Structure and stability of C24 and B12N12 isomers

Volume 201, number 1,2,3,4

CHEMICALPHYSICSLETTERS

1 January 1993

Structure and stability of Cz4 and B12N12isomers Frank Jensen and Hans Toftlund Departmentof Chemistry,Odense University.D&S230 OdenseM.. Denmark Received 12 September 1992;in final form 7 October 1992

The structure and stability of four possible isomers of C2, and BUNr2have been investigated by means of ab initio calculations at the MP2/DZP level. The four geometries are a monocyclic ring, a graphite-likesheet and two fullerene structures. For C1. it is found that the graphite-like isomer is lowest in energy, while a B,*N,*fullerene consisting of 4- and &membered rings appears to be quite stable. It is possible that this fulltxne plays the same role for boron nitride as C, does for carbon.

1. Introduction The chemistry of fullerenes, of which Cso is the best known, has rapidly become an active area of research [ 11. The discovery that macroscopic quantities of C6ccan be obtained relatively easily has made it possible to prepare chemical derivatives of fullerenes. Recent results have also shown that some of the carbon atoms in fullerenes can be substituted by other elements like boron, nitrogen and metal atoms

[21. One of the basis building blocks of fullerenes are cyclic C6 units, corresponding to benzatriyne. A structure consisting only of fused C6 units is planar and represents graphite sheets. Introducing Smembered rings produces a curved surface, and for suitable combinations of 5- and 6-membered rings it is possible for the surface to close on itself, forming fullerenes [ 3 1. C2,, consists only of Smembered rings and Go is the smallest where all 5-membered rings are disjoint. A combination of 7- and 6-membered rings gives a negative curvature surface, which by itself is unable to give a closed surface, but instead makes three-dimensional networks [ 4,5]. Combining 5-, 6- and 7-membered rings makes structures possible where both positive and negative curvature regions exist [ 41. One may derive fullerenes smaller than C6,, either by reducing the number of 6-membered rings, or by replacing S-membered rings with 4-membered rings. The smaller 4-membered rings would increase the surface curvature and make self-

closure easier for a smaller number of carbons. However, 4-membered rings would have significantly more strain than 5-membered rings, and certain resonance structures may correspond to formal cyclobutadiene units which are recognized as destabilizing. For these reasons it is usually assumed that the most stable carbon fullerenes have structures made of 5- and 6-membered rings only. As both the graphite and diamond allotropes of carbon have boron nitride analogues, we here wish to consider whether also B,N, compounds may posses fullerene geometries. As for the all-carbon case one can consider small rings as the building blocks. A significant difference, however, is that odd-membered rings invariably will have either two boron atoms or two nitrogen atoms linked. Structures with such B2 or N2 units are likely to be significantly less stable than those with alternating BN units. This brings out the important conclusion that possible BN-fullerenes preferably should be formed from combinations of 4- and 6-membered rings, i.e. cyclic BzN2 and B3N3. The use of 4-membered, instead of 5-membered, rings for making the surface close on itself indicates that the smallest “stable” BN-fullerene (analogous to CsO) would contain less than 60 atoms. Cso is the smallest fullerene where all the 5membered rings are disjoint, and CZ4represents the smallest fullerene which can be composed of 4- and 6-membered rings having all the 4-membered rings disjoint. We here present computational evidence that B12Ni2may play the same role for boron nitride

0009-2614/93/$06.00 Q 1993 Elsevier Science Publishers B.V. All rights reserved.

