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Do C36 and C36H6 molecules have [36-D6h]fullerene structure?
22 September 2000
Chemical Physics Letters 328 Ž2000. 32–38 www.elsevier.nlrlocatercplett
Do C 36 and C 36 H 6 molecules have w36-D6h xfullerene structure? Akihiro Ito, Tae Monobe, Takao Yoshii, Kazuyoshi Tanaka) Department of Molecular Engineering, Graduate School of Engineering, Kyoto UniÕersity, Sakyo-ku, Kyoto 606-8501, Japan Received 19 June 2000; in final form 10 August 2000
Abstract In order to clarify whether C 36 has a fullerene structure with D6h symmetry, B3LYP calculations were performed for hydrogenated species of the putative w36-D6h xfullerene ŽC 36 H n ; n s 1, 2, 4, and 6. as well as mono- and dianions of C 36 H 6 . Contrary to the experimental results, it appears that the hydrogenated w36-D6h xfullerene no longer has a diradical character corroborating the high reactivity. If the long-lived C 36 H 6 is derived from w36-D6h xfullerene, the first electron affinity is predicted to be 0.60 eV, lower than that of intact C 36 , 2.5 eV, and, furthermore, the 13 C-NMR spectrum for C 36 H 6 would show a signal in the extremely low field region. q 2000 Elsevier Science B.V. All rights reserved.
1. Introduction The cage-like molecules containing carbon atoms less than 60 are classified into the ‘lower’ fullerene family. It has been well known that the general lower fullerenes built up only from pentagons and hexagons such as in the conventional fullerenes inevitably contain fused pentagon rings, that is, they violate the ‘isolated pentagon rule’ w1,2x and, therefore, are considered to be highly strained w3x. Thus the lower fullerenes enjoy much less popularity except for being regarded as an intermediate in the formation of C 60 , C 70 , and the higher fullerenes w4x since separation of macroscopic quantities of lower fullerenes was quite far from expectation. However, in 1998, Zettl and co-workers reported preparation of a C 36 -based solid material and identified that the constituent C 36 has a cage-like structure ) Corresponding author. Fax: q81-75-771-0172; e-mail: [email protected]
with D6h symmetry from the solid state 13 C-NMR spectrum w5x. Moreover, they also observed a large increase in electrical conductivity of the C 36 solid upon doping with alkali metals like sodium and potassium. After this discovery, several theoretical investigations were launched simultaneously w6–15x. In particular, Cohen and co-workers have indicated that a trigonal D6h –C 36 crystal is a possible candidate for high-temperature superconductor w7x. This prediction suggests that C 36 could be an interesting material next to C 60 w16,17x. It should be noted, however, that the more detailed experimental investigations on its geometrical structure have not yet appeared since the first report by Zettl’s group. This strongly indicates that C 36 is too reactive to accept the conventional structural analyses. In fact, Zettl and co-workers observed a C 36 derivative with mrz s 438, which is 6 atomic mass units Ža.m.u.. higher than that of C 36 from the time-of-flight ŽTOF. mass spectrum of the purified film sample. This indicates that reactions of the C 36 clusters with moisture takes
0009-2614r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 0 0 . 0 0 9 1 1 - 8
A. Ito et al.r Chemical Physics Letters 328 (2000) 32–38
place through the purifying process. Therefore, independent confirmation of reproduction is clearly of great importance to the fullerene science community. After a two year interval, however, Shinohara and co-workers have reported successful production of C 36 -related compounds, i.e. C 36 H 6 and C 36 H 6 O w18x. In particular, they succeeded in isolating C 36 H 6 by using a high-performance liquid chromatography ŽHPLC. technique. More importantly, from the TOF mass spectrum of the as-produced soot, rather than the signal corresponding to the intact C 36 , they found two at mrz s 436 and 452 assigned to C 36 H 4 and C 36 H 4 O. According to ‘An Atlas of Fullerenes’ w3x, 15 different isomers are possible for the C 36 fullerene molecule. Theoretically, there is no disagreement on the point that isomer 15 Žor w36-D6h xfullerene after the IUPAC nomenclature w19x. is the most probable of all the isomers Žisomer numbers are according to Ref. w3x.. Energetic stability of the lower fullerenes well correlates with the minimum possible numbers of the shared pentagon–pentagon bonds w3,20x. Of the C 36 fullerenes, isomers 14 and 15 have that minimal value of 12; isomers 9, 11, and 12 have 13 w3x. However, the issue of the relative stability of these C 36 isomers is still open to debate. Moreover, as a result of future investigations of the isolated C 36 H 6 molecule, structures other than conventional fullerenes might be established. In this Letter, some clues have been given in order to confirm whether the isolated C 36 H 6 has a w36-D6h xfullerene structure on the basis of hybrid HFrDF calculations. In particular, we focus on the reactivity of intact C 36 and its partially hydrogenated species ŽC 36 H n ; n - 6. and the magnetic properties related to the future high-resolution NMR experiment.
