Journal of Chemistry

Volume 2013 (2013), Article ID 960156, 6 pages

http://dx.doi.org/10.1155/2013/960156

Research Article

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

Carrie Sanders and Douglas L. Strout

Department of Physical Sciences, Alabama State University, Montgomery, AL 36101, USA

Received 25 May 2013; Revised 29 July 2013; Accepted 1 August 2013

Academic Editor: Abdou Boucekkine

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.

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.

1. Introduction

Complex nitrogen molecules are of interest for their potential as high-energy 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 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.

(a)

(b)

(c)

Figure 1: Isomers of N₂₄: (a) triangular (T) isomer, (b) square (S) isomer, and (c) hexagonal (H) isomer.

N ₂₀C 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
+40.9

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

Figure 2: Isomers 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.

N ₁₈C 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
−24.7

(a)

(b)

(c)

(d)

Figure 3: Isomers 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)

Figure 4: 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.

N ₁₆C 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
−4.1

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 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

(kcal/mol)

(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.

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/HBCU-UP Grant 0505872). Carrie Sanders is supported by NSF/HBCU-UP as an undergraduate STEM Scholar. This work was also supported by the National Institutes of Health (NIH/NCMHD 1P20MD000547-01) and the Petroleum Research Fund, administered by the American Chemical Society (PRF 43798-B6). The taxpayers of the state of Alabama in particular and the United States in general are gratefully acknowledged.

References

K. O. Christe, W. W. Wilson, J. A. Sheehy, and J. A. Boatz, “N₅⁺: a novel homoleptic polynitrogen ion as a high energy density material,” Angewandte Chemie—International Edition, vol. 38, no. 13-14, pp. 2004–2009, 1999.

A. Vij, J. G. Pavlovich, W. W. Wilson, V. Vij, and K. O. Christe, “Experimental detection of the pentaazacyclopentadienide (pentazolate) anion, cyclo-N₅,” Angewandte Chemie—International Edition, vol. 41, no. 16, pp. 3051–3054, 2002.

R. N. Butler, J. C. Stephens, and L. A. Burke, “First generation of pentazole (HN₅, pentazolic acid), the final azole, and a zinc pentazolate salt in solution: a new N-dearylation of 1-(p-methoxyphenyl) pyrazoles, a 2-(p-methoxyphenyl) tetrazole and application of the methodology to 1-(p-methoxyphenyl) pentazole,” Chemical Communications, vol. 8, pp. 1016–1017, 2003.

D. A. Dixon, D. Feller, K. O. Christe et al., “Enthalpies of formation of gas-phase N₃, N₃⁻, N₅⁺, and N₅⁻ from Ab initio molecular orbital theory, stability Predictions for N₅⁺N₃⁻ and N₅⁺N₅⁻, and experimental evidence for the instability of N₅⁺N₃⁻,” Journal of the American Chemical Society, vol. 126, no. 3, pp. 834–843, 2004.

C. Knapp and J. Passmore, “On the way to “solid nitrogen” at normal temperature and pressure? Binary azides of heavier group 15 and 16 elements,” Angewandte Chemie—International Edition, vol. 43, no. 37, pp. 4834–4836, 2004.

R. Haiges, S. Schneider, T. Schroer, and K. O. Christe, “High-energy-density materials: synthesis and characterization of N₅⁺[P(N₃)₆]⁻, N₅⁺ [B(N₃)₄]⁻, N₅⁺ [HF₂]⁻n HF, N₅⁺ [BF₄]⁻, N₅⁺ [PF₆]⁻, and N₅⁺ [SO₃F]⁻,” Angewandte Chemie—International Edition, vol. 43, no. 37, pp. 4919–4924, 2004.

M.-H. V. Huynh, M. A. Hiskey, E. L. Hartline, D. P. Montoya, and R. Gilardi, “Polyazido high-nitrogen compounds: hydrazo-and azo-1,3,5-triazine,” Angewandte Chemie—International Edition, vol. 43, no. 37, pp. 4924–4928, 2004.

T. M. Klapotke, A. Schulz, and J. McNamara, “Preparation, characterization and ab initio computation of the first binary antimony azide, Sb(N₃)₃,” Journal of the Chemical Society, Dalton Transactions, no. 14, pp. 2985–2987, 1996.

T. M. Klapotke, H. Noth, T. Schutt, and M. Warchhold, “Tetraphenylphosphonium hexaazidoarsenate(V): the first structurally characterized binary AsV-azide species,” Angewandte Chemie—International Edition, vol. 39, no. 12, pp. 2108–2109, 2000.

T. M. Klapotke, R. Krumm, P. Mayer, and I. Schwab, “Binary tellurium(IV) azides: Te(N₃)₄ and [Te(N₃)₅]⁻,” Angewandte Chemie—International Edition, vol. 42, no. 47, pp. 5843–5846, 2003.

M. I. Eremets, A. G. Gavriliuk, I. A. Trojan, D. A. Dzivenko, and R. Boehler, “Single-bonded cubic form of nitrogen,” Nature Materials, vol. 3, no. 8, pp. 558–563, 2004.