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as CbOdoes for the all carbon system. For comparison purposes we have also performed calculations on Cz4. There have only been a few prior considerations of boron nitride fullerenes. La Placa et al. have suggested a B36N24analogue of Cso which contains Bz units but no N2 moieties [6]. Andreoni et al. mention the possibility of a B3,-,N3,,compound [ 71, but the stability of this isomer is probably less than the BJ6Na4isomer due to the existence of both B2 and Nz units. Neither of these are likely to represent optimum isomers due to the existence of 5-membered rings, as discussed above. Bowser and co-workers have suggested that a hybrid analog suchas C12B24N24 may be stable [ 8 1. La Placa et al. also searched for stable clusters in the ions produced by laser ablation of graphite-like boron nitride [ 6 1. Contrary to previous investigations by Becker and Dietze [ 91 they found only small mass clusters. Ca4 fulIerenes, on the other hand, have been considered several times. Three idealized compositions can be considered, a Dsd symmetric form consisting of two 6-membered rings joined by twelve 5-membered rings, an Oh symmetric form made of six 4membered ring and four 6-membered rings (a truncated octahedron), and finally an isomer with eight 3-membered rings and six g-membered rings, of O,, symmetry [ 31, The latter is not considered further since it probably is significantly less stable than the other two. Density functional calculations indicate that the [ 5,6]-isomer is more stable than the [ 4,6]isomer in terms of binding energy per atom, although the HOMO-LUMO energy gap suggests the contrary [ lo]. The latter ordering is also indicated by Hilckel MO calculations [ 3 1. INDO calculations have predicted that the [ 4,6 ] -fullerene form should have a triplet ground state [ 111. Both the [ 4,6]- and the [5,6]-isomers have been used in MNDO calculations for comparing stabilities with larger fullerenes [ 12,131. Experimental evidence suggests that C, carbon clusters with n less than 10 have linear ground states, while monocyclic isomers dominate for n between 10 and 20 [ 141. For n larger than 2 1, structures assigned to be “planar bicyclic” arise, while fullerene forms appear around n = 30 [ 141. Cs2 is the smallest cluster which can be observed by Cz extrusion of CeO, 90

1 Januaiy 1993

and Csz is in general considered to be the smallest “stable” fullerene [ 15 1. An ab initio computational study of C,, showed that of the two possible monocyclic forms, a cumulene (C=C-C-C) and an acetylenic (C=C-C=C) type, the latter is favored at the HF level, while the former is the lowest in energy at the MP2 level [ 16 1. The energy difference between the two types was calculated to be 86 kcal/mol at the MP2 level with a large AN0 basis. Possible isomeric forms have also been considered for C,, by means of ab initio techniques [ 17 1. The cyclic polyacetylene is here lower than the cumulene by x 10 kcal/mol when electron correlation is included by the MP2 procedure, but the fullerene form is predicted to be ~20 kcal/mol below the polyacetylene. The calculations alao indicate that the Czo fullerene does not have the full I,, symmetry. In the present case we have considered four isomers for Cz4 and Bi2NLZ,a monocyclic (which may be either cumulenic or polyacetylenic), a graphitelike sheet consisting of fused 6-membered rings, and the [ 5,6]- and [ 4,6]-fullerenes. Cz4 is the smallest cluster (after C,) for which a sheet structure can be made without “dangling” bonds [ 181. It formally corresponds to the hexayne of coronene.

2. Computational details Only singlet states have been considered in this work. Frequency and wavefunction stability calculations have been performed at the RHF/STO-3G level. Reported geometries have been optimized at the RHF/DZP level, except for the [5,6]-BN-fullerene which was only optimized with the STO-3G basis set, and relative energies were calculated at the MPZ/DZP level. The DZP basis is the 4s2p contraction [ 19 ] of the Huzinaga 9s5p basis [ 20 1, augmented with a single d function (exponents used were 0.70 (B), 0.75 (C) and 0.80 (N), only the 5 pure d components were included). MP2 calculations employed the frozen core approximation. All calculations employed the GAUSSIAN 90 [21] or GAUSSIAN 92 [ 221 program packages.