2. Method of calculations The geometries described in this study were fully optimized using a hybrid HFrDF method ŽB3LYP. that combines Becke’s three-parameter non-local exchange functional w21x with the non-local correlation functional of Parr and co-workers w22x using the 6-31G ) basis set w23x. Single polarization function was added for hydrogens of hydrogenated species.
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For the species with spin multiplicity, the unrestricted B3LYP ŽUB3LYP. methods were employed. Magnetic shieldings and nuclear independent chemical shifts ŽNICS. w24x were also evaluated using the gauge-independent atomic orbital ŽGIAO. method w25x with the 6-311G ) basis set w23x at B3LYPr631G ) optimized geometries. The magnetic shielding of tetramethylsilane ŽTMS. as a standard was computed at the same level of theory in order to calibrate the isotropic chemical shifts Ž d .. All calculations were performed with the GAUSSIAN 94 package of ab initio MO programs w26x.
3. Results and discussion 3.1. Importance of open-shell structures: C36 as highly reactiÕe species Although the electronic structures of w36-D6h xfullerene have been reported repeatedly in preceding papers w8,10,11,13,14x, we would like again to review the electronic structures of the isomer. The most important point is that w36-D6h xfullerene can be regarded as acene-based cage-like molecules in a geometrical sense w14x. In fact, the frontier orbitals show the corresponding features with a small HOMO–LUMO gap w10x. It is possible that this situation causes the second-order Žor pseudo-. Jahn–Teller distortion w27x. As a matter of fact, the preceding calculations result in the D6h C 6v symmetry breaking w8,10x. However, at the B3LYPr631G ) level, an energetically favored C 6v structure could not be found and, furthermore, the D6h -symmetrical structure was confirmed to be a local minimum by frequency analysis, suggesting that w36D6h xfullerene corresponds to a weak pseudo-Jahn– Teller system. As is well-known in the pseudoJahn–Teller effect, the system concerned remains stable with respect to this displacement, unless the energy gain due to the displacement surpasses the loss of energy due to elastic distortion of other bonds. In highly strained molecules such as C 36 , the loss of energy by this elastic distortion is expected to be large. Moreover, vibronic coupling is anticipated to be small when the mixing states involve nonbonding orbitals w27x. In addition, Choi and Kim also
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A. Ito et al.r Chemical Physics Letters 328 (2000) 32–38
reported that w6xcyclacene has D6h symmetry at the B3LYPr6-31G ) level w28x. According to the above arguments, we conclude that w36-D6h xfullerene maintains its D6h symmetrical structure owing to a weak pseudo-Jahn–Teller effect. More importantly, the HOMO Ž5b1u . and LUMO Ž5b 2g . are localized over the rims of the hexacene belt w10,13,14x, similar to those of polyacene andror oligoacenes w29x. These MOs have a non-bonding character and overlap each other in their spatial distributions, suggesting a strong exchange repulsion energy, which favors the triplet state. Hence a triplet diradical state of w36-D6h xfullerene is worthy of consideration as inferred from the well-known guiding principle in the chemistry of high-spin organic molecules w30x. In fact, the 3A 2u state is predicted to lie 3.7 kcal moly1 below the 1A 1g state 1 at the B3LYPr6-31G ) level w14x. On the other hand, as pointed out by Fowler and co-workers w11x, the singlet diradical state should also be considered as a plausible ground state of w36-D6h xfullerene with the small HOMO–LUMO gap. In the usual DFT scheme, it is difficult to investigate the singlet states from multi-configurational point of view. Therefore, we performed CASŽ6,6.rSTO-3G calculations of w36D6h xfullerene by using B3LYPr6-31G ) optimized geometry. As a result, it was found that the singlet state also has a diradical character Žthe fractional occupation numbers of the 1A 1g state; 9e 1g Ž0.40., 5b1u Ž0.99., 5b 2g Ž1.01., 10e 2g Ž0.05.x and furthermore, the 1A 1g state lies 0.13 kcal moly1 below the 3A 2u state. This suggests that the more reliable level of calculations should also predict the singlet ground state of w36-D6h xfullerene, although even the CASŽ6,6.r6-31G ) rrCASŽ6,6.r6-31G ) calculations are prohibitively time-consuming. In the field of cluster physics and chemistry, reactivity or stability of clusters in question is often argued in terms of valency w31–33x. In the present case, a hypervalent state of C 36 might be realized in
1 To check the closed-shell instability, we performed unrestricted B3LYP calculations for the singlet state of C 36 . However, the resulting 50:50 singlet–triplet state is found to be rather high above the closed-shell state, indicating stability of the restricted wavefunction.
