NANO LETTERS
Nitrogen Violation of the Isolated Pentagon Rule
2006 Vol. 6, No. 5 890-895
Christopher P. Ewels* LPS, CNRS UMR8502, Batıˆment 510, UniVersite´ Paris Sud, 91405 Orsay, France, and Institut des Mate´ riaux Jean Rouxel, CNRS-UniVersite´ de Nantes, UMR6502, 2 rue de la Houssinie` re, B.P. 32229, 44322 Nantes, France Received July 22, 2005; Revised Manuscript Received March 23, 2006
ABSTRACT We examine a range of fullerene isomers with and without the presence of nitrogen using density-functional-based calculations. We show that nitrogen stabilizes those with neighboring pentagons, allowing sp2 bonded carbon networks to overcome the conventional rule that paired pentagons are not allowed through energetic constraints. This implies a new family of azafullerenes containing nitrogen-stabilized pentagon pairs, many of which will be considerably smaller than C60. We discuss the relevance for nitrogen-doped nanotube structures and the topological importance for nanotube distortion and closure.
The isolated pentagon rule (IPR), one of the tenets of carbon nanoscience, was first proposed by Kroto in 19871 soon after the discovery of C60.2 It states that neighboring pentagons in a carbon network are energetically unstable, and it accounts for the stability of (Ih)C60 because this is the smallest closed-cage fullerene to obey the IPR. We show here that nitrogen substitution can violate the IPR, opening the door to a new family of azafullerene molecules containing paired pentagon structures. Paired pentagons allow fullerenes smaller than C60, new isomers with sharper surface angles, and unusual morphologies in nitrogen-doped carbon nanostructures. The IPR can be understood chemically in C60 if the molecule is considered as consisting of single (pentagon) and double (hexagon-hexagon) bonds because in this case a neighboring pentagon pair leads to chemical frustration of the two shared carbon atoms. Separating pentagons also minimizes cage strain. The IPR is observed in many carbon nanostructures,3 including closure of nanotube tips, nanotube junctions between sections of different chirality, and sections of nanotube with decreasing diameter. It is violated only in reactive smaller closed-cage fullerenes Cn (n < 60) where neighboring pentagon pairs are unavoidable. Azafullerene studies have to date concentrated on nitrogensubstituted variants of icosahedral C60. The first azafullerene species to be unambiguously identified was mono aza[60]fullerene (C59N);4,5 however, this is a chemically reactive radical species that rapidly dimerizes giving the aza[60]fullerene dimer (C59N)2.6,7 C58N2 has been observed as short-lived ionic species C58N2- in laser desorption mass spectra of pyridinophanes.8 * E-mail:
[email protected]. 10.1021/nl051421n CCC: $33.50 Published on Web 04/07/2006
© 2006 American Chemical Society
Theoretical modeling of directly N-substituted C58N2 isomers gives 1,4-substitution in the cyclohexatriene unit (N atoms on opposite sides of a hexagonal ring) as the lowest energy isomer using both semiempirical9,10 and DFT/B3LYP techniques.11,12 Magnetron sputtering experiments grew fullerene-like carbon nitride films consisting of multilayered carbon onions. Quantitative electron energy loss spectroscopy (EELS) studies coupled with density functional (DFT) calculations suggest that the onions are centered on C48N12, a molecule with the icosahedral C60 structure but one carbon per pentagon substituted by nitrogen.13 Mass spectra of arc vaporization discharge from graphite in the presence of pyrrole vapor show various peaks in the 720-900 amu range,14 assigned to C59N and C60-xNx (x ) 2n, n ) 1,23) with some missing n; however, other assignments could be imagined. Other arc vaporization studies of graphite with NH3 or N2 find a range of peaks from 328 to 868 amu.15 Alternative azafullerenes have also been proposed based on C3N4 stoichiometry such as C24N32.16,17 Theoretical studies on aza-substituted C60 have to date studied only direct N substitution into icosahedral C60.18 However, the presence of nitrogen within a graphitic network calls into question many of the underlying assumptions of the IPR. Tetrahedrally bonded nitrogen may absorb much of the local strain caused by pentagon pairs. Neighboring pentagons lead to two shared carbon atoms, which are only able to form formally single bonds; this is the stable bonding state for tetrahedrally bonded nitrogen. Thus, we might expect nitrogen to significantly stabilize paired pentagons. Alternatively, if the nitrogen rests close to planar it may donate an additional π electron to the pentagons, rendering them aromatic.
Figure 1. C58N2 (a) before and (b) after the central hexagon bond is rotated by 90°. The right-hand structure contains two pentagon pairs and is more stable by 0.54 eV. Nitrogen atoms are marked in blue; pentagons are filled in gray.