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3. Results and discussion As mentioned in section 1 the monocyclic Cz4 ring can either be of a cumulene type (C=C=C=C) with the full Dz.,,, symmetry, or consist of acetylene units (C-C-C=C) and have DIZh symmetry. The graphite-like structure belongs to the De,, point group while the [ 5,6]-fitllerene ideally has Dsd symmetry and the [4,6]-fullerene has Oa symmetry. The corresponding B,zNr2 species have DLlh (monocyclic), Djh (sheet), and C3 and T,, ( [ 5,6]- and [4,6]-fullerene) symmetry. Several possible B,zNr2 [ 5,6]-fullerenes can be considered, we have chosen to perform calculations on the isomer that has alternating BN units in the 6-membered rings and their adjacent bonds. This has the consequence that the atoms not part of the 6-membered rings form a ring of alternating BB and NN units. An isomer with alternating BN units in the 6-membered rings and the BB and NN units as the adjacent bonds was found to be 506 kcal/mol higher in energy at the HF/STO-3G level. The [ 4,6]fullerene has alternating BN bonds throughout. Within the above symmetry constraints each species was initially optimized at the RHF/STO-3G level and the internal stability (i.e. with respect to other singlet states) of the wavefunction was checked. The lowest energy wavefunction for the Cz4 cumulene isomer was found to be symmetry-broken [ 23 1, 72 kcal/mol lower in energy than the DZ4,,wavefunction. At the MP2/STO-3G level, however, the symmetry broken wavefunction is 173 kcal/mol higher in energy than the symmetric solution. Symmetry broken wavefunctions have also been encountered for Crs [ 161. For Cl8 the cumulene structure is 86 kcal/mol lower in energy than the polyacetylene at the MP2 level with an AN0 type basis, while the acetylenic form remains below the cumulene for CZo [ 171. In the present Czd case the acetylenic form is 68 kcal/ mol below the cumulene at the MP2/STO-3G level, indicating that the polyacetylene form may be the lowest energy monocyclic structure, although the STO-3G basis is clearly too small to make any firm conclusions. Due to the problems of symmetry breaking of the wavefunctions for the DZ4,,symmetric species only the acetylenic D12h structure is discussed below. Both the CZ4 fullerenes are UHF unstable, but the resulting UHF wavefunctions are

heavily spin contaminated and no further attempt was made to obtain non-singlet states. All the BN species are stable with respect to an UHF type wavefunction. The carbon [5,6]-fullerene was found to have a lower symmetry than the corresponding regular polyhedron. The origin of this symmetry reduction is the same as the cumulene to polyacetylene distortion. The lowest energy wavefunction corresponds to the Kekuld structure shown as A in fig. 1, and not the radiallene resonance form B. This is understandable since both 6-membered rings are aromatic in A, but not in B. The atoms not part of the 6-membered rings form a cyclic array of 12 atoms which, according to resonance form A, will have alternating single and double bonds. A perfect Dw symmetric for CZ4would require all these C-C bond lengths to be equal. At the HF level a bond alternation takes place which gives a twist angle between the two 6-membered rings of 32.9”, compared to the ideal 30”, and consequently the symmetry is lowered from Dbd to De. It is of course possible that the full symmetry may be obtained by geometry optimization at correlated levels, but as the geometries will be quite similar, the use of the HF optimized geometry will have little influence on relative energies. Two corresponding resonance forms for the [ 4,6]-fullerene are shown as C \ -

@

\

’ -

‘I /

A

B

C

D

Fi& I. Resonance structures for [ 5,6]-fidlerene (A, B) and [4,6]fullerene (C, D).

