a high-energy material.

Table 1 :
Relative energies of N 20 C 4 isomers are shown in Figure2.All energies are calculated with cc-pVDZ basis set.Energies are in kcal/mol.Point group symmetries of each isomer are listed with the isomer name.

Table 2 :
Relative energies of N 18 C 6 isomers are shown in Figure3.All energies are calculated with cc-pVDZ basis set.Energies are in kcal/mol.Point group symmetries of each isomer are listed with the isomer name.

Table 3 :
Relative energies of N 16 C 8 isomers are shown in Figure 4.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 Table1.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

Table 4 :
Heat of formation for N 20 C 4 , N 18 C 6 , and N 16 C 8 .Energies are calculated using CCSD(T)//HF energies.Energies are in kcal/mol and kcal/g.
Table 3 alsoshows 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.