connection with the fact that only the C 36 H 6 species can be isolated. Although we explored the electronic states with quintet Žtetravalent. and septet Žhexavalent. spin multiplicity, no quintet state was found in the present study and, furthermore, it was predicted that the septet state lies 31.8 kcal moly1 above the singlet state. Hence, w36-D6h xfullerene can be regarded as a divalent ’pseudoatom’. The most important point is that w36-D6h xfullerene is a very reactive species due to its diradical character. Actually, Koshio et al. could not detect the intact C 36 throughout their production process of C 36 -related compounds w18x. 3.2. Hydrogenated C36 : Is it a still reactiÕe species? As a result of an exhaustive computational search of C 36 H 6 on the assumption of the D6h carbon skeleton, Heine et al. found that thermodynamically favored structure has D 3h symmetry w34x. That structure corresponds to the highest symmetrical one in numerous possible structures. Herein, we must go a step further and clarify the point: why does the hydrogenation reaction stop at the C 36 H 6 stage? In Section 3.2, we examine the reactivity of w36D6h xfullerene by making inspection of electronic structures for some hypothetical fractionally hydrogenated C 36 derivatives; C 36 H, C 36 H 2 , C 36 H 4 , and C 36 H 6 . First, we briefly mention the geometrical features of these derivatives. 3.2.1. C36 H As described in Section 3.2, the first hydrogenation reaction is predicted to occur at the edge of the hexacene belt. The optimized structure for the C 36 H is shown in Fig. 1a. By this hydrogenation, the molecule is transformed into a C s-symmetric structure with doublet multiplicity. The bond lengthening is observed only in the vicinity of the methine carbon. Bond alternation takes place along the hydrogenated acene edge. Interestingly, the Mulliken spin density is localized over the non-hydrogenated edge of the hexacene belt ŽC1; 0.25, C2; 0.28, C3; 0.32, C4; 0.32.. This suggests that if the hydrogenation reaction occurs stepwise, the second hydrogen atom can attack any carbon atom on that edge. When
A. Ito et al.r Chemical Physics Letters 328 (2000) 32–38
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Fig. 1. Optimized geometries for Ža. C 36 H 1 , Žb. C 36 H 2 , Žc. C 36 H 4 , and Žd. C 36 H 6 at the B3LYPr6-31G ) ) level of theory. Bond lengths ˚ . are shown only for the symmetry-independent fragments and those for the competing triplet state are in italics. Hydrogen atoms are Žin A shown in black. Atom numbering except for C 36 H 6 indicates a carbon atom having a Mulliken spin density larger than 0.2.
the hydrogenation is not regiospecific, the isolated C 36 H 6 results in a mixture of many isomers. 3.2.2. C36 H2 According to the conjecture by Heine et al., the thermodynamically favored structure in C 36 H 2 n can be accounted for by a simple chemical rule of 1,4addition w33x. In the case of C 36 H 2 , the C 2v-symmetric structure is promising, as shown in Fig. 1b. As for the singlet state Ž1A 1 ., the geometrical features
are similar to those for the hydrogenated hemisphere of C 36 H 1 and, consequently, bond alternation takes place on the both edges of the cyclic hexacene belt. On the other hand, the optimized geometry with triplet multiplicity Ž3 B 2 . shows that the bond alternation is dissolved. Associated with this geometrical change, the Mulliken spin density is localized on the non-hydrogenated hemisphere ŽC1; 0.25, C2; 0.24, C3; 0.20.. Moreover, the 1A 1 state is stable by 8.0 kcal moly1 compared with the 3 B 2 state.