Substitutional N has been shown to bind to pentagons in the graphitic lattice;19 however, there is no work to date on the interaction of N with paired pentagons. For this reason we have modeled a variety of C60 derivatives with and without substitutional nitrogen, using a local density functional code AIMPRO.20 A 90° rotation of two C atoms about their bond center (a Stone-Wales (SW) rotation21) in icosahedral C60 moves two pentagons, leading to the formation of a C2V isomer containing two pentagon pairs (no. 1809). Our calculations show this to be 1.6 eV less stable than C60, consistent with previous work.22,23 Remarkably however, repeating this transformation for C58N2, with nitrogen sites chosen such that each lies on one of the shared pentagon sites, actually inVerts the energies. In this case the C2V isomer containing two paired pentagons is 0.54 eV more stable than its isolated pentagon equivalent (see Figure 1). We also modeled this C2V fullerene with the two nitrogen atoms in other sites, but this was the lowest energy configuration we found (the closest energetically has one N switched to the other shared site in its paired pentagon and is 0.03 eV less stable than the ground state). This structure is also 0.28 eV more stable than the previously obtained lowest energy C58N2 isomer with (1,4) N substitution,9-12 and we note that there may be other lower energy paired pentagon isomers. Thus, the ground state for the C58N2 azafullerene is not the isolated pentagon icosahedra but an alternative paired pentagon isomer; nitrogen does indeed violate the isolated pentagon rule. The bond lengths around the paired pentagons are given in Table 1 along with those for pentalene for comparison, the smallest paired pentagon molecule (a highly reactive species proposed in 192224 and finally isolated in 199725). However, because its nonpentagon bonds are all singly hydrogenated, pentalene has a different chemical structure to pentagon pairs in a carbon network. We refer hereafter to a paired pentagon containing one nitrogen atom as an “azapentalene” unit. The paired pentagon bond lengths in C58N2 are closer to those of aromatic carbon, and the long bonds in (C2V)C60 Nano Lett., Vol. 6, No. 5, 2006
Table 1. Calculated Bond Lengths (Å) for Paired Pentagons in C60 (no. 1809) Containing Two Paired Pentagons, and for the Same Unit with a Substitutional Nitrogen Atom at the Junction of r1-r2-r3a
r1 r2 r3 r4 r5
C60-SW
C58N2-SW
1.458 1.391 1.404 1.451 1.456
1.400 1.390 1.398 1.403 1.427
pentalene 1.399 1.396 1.427 1.436
1.439 1.355 1.457 1.353 1.474
a Italics indicate bonds on the opposite side of the paired pentagon to the nitrogen. Bond r4 is nearest to the other paired pentagon. In C60 we find pentagon bonds of 1.439 Å and hexagon bonds of 1.387 Å.
are shortened. This is reflected in the Kohn-Sham eigenvalues (Figure 2); for the Ih-substituted C58N2 the two donor nitrogen electrons are forced to occupy antibonding states, whereas in the SW rotated C2V isomer these electrons occupy local bonding states. The calculated infrared absorption spectra for the two C58N2 isomers discussed here are shown in Figure 3. Although the separated pentagon isomer has strong absorptions at 746 and 1588 cm-1, the signature of the paired pentagon isomer is quite different, with strongest absorption at 1398 cm-1 (C-C stretch along the top of the two azapentalene units), 689 cm-1 (out of plane wag mode for N), 1604 cm-1 (C-C stretch on hexagon-hexagon side bond neighboring azapentalene) and 1353 cm-1 (multiple C-N stretch modes within the azapentalene). Thus, notably the 1350-1400 and 689 cm-1 modes appear to be characteristic of azapentalene units. For comparison, previous calculations for C48N12 show IR absorptions at 440 and 1310 cm-1,26 or 891
pentagon structures to be lower in energy than the isolated pentagon C60-xNx (x ) 2,4,6) equivalent. C54N6 has the highest nitrogen content in a 60-atom paired pentagon cage given the restriction of one N atom per paired pentagon. In the literature there are a significant number of publications devoted to the molecule C48N12, a structural analogy of (Ih)C60 with one carbon atom per isolated pentagon replaced by nitrogen. Given the stability shown in the above structures for nitrogen-containing paired pentagon isomers over their isolated pentagon counterparts, this suggests that the current models for C48N12 may not be stable. Although we cannot compare these directly to paired pentagon analogues, we find a system containing C48N12 and C60 together is 2.7 eV less stable than a system containing two C54N6 paired pentagon molecules. Experimental assignment of C48N12 used quantitative electron energy loss spectroscopy to study N-containing carbon onion structures.13 However the 1 nm probe size makes it difficult to exclude the N signal from the surrounding shells of the carbon onion, and in addition because the signal is taken in transmission it is difficult to deconvolute the fullerene signal from that of the surrounding shells. We suggest it may therefore be prudent to revisit the models of C48N12. Figure 2. Calculated Kohn-Sham eigenvalues in electronvolts around the HOMO-LUMO gap for (a) classic (Ih) C60, (b) (C2V) C60 with one bond rotation (two sets of paired pentagons, no. 1809), (c) C58N2 (Figure 1a), and (d) C58N2 (Figure 1b). Filled (empty) squares show filled (empty) states.