G. Chung, M. W. Schmidt, and M. S. Gordon, “An Ab initio study of potential energy surfaces for N₈ isomers,” The Journal of Physical Chemistry A, vol. 104, no. 23, pp. 5647–5650, 2000.

D. L. Strout, “Acyclic N₁₀ fails as a high energy density material,” Journal of Physical Chemistry A, vol. 106, no. 5, pp. 816–818, 2002.

M. D. Thompson, T. M. Bledson, and D. L. Strout, “Dissociation barriers for odd-numbered acyclic nitrogen molecules N₉ and N₁₁,” Journal of Physical Chemistry A, vol. 106, no. 29, pp. 6880–6882, 2002.

Q. S. Li and Y. D. Liu, “Structures and stability of N₁₁ cluster,” Chemical Physics Letters, vol. 353, no. 3-4, pp. 204–212, 2002.

Q. S. Li, H. Qu, and H. S. Zhu, “Quantum chemistry calculations of nitrogen cages N₁₀,” Chinese Science Bulletin, vol. 41, no. 14, pp. 1184–1188, 1996.

Q. S. Li and J. F. Zhao, “Theoretical study of potential energy surfaces for N₁₂ clusters,” The Journal of Physical Chemistry A, vol. 106, no. 21, pp. 5367–5372, 2002.

H. Qu, Q. S. Li, and H. S. Zhu, “Quantum chemical calculations of nitrogen cages N₁₂,” Chinese Science Bulletin, vol. 42, no. 6, pp. 462–465, 1997.

L. Gagliardi, S. Evangelisti, A. Bernhardsson, R. Lindh, and B. O. Roos, “Dissociation reaction of N₈ azapentalene to 4N₂: a theoretical study,” International Journal of Quantum Chemistry, vol. 77, no. 1, pp. 311–315, 2000.

L. Gagliardi, S. Evangelisti, P. O. Widmark, and B. O. Roos, “A theoretical study of the N₈ cubane to N₈ pentalene isomerization reaction,” Theoretical Chemistry Accounts, vol. 97, no. 1–4, pp. 136–142, 1997.

M. W. Schmidt, M. S. Gordon, and J. A. Boatz, “Cubic fuels?” International Journal of Quantum Chemistry, vol. 76, no. 3, pp. 434–446, 2000.

H. Zhou, N.-B. Wong, G. Zhou, and A. Tian, “Theoretical study on “multilayer” nitrogen cages,” Journal of Physical Chemistry A, vol. 110, no. 10, pp. 3845–3852, 2006.

H. Zhou, N.-B. Wong, G. Zhou, and A. Tian, “What makes the cylinder-shaped N₇₂ cage stable?” Journal of Physical Chemistry A, vol. 110, no. 23, pp. 7441–7446, 2006.

L. Y. Bruney, T. M. Bledson, and D. L. Strout, “What makes an N₁₂ cage stable?” Inorganic Chemistry, vol. 42, no. 24, pp. 8117–8120, 2003.

S. E. Sturdivant, F. A. Nelson, and D. L. Strout, “Trends in stability for N₁₈ cages,” Journal of Physical Chemistry A, vol. 108, no. 34, pp. 7087–7090, 2004.

D. L. Strout, “Cage isomers of N₁₄ and N₁₆:  nitrogen molecules that are not a multiple of six,” Journal of Physical Chemistry A, vol. 108, no. 49, pp. 10911–10916, 2004.

D. L. Strout, “Isomer stability of N₂₄, N₃₀, and N₃₆ cages:  cylindrical versus spherical structure,” The Journal of Physical Chemistry A, vol. 108, no. 13, pp. 2555–2558, 2004.

S. Jasper, A. Hammond, J. Thomas, L. Kidd, and D. L. Strout, “N₂₂C₂ versus N₂₄: role of molecular curvature in determining isomer stability,” Journal of Physical Chemistry A, vol. 115, no. 42, pp. 11915–11918, 2011.

J. P. Perdew and M. Ernzerhof, “Rationale for mixing exact exchange with density functional approximations,” Journal of Chemical Physics, vol. 105, no. 22, p. 9982, 1996.

M. Ernzerhof and G. E. Scuseria, “Assessment of the Perdew-Burke-Ernzerhof exchange-correlation functional,” Journal of Chemical Physics, vol. 110, no. 11, p. 5029, 1999.

C. Adamo and V. Barone, “Toward reliable density functional methods without adjustable parameters: the PBE0 model,” Journal of Chemical Physics, vol. 110, no. 13, p. 6158, 1999.

G. D. Purvis and R. J. Bartlett, “A full coupled-cluster singles and doubles model: the inclusion of disconnected triples,” Journal of Chemical Physics, vol. 76, no. 4, p. 1910, 1982.

G. E. Scuseria, C. L. Janssen, and H. F. Schaefer III, “An efficient reformulation of the closed-shell coupled cluster single and double excitation (CCSD) equations,” Journal of Chemical Physics, vol. 89, no. 12, p. 7382, 1988.

T. H. Dunning Jr., “Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen,” Journal of Chemical Physics, vol. 90, no. 2, p. 1007, 1989.

M. J. Frisch, G. W. Trucks, H. B. Schlegel, et al., Gaussian 09, Revision C.01, Gaussian, Inc., Wallingford, Conn, USA, 2010.