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A. Ito et al.r Chemical Physics Letters 328 (2000) 32–38
3.2.3. C36 H4 Based on the assumption that the additional dihydrogenation of C 36 H 4 produces the D 3h-symmetric isomer of C 36 H 6 , the C 2v-symmetric structure shown in Fig. 1c is indispensable for C 36 H 4 , although the calculated spin density distribution for the abovementioned C 36 H 2 does not support the proposed structure. Moreover, a species corresponding to C 36 H 2 was not observed by Koshio et al. w18x, suggesting that tetrahydrogenation occurs all at once. As shown in Fig. 1c, the bond lengths remain virtually unchanged for both the singlet Ž1A 1 . and triplet Ž3 B 2 . states. In the 3 B 2 state, the Mulliken spin density concentrates on the expected two carbons ŽC1 and C1X ; 0.34., to which two more hydrogen atoms are attached to generate the D 3h -symmetric C 36 H 6 . However, the 3 B 2 state lies 17.2 kcal moly1 above the 1A 1 state.
3.2.4. C35 H6 The optimized geometry of the D 3h -symmetric C 36 H 6 is shown in Fig. 1d. As a result of hexahydrogenation, this molecule can be regarded as 30electron p-system analogous to the so-called spheriphane as pointed out by Fowler and co-workers w10x. This can be clearly seen also from magnetic point of view, as described in the later section. Although calculation results of the 1,4-addition isomers of C 36 H 2 and C 36 H 4 show that the triplet state is far above the corresponding closed-shell singlet state, the possibility of existence of openshell singlet state is not abandoned. Therefore, we performed CASSCFŽ6,6.rSTO-3GrrB3LYPr631G ) ) level of calculation for these species. However, both C 36 H 2 and C 36 H 4 has no mixing configuration in contrast to the intact C 36 . To understand the reason, we examined the HOMO–LUMO gaps for C 36 , C 36 H 2 , C 36 H 4 , and C 36 H 6 . As is well known, density functional calculations often underestimate the HOMO–LUMO gap. Therefore, at the RHFr6-31G )rrB3LYPr6-31G ) Ž ) . level, we recalculated the HOMO–LUMO gap: C 36 Ž3.7 eV.; C 36 H 2 Ž5.7 eV.; C 36 H 4 Ž6.7 eV.; C 36 H 6 Ž8.4 eV.. In C 36 , the energy level of the HOMO is relatively high, whereas that of the LUMO is around -2 eV and, thus the HOMO–LUMO gap of 3.7 eV is small. Hence the configuration corresponding to the excita-
tion of two electrons from the HOMO to the LUMO can be expected to be an important contributor as well to the ground-state wavefunction. However, the HOMO–LUMO gap increases with increasing the number of attached hydrogens, indicating the difficulty of configuration-mixing, that is, having no diradical character. It is thus expected that the reactivity of the observed C 36 H 4 and C 36 H 6 is not so high when compared with the intact C 36 . This might suggest that the entity of C 36 H 6 is beyond the expectation by the previous theoretical considerations. Finally, it may be worth mentioning, incidentally, the electronic structures for mono- and dianionic species of C 36 H 6 with D 3h symmetry. In contrast to C 36 , C 36 H 6 has degenerate LUMOs and, hence, the mono- and dianion of C 36 H 6 are expected to have a Jahn–Teller-distorted structure. In fact, we found the C 2v -deformed structure for these anionic species. Relative energies for the mono- and dianion of C 36 H 6 are listed in Table 1. In the dianion, the competing triplet state with C 2v symmetry lies 3.0 kcal moly1 below the singlet state. However, these two states must be considered to be essentially isoenergetic. More importantly, DSCF adiabatic first electron affinity for C 36 H 6 is predicted to be 0.60 eV. This indicates that C 36 H 6-based material is still pertinent
Table 1 Relative energies, D Er e l , Žkcal moly1 . for some electronic states of w36-D6h xfullerene and its hydrogenated species at the ŽU.B3LYPr6-31G ) Ž ) . level Symmetry
Electronic state
D Er e l
C 36
D6h
1
C 36 H 2
C 2v C 2v C 2v C 2v D 3h C 2v C 2v C 2v
0.0 y3.7 31.8 0.0 8.0 0.0 17.2 0.0 y16.2 53.0 50.0
C 36 H 4 C 36 H 6 C 36 Hy 6 C 36 H 62y
A 1g A 2u 7 A 2u 1 A1 3 B2 1 A1 3 B2 1 X A1 2 B2 1 A1 3 B2 3
a
a Energy relative to the neutral singlet state of each hydrogenated form, where the positive value stands for the stabilization; C 36 Ž1A 1g .: y1371.2567 hartree, C 36 H 2 Ž1A 1 .: y1372.5355 X hartree, C 36 H 4 Ž1A 1 .: y1373.8098 hartree, C 36 H 6 Ž1A 1 .: y1375.0737 hartree.