Figure 3. Calculated infrared absorption spectra for the two isomers of C58N2 shown in Figure 1. The thick solid line is the paired pentagon isomer 1b; the thin dotted line is isolated pentagon isomer 1a. The lower energy paired pentagon isomer shows characteristic absorption features in the 1350-1400 cm-1 range.
584, 1309, and 1169 cm-1,27 depending on the isomer and level of theory. It is possible to produce other C60 isomers containing different numbers of paired pentagons, up to that shown in Figure 4 where all 12 pentagons are paired (in two “rows” of three). For pure C60 this structure is 5.40 eV less stable than (Ih)C60, but for C54N6 it is once again more stable than the (Ih)C54N6 isolated pentagon analogue, this time by 0.85 eV. We also modeled other paired pentagon isomers with varying nitrogen content, and always found the paired 892
Just as C60 is the smallest fullerene to obey the IPR, the D3 isomer of C50 shown in Figure 5a is the smallest fullerene to contain all of its pentagons in pairs (“isolated paired pentagons” or IPP). A mixture of paired and single pentagons allows a family of smaller azafullerenes from C60-xNx to C50-xNx (Figure 51). A chlorine-functionalized (D5h)C50 fullerene, C50Cl10, has been isolated recently,28 and similar C50H10 structures were proposed as stable in the early 1990s.29 These chlorinated fullerenes differ from the azafullerenes proposed here because the two shared carbon atoms of the pentagon pairs are both functionalized, whereas our calculations show that aza-substitution for both of these atoms is not stable because of nitrogen-nitrogen repulsion. Azafullerenes smaller than C50-xNx must include at least triple pentagons (either in lines or around a central carbon); however, there is no reason to expect that nitrogen will not stabilize pentagon lines in the same fashion as pentagon pairs. Triplet pentagons occur in C28, the smallest tetrahedral fullerene structure.30 This is an open-shell fullerene,1 and early Hu¨ckel30 and MOPAC31 calculations suggested that replacing the central carbons with nitrogen should stabilize this fullerene as C24N4. Analogous to the C60 bond rotation calculation above, we considered two C50 isomers (see Figure 5), the ground state D3 isomer (Figure 5a) with six paired pentagons and an alternative D3 isomer containing two triple pentagon patches (Figure 5c), which is 3.79 eV less stable. Substituting two nitrogen atoms (at the center of each triple pentagon unit, or one atom in each of two paired pentagons) still gave the paired pentagon D3 isomer more stable (by 1.60 eV). Thus, although aza-substitution stabilizes paired pentagons it does not stabilize clustered triple pentagons to the same extent, Nano Lett., Vol. 6, No. 5, 2006
Figure 4. C54N6, two views of the same isomer containing only paired pentagons, each with a single N atom. The pentagons are arranged in two symmetric rows of three. This is 0.85 eV more stable than an C54N6 isomer obeying the IPR.
Figure 5. Structures for C50-nNn based on the C50 (a) D3 (b) D5h, and (c) D3 (two triple pentagon) isomers. (a and b) C44N6, (c) C48N2. For C50 equivalent a is the most stable, b is 0.19 eV less stable, and c is 3.79 eV less stable because of its highly distorted structure. For C44N6, nitrogen further stabilizes a, now 0.77 eV more stable than b. Nitrogen atoms are marked in blue; pentagons are filled in gray.
probably because of the large pyramidalisation angle imposed on the nitrogen by the three pentagons, which precludes π bonding with its neighbors. We note that the ground state D3 C50 isomer is 0.19 eV more stable than an alternative D5h isomer (Figure 5b) with five paired pentagons, in agreement with previous calculaNano Lett., Vol. 6, No. 5, 2006
tions.32 Substituting six nitrogen atoms (one N per paired pentagon, one in a single pentagon for D5h) gave the D3 isomer 0.77 eV more stable; that is, pairing all of the pentagons significantly stabilizes the C44N6 azafullerene (suggesting an azapentalene-based “isolated paired pentagon rule”). 893
Figure 6. Alternative unstable structural variants of C48N12 featuring -Nd and -CtN units: ring structures (equivalent to short nanotube bands) terminated with pyridinic nitrogen arranged in (a) zigzag and (b) armchair orientations, and (c) flat sheet terminated with -CtN. The C48N12 closed-cage azafullerene is significantly more stable by (a) 8.48 eV, (b) 6.69 eV, and (c) 4.45 eV (discussed further in the text).