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and D in fig. 1. C has four aromatic and four radiallene 6-membered rings, while all the 6-rings in D are aromatic. Furthermore, C has six formal cyclobutadiene units compared to none for the radiallene form D. Other resonance structures can be drawn, but all of these have at least one cyclobutadiene unit. Consequently, resonance form D is expected to dominate for the [4,6]-fullerenes. The optimized geometries (see below) are consistent with these simple resonance arguments, i.e. A is representative for the [ 5,6]-fullerene while D dominates the [4,6]fullerene. At the HF/STO-3G level frequency calculations were performed which proved that all the reported structures are minima on the potential energy surface (PES ). The theoretical level is too low to be able to make quantitative predictions of vibrational spectra of these species, but the lowest frequency for all the carbon and boron nitride fullerenesis higher than 350 cm-‘, suggestingthat, kinetically, they may be quite stable. The BL2Ni2[4,6]-fullerene has nine IR active vibrations and the HF/STO-3G calculation indicates that two of these bands should completely dominate the spectrum. A calculated vibration at 1649 cm-’ has an IR intensity of 1478 km/mol and the second most intense band is at 909 cm-’ with an intensity of 666 km/mol, The remaining 7 bands have calculatedintensitiesbelow 50 km/mol, i.e. less than 4% of the strongest band. The sheet-like BlzNlz structure has six frequencies below 350 cm-’ (lowest vibration is 66 cm-‘), all of which are asymmetric with respect to the plane of symmetry. The corresponding Cz4 species has four frequencies below 350 cm-’ (lowest vibration is 81 cm-‘), again

1 January 1993

all being asymmetric with respect to the oh plane. Both the monocyclic structures are quite floppy as indicated by several low-lyingbands (nine bands below 350 cm-‘, lowest frequency is 40 cm-l for Cz4, and ten bands below 350 cm-‘, lowest frequency is 25 cm-l for B,,N,,). This might indicate that other conformations exist for such species. The HF/STO-3G geometries were re-optimized using the DZP basis set and improved estimates of relative energies were obtained by MP2 calculations on the HF optimized geometries. These results together with the orbital energies of the HOMO and LUMO are given in table 1. Drawings of the optimized geometries are shown in figs. 2 and 3. The bond distances for the monocyclic and sheet-like forms are unremarkable and conform well with expectations. Note that the monocyclic BIIN12isomer is calculated to be “cumulenic”, i.e. with equal bond lengths.The graphitic forms have characteristicshort distances for the peripheral bonds, these correspond formally to carbon-carbon triple bonds or boron nitride double bonds. The variation in bond lengths for the fullerenes confirms that resonance forms A and D (fig. 1) are dominating. For both the HF and MP2 levels of theory the lowest energy structure for C2,,is the graphite-like species. The [ 5,6]-fullerene is22 kcal/mol lower in energy than the [ 4,6 ]-isomer, as expected, while the monocyclic acetylene structure is much higher. Experimental data on cationic and anionic carbon clusters suggestthat the major isomer for Cz4is monocyclic with a small amount of a bicyclic form [ 141. Calculation at the semi-empirical AM1 and PM3 levels indicate that bicyclic isomers should be sig-

Table 1 Relative energies of species shown in figs. 2 and 3 .) C24

symmetry (MPZ/DZP) AE (HF/DZP) AE

hOM0 ~LIJMO

AC

B,zN,I

1

2

3

4

1

D12h 126.6 15.0 -0.32 -0.01 0.31

D6h 0.0 0.0 -0.32 0.02 0.34

Oh 29.8 47.9 -0.30 -0.02 0.28

D6 7.5 21.9 -0.29 -0.02 0.27

DIZb 12.7 -55.2 -0.39 0.08 0.47

2 D3h

0.0 0.0 -0.39 0.06 0.45

‘) Structure 1 is monocyclic,2 is a graphite-like sheet, 3 is [4,6]-fullerene and 4 is [ 5,6]-fullerene. ‘) On HF/STO-3G optimized geometry. Relative energies in kcal/mol, orbital energies in au.