A. Ito et al.r Chemical Physics Letters 328 (2000) 32–38 Table 2 Calculated 1 H-, 13 C-NMR chemical shifts Ž d , ppm. a , and NICS of C 36 H 6 at the GIAO-HFr6-311G ) ) rrB3LYPr6-31G ) ) level Atom b Žor ring center.
Intensity
d Žor NICS.
C1 C2 C3 C4 C5 H6 a b c d
1r6 1r6 1r3 1r6 1r6
214.7 181.6 178.1 80.4 171.7 5.1 y10.7 y3.2 y13.5 y6.1
a
The magnetic shielding of tetramethylsilane ŽTMS. as a standard was computed at the same level of theory in order to calibrate the isotropic chemical shifts Ž d .. b Atom numbering Žor ring center designation. corresponds to that in Fig. 1d.
to n-type doping. However, its electron-accepting ability is not so strong as that of C 36 -based one Ž DSCF adiabatic first electron affinity for w36D6h xfullerenes 2.3 eV w14x.. 3.3. NMR chemical shifts and local aromaticities for C36 H6 with D 3h symmetry It is well known that the NMR measurement directly gives the important clues to identify the structure and symmetry of isolated C 36 H 6 molecules. Here we have calculated the 1 H- and 13 C-NMR chemical shifts within the GIAO approach using the B3LYPr6-31G ) ) optimized structure. As can be seen in Table 2, the calculated chemical shifts have some notable points. First, C 36 H 6 has a magnetically and chemically independent methine carbon. The corresponding chemical shifts for its 1 H and 13 C is predicted to be 5.1 and 80.4 ppm respectively. More importantly, the most downfield chemical shift exceeds 200 ppm. As is well known in 13 C-NMR for hydrocarbons, those containing carbonyl groups or allene moieties are the only compounds that give a signal with chemical shift larger than 200 ppm, and furthermore, to the best of our knowledge, for all the isolated fullerenes, no signals have been observed in such a region. Therefore, the existence of signal
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around 200 ppm will give a strong evidence for w36-D6h xfullerene structure. On the other hand, as listed in Table 2, the calculated NICS values for C 36 H 6 show the picture that C 36 H 6 can be regarded as a kind of spheriphane, as suggested by Fowler et al. w10x; 5- and 6-membered rings having methine carbon show non-aromaticity, while the other 6-membered rings have negative large NICS values comparable with that of benzene. 4. Conclusion In order to answer the title question, we carried out quantum chemical calculations for the putative hydrogenated w36-D6h xfullerenes. Contrary to the current experimental consensus, all the hydrogenated species studied here are predicted not to have diradicaloid electronic structure, while the intact w36D6h xfullerene can be regarded as a diradical. This suggests that the hydrogenation reactions do not reach C 36 H 6 stage. Besides, judging from the spin density for C 36 H 1 , further hydrogenation reactions do not necessarily proceeds via 1,4-addition intermediates. Moreover, thermodynamically stable C 36 H 6 with D 3h symmetry has unusual carbon atoms showing 13 C-NMR chemical shift exceeding 200 ppm, giving a strong evidence for w36-D6h xfullerene structure. Acknowledgements We are grateful to Professor H. Shinohara and Mr. A. Koshio for providing preprints ŽRef. w18x. prior to publication and valuable discussion. Numerical calculations were partly carried out at the Supercomputer Laboratory of the Institute for Chemical Research of Kyoto University. References w1x T.G. Schmalz, W.A. Zeitz, D.J. Klein, G.E. Hite, J. Am. Chem. Soc. 110 Ž1988. 111. w2x H.W. Kroto, Nature ŽLondon. 329 Ž1987. 529. w3x P.W. Fowler, D.E. Manolopoulos, An Atlas of Fullerenes, Oxford University Press, New York, 1995. w4x G. von Helden, N.G. Gotts, M.T. Bowers, Nature ŽLondon. 363 Ž1993. 60.