It is possible to imagine larger cage azafullerenes built around paired rather than isolated pentagons. However, azafullerene size may ultimately be limited by the propensity of nitrogen to stabilize pentagon and paired pentagon formation. Paired pentagon stabilization is weaker or nonexistent in other species of heterofullerene. We repeated the Ih/C2V C58X2 comparison and found the C2V isomer to be more stable when X is CH (0.31 eV) or CF (0.17 eV) but less stable for P (0.18 eV) and B (1.06 eV). Because paired pentagons are only likely to form during growth, when F and H are unlikely to bind, this suggests that N should be the best candidate for the growth of stable paired pentagon fullerenes. It is possible to imagine alternative isomers once nitrogen is allowed to adopt pyridinic divalent structures or -CtN units. However, when we investigated a number of such structures (shown in Figure 6) for C48N12, we always found them to be considerably less stable than closed-cage fullerenes. This suggests that closed-cage azafullerenes will be prefer894
able where possible, although for small CxNy structures where closed cages cannot form, pyridinic bonding may still play a role. Pyridinic N-containing CxNy molecules will also be more reactive than their closed-cage cousins. Azapentalene units may also be expected in nitrogen-doped nanotubes and CNx thin films. Pentagonal pairs were proposed to account for flat 90° closed tips seen in boron nitride nanotubes.33 Although requiring a N-N shared pentagon bond, the energetic cost of this is offset against improved sphericity compared to tip closure using B-N squares34 (we note that the chemical driving force for paired pentagons in BN is very different from that of the azofullerenes described above, where pairing the pentagons serves to decrease rather than increase the sphericity). In heavily N-doped multiwalled carbon nanotubes, abrupt 90° internal “bamboo” walls are seen,35 and azapentalene units are a stable way to provide this bond angle. In addition, the internal walls of N-doped MWNTs often show buckling with 90° bond angles not visible in undoped tubes.36 The heavily Nano Lett., Vol. 6, No. 5, 2006
distorted structures of fullerene-like CNx films also contain sharp bond angles consistent with azapentalene units.13 Azapentalene units allow a range of structural and geometrical flexibility in layered CNx materials not possible in their undoped cousins. In summary, we show that substitutional nitrogen violates the isolated pentagon rule in carbon networks by stabilizing paired pentagons (azapentalene) and increasing the pentagon aromaticity. Azapentalene units allow for sharp bond angles in carbon sheets not possible in undoped systems and can explain the structural features seen in other CNx materials such as N-doped nanotubes and fullerene-like CNx thin films. In addition, they open the door to a new family of paired pentagon azafullerenes, with a wider mass range than that of pure carbon fullerenes. Many such azafullerenes will be open shell and potentially reactive, with chemical and physical properties radically different from those of conventional fullerenes. Acknowledgment. Thanks to C. Colliex, T. Minea, M. Heggie, B. Bouchet-Fabre, and O. Ste´phan for stimulating discussion, and P. Briddon and R. Jones for development of AIMPRO. This research has been supported by a Marie Curie Individual Research Fellowship of the European Community under contract no. MCFI-2002-01436. Supporting Information Available: Detailed theoretical method. This material is available free of charge via the Internet at http://pubs.acs.org. References (1) Kroto, H. W. Nature 1987, 329, 529. (2) Kroto, H. W.; Heath, J. R.; S. O’Brien, C.; Curl, R. F.; Smalley, R. E. Nature 318, 162-163 1985. (3) Carbon Nanotubes: Synthesis, Structure, Properties and Applications; Dresselhaus, M., Dresselhaus, G., Avouris, P., Eds.; Springer: Berlin, 2000. (4) Hummelen, J. C.; Knight, B.; Pavlovich, J.; Gonzlez, R.; Wudl, F. Science 1995, 269, 1554. (5) Nuber, B.; Hirsch, A. J. Chem. Soc., Chem. Commun. 1996, 1421. (6) Brown, C. M.; Beer, E.; Bellavia, C.; Cristofolini, L.; Gonzalez, R.; Hanfland, M.; Hausermann, D.; Keshavarz, M.; Kordatos, K. K.; Prassides, K.; Wudl, F. J. Am. Chem. Soc. 1996, 118, 8715. (7) Pichler, T.; Knupfer, M.; Golden, M. S.; Haffner, S.; Friedlein, R.; Fink, J.; Andreoni, W.; Curioni, A.; Keshavarz, K. M.; BellaviaLund, C.; Sastre, A.; Hummelen, J.-C.; Wudl, F. Phys. ReV. Lett. 1997, 78 22, 4249.
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