92

3

4 Th

-93.0 -72.8 -0.43 0.10 0.53

Cl

116.4*) 156.1‘) -0.38 0.05 0.43

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1 January 1993

Fig. 2. HF/DZP optimized geomcztries for C2, (distances in A).

nitlcantly higher in energy than the monocyclic form. It is not clear what the source of this disagreement between theory and experiment is. It is unlikely that the isomer stability of the ionic species should be significantly different from the neutral cluster, but it is possible that the experimental conditions kinetically favor formation of the monocycle relative to other isomers. The MPZ/DZP level is usually found to give quite accurate relative energies, although there is little experience for systems of the current size. Extending the theoretical level to larger basis sets and inclusion of more electron correlation is currently impractical.

For Br2Nr2 we find the [4,6]-fullerene isomer to be the lowest of the four structures considered, again both at the HF and MP2 levels of theory. As anticipated, the [ 4,6]-fullerene is more stable than the [ 5,6]-isomer; the MP2 energy difference is 209 kcal/ mol. The [ 4,6]-fullerene is also more than 90 kcal/ mol below either of the two other isomers considered. This strongly suggests that the Th symmetric fullerene is an important energy minimum on the Br2NLZPES. We note that inclusion of electron correlation favors the spatially less extended structures both for the Czr and B,rN,, systems, i.e. the relative stability order fullerene :graphite-like : monocyclic 93

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483

< BNBI


Bl.O'

3 Fig. 3. HF/DZP (HF/STO_3Gin parentheses) optimized geometriesfor B12N12 (distances in A].

increases upon going from the HF to the MP2 level. The same trend is also found for Czo [ 171, and as discussed by Parasuk and AlmlBf, there is a possibility that part of this may be due to approximations in the computational procedure. The HOMO and LUMO orbital energies, which contain information on the redox properties of the compounds via Koopman’s theorem, show the same trend as the relative energies. A large HOMO-LUMO gap is traditionally associated with chemical stability, and in this respect the graphite-like C, and the 94

B,2N,2 [4,6]-fullerene are the most stable species. This measure also allows a comparison between the two systems and clearly shows that the boron-nitride compound should be significantly less reactive than the corresponding all-carbon system. The calculated HOMO-LUMO gap of 0.27 au for Czl [ 5,6]fullerene is identical to the reported value for CsOat the same level [ 241, and significantly smaller than the 0.53 au for the BLZN12[4,6]-fullerene. Taken together with the above relative energies this suggests that a [ 4,6]-fullerene BlzNlz species may be both ki-

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netically and thermodynamically stable, and that [4,6]-fullerenes in general may play the same role for boron nitride as I&6]-fullerenes do for the allcarbon system. We have made some preliminary searches for B12NL2molecules in laser desorption experiments on a synthetic amorphous boron nitride. Although a peak at 300 amu, corresponding to the leading line for B,rN,r ( “% and “B in natural abundance), has been observed, the reproducibility of the experiments is poor. Previous work by other groups [ 6,9 ] seems to indicate that B,,N, (n > m) clusters formed in the plasma tend to loose N2 and BN molecules. Incorporation of amorphous BN into a suitable host substrate which can anneal the excited B,,N,,,clusters might be a viable strategy. Work along these lines is in progress.

4. Conclusion Ab initio calculations at the MP2/DZP level for Cz4 and B12Nt2indicate that boron nitride structures analogous to carbon fullerenes should be stable species. An important difference, however, is that while [ 5,6]-fullerenes are the preferred isomers for carbon, [ 4,6 ]-fullerenes are the low energy structures for boron nitride. B12Nr2is the boron nitride analog of Go, and the computational results suggest that it has a chemical stability greater than Cb,,. The calculations also indicate that a graphite-like species is the lowest energy isomer for C2.,, although experimental evidence for the corresponding ions indicates a monocyclic geometry. The reason for this disagreement is unclear.

Acknowledgement This work was supported by a grant from the Danish Natural Science Research Council (grant No. 11-9686) to FJ. References [ I ] R.E. Smalley,Accounts Chem. Res. 25 ( 1992) 98; J.P. Hare and H.W. Kroto, Accounts Chem. Res. 25 ( 1992) 106;

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