# Carbon Substitution on N24 Cages: Crossover between Triangular and Hexagonal Structures

Authors: Carrie Sanders; Douglas L. Strout
Journal: Journal of Chemistry
 (2013)

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## Abstract

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 N22C2 have shown that carbon inclusion narrows the gap between triangular and fullerene-like structures. In the current study, three isomers of N24 are used as frameworks for carbon substitution. Theoretical calculations are carried out on isomers of N20C4, N18C6, and N16C8, with the goal of determining what level of carbon substitution causes the carbon fullerene-like structures to become energetically preferred.


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## Body

## 1. Introduction

Complex nitrogen molecules are of interest for their potential as high-energy materials. Synthetic successes [1–4] such as the N5+ and N5- ions, as well as various azido compounds [5–10] and even a network polymer of nitrogen [11], demonstrate the potential for novel high-energy molecules. Theoretical studies of high-energy nitrogen include cyclic and acyclic compounds [12–19], as well as nitrogen cages [20–26]. A theoretical study [27] of N24 cages predicted that N24 prefers a tightly curved, cylindrical structure with triangular endcaps. Many all-nitrogen molecules dissociate with low barriers, which limits the utility of these molecules in energetic applications. Incorporation of heteroatoms such as carbon into an otherwise all-nitrogen 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 well-known behavior of carbon, whose most stable cages are spheroidal in shape and consist of pentagons and hexagons. A previous study [28] on N22C2 cages illustrated this difference between carbon and nitrogen. The triangular, cylindrical form of N22C2 is the most stable isomer, but the energy difference between the cylinder and the spheroid is less than that for the same isomers of N24. Carbon substitution stabilizes the spheroidal isomer relative to the others. Since C24 prefers a spheroidal structure, additional incremental substitution of additional carbon on N24 must necessarily lead to an energetic crossover from favoring the cylinder to favoring the spheroid. In the current study, the N22C2 results are extended by theoretical calculations to N20C4, N18C6, and so forth, to determine the cage composition at which the structural crossover occurs. Triangular, square, and hexagonal isomers from the N24 study are used as the basis for carbon substitution.


## 2. Computational Methods

Geometries are optimized with the Hartree-Fock method. Single-energy points are calculated with the PBE1PBE density functional method [29–31] 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 N24 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 N16C8. 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.


## 3. Results and Discussion

The three N24 frameworks in this study are shown in Figure 1. They include the triangular (T) cylinder, the hexagonal (H) fullerene-like spheroid, and a square (S) isomer with fourfold symmetry. Carbon atoms are substituted on these structures in C2 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 open-shell electrons. Carbon substitution isomers are selected for study based on criteria established by the N22C2 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 C4 axis. Additionally, the C2 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.Isomers of N24: (a) triangular (T) isomer, (b) square (S) isomer, and (c) hexagonal (H) isomer.
(a)
(b)
(c)N
20
C
4. The above criteria generate eight isomers of N20C4, 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 C2 pairs are far apart. This may be due to the polarization of the C–N bonds around the C2 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 N22C2 and 100 kcal/mol for N24. The progressive favoring of the hexagonal isomer with increasing carbon is evident. Additionally, square isomer S2 is less than 20 kcal/mol above T1.Table 1
Relative energies of N20C4 isomers are shown in Figure 2.  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.
Molecule
HF
PBE1PBE//HF
CCSD(T)//HF
T1 (C2h)
0.0
0.0
0.0
T2 (Cs)
+7.3
+4.8
+6.7
S1 (C2v)
+9.0
+20.5
+26.5
S2 (D2h)
+1.9
+13.9
+16.5
H1 (C2v)
+31.0
+49.9
+55.2
H2 (C2)
+21.4
+40.1
+44.0
H3 (C2)
+21.2
+39.0
+42.6
H4 (C2)
+20.1
+37.0
+40.9Isomers of N20C4: (a) isomer T1, (b) isomer T2, (c) isomer S1, (d) isomer S2, (e) isomer H1, (f) isomer H2, (g) isomer H3, and (h) isomer H4. Carbon atoms are shown in black, and nitrogen atoms are shown in yellow.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)N
18
C
6. Four isomers of N18C6 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 C3 axis while also avoiding C4 chains has three C2 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 N18C6 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 N18C6, but additional carbon substitution is still expected to favor the hexagonal isomer, which in the limit of 100% carbon would be the well-known C24 fullerene.Table 2
Relative energies of N18C6 isomers are shown in Figure 3.  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.
Molecule
HF
PBE1PBE//HF
CCSD(T)//HF
T (C3v)
0.0
0.0
0.0
S (C2v)
−55.0
−46.7
−39.5
H1 (C1)
−48.0
−32.9
−26.0
H2 (Cs)
−46.9
−31.3
−24.7Isomers of N18C6: (a) isomer T, (b) isomer S, (c) isomer H1, and (d) isomer H2. Carbon atoms are shown in black, and nitrogen atoms are shown in yellow.
(a)
(b)
(c)
(d)Isomers of N16C8: (a) isomer S, (b) isomer H1, and (c) isomer H2. Carbon atoms are shown in black, and nitrogen atoms are shown in yellow.
(a)
(b)
(c)N
16
C
8. Since the T isomer of N18C6 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 N16C8 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 N16C8, 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 N16C8 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 N14C10, N12C12, and so on would only increase the hexagonal structure’s energetic advantage.Table 3
Relative energies of N16C8 isomers are shown in Figure 4.  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.
Molecule
S (D4h)
H1 (D2)
H2 (D2d)
HF
0.0
−6.9
−4.2
PBE1PBE//HF
0.0
−4.6
+0.4
PBE1PBE
0.0
−6.0
−1.3
CCSD(T)//HF
0.0
−4.8
−0.8
CCSD(T)//PBE1PBE
0.0
−7.6
−4.1Heat 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:
(1)N20C4+48NH3⟶2C2H4+34N2H4N18C6+48NH3⟶3C2H4+33N2H4N16C8+48NH3⟶4C2H4+32N2H4
Heat of formation for NH3, C2H4, and N2H4 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 eight-carbon atoms, the molecules have a very high heat of formation. Any of the molecules in this study would be a high-energy material that releases large amounts of energy on decomposition.Table 4
Heat of formation for N20C4, N18C6, and N16C8. Energies are calculated using CCSD(T)//HF energies. Energies are in kcal/mol and kcal/g.
Molecule
Isomer
Δ
H
f  (kcal/mol)
Δ
H
f  (kcal/g)
N20C4  (M = 328 g/mol)
T1
+1003.8
+3.06
T2
+1010.5
+3.08
S1
+1030.3
+3.14
S2
+1020.3
+3.11
H1
+1059.0
+3.23
H2
+1047.8
+3.19
H3
+1046.4
+3.19
H4
+1044.7
+3.19
N18C6  (M = 324 g/mol)
T
+988.0
+3.05
S
+948.5
+2.93
H1
+962.0
+2.97
H2
+963.3
+2.97
N16C8  (M = 320 g/mol)
S
+880.1
+2.75
H1
+875.5
+2.74
H2
+879.3
+2.75


## 4. Conclusion

Following previous trends established for N24 and N22C2, 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 one-third of carbon, the N16C8 hexagonal isomer should be highly energetic and, if synthesized, have potential as a high-energy material.



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*Source: 960156-2013-08-31.xml*