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w5x C. Piskoti, J. Yarger, A. Zettl, Nature ŽLondon. 393 Ž1998. 771. w6x J.C. Grossman, M. Cote, ˆ ´ S.G. Louie, M.L. Cohen, Chem. Phys. Lett. 284 Ž1998. 344. w7x M. Cote, ˆ ´ J.C. Grossman, M.L. Cohen, S.G. Louie, Phys. Rev. Lett. 81 Ž1998. 697. w8x Z. Slanina, X. Zhao, E. Osawa, Chem. Phys. Lett. 290 Ž1998. 311. w9x E. Halac, E. Burgos, H. Bonadeo, Chem. Phys. Lett. 299 Ž1999. 64. w10x P.W. Fowler, T. Heine, K.M. Rogers, J.P.B. Sandall, G. Seifert, F. Zerbetto, Chem. Phys. Lett. 300 Ž1999. 369. w11x P.W. Fowler, D. Mitchell, F. Zerbetto, J. Am. Chem. Soc. 121 Ž1999. 3218. w12x R.A. Jishi, M.S. Dresselhaus, Chem. Phys. Lett. 302 Ž1999. 533. w13x M.N. Jagadeesh, J. Chandrasekhar, Chem. Phys. Lett. 305 Ž1999. 298. w14x A. Ito, T. Monobe, T. Yoshii, K. Tanaka, Chem. Phys. Lett. 315 Ž1999. 348. w15x E. Burgos, E. Halac, H. Bonadeo, Chem. Phys. Lett. 320 Ž2000. 14. w16x R.C. Haddon, Acc. Chem. Res. 25 Ž1992. 127. w17x P.-M. Allemand, K.C. Khemani, A. Koch, F. Wudl, K. Holczer, S. Donovan, G. Gruner, J.D. Thompson, Science ¨ 253 Ž1991. 301. w18x A. Koshio, M. Inakuma, T. Sugai, H. Shinohara, J. Am. Chem. Soc. 122 Ž2000. 398. w19x E.W. Godly, R. Taylor, Pure Appl. Chem. 69 Ž1997. 1411.
w20x E.E.B. Campbell, P.W. Fowler, D. Mitchell, F. Zerbetto, Chem. Phys. Lett. 250 Ž1996. 544. w21x K. Ragavachari, Theor. Chem. Acc. 103 Ž2000. 361, and references therein. w22x C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 Ž1988. 785. w23x W.J. Hehre, L. Radom, P. von R. Schleyer, J.A. Pople, Ab Initio Molecular Orbital Theory, Wiley, New York, 1986. w24x P. von R. Schleyer, C. Maerker, A. Dransfeld, H. Jiao, N.J.R. van Hommes, J. Am. Chem. Soc. 118 Ž1996. 6317. w25x K. Wolinski, J.F. Hilton, P. Pulay, J. Am. Chem. Soc. 112 Ž1990. 8251. w26x M.J. Frisch et al., GAUSSIAN 94, Revision, D.4, Gaussian, Inc., Pittsburgh, PA, 1995. w27x I.B. Bersuker, V.Z. Polinger, Vibronic Interactions in Molecules and Crystals, Springer, Berlin, 1989. w28x H.S. Choi, K.S. Kim, Angew. Chem. Int. Ed. 38 Ž1999. 2256. w29x K. Tanaka, K. Ohzeki, S. Nankai, T. Yamabe, H. Shirakawa, J. Phys. Chem. Solids 44 Ž1983. 1069. w30x W.T. Borden, in: W.T. Borden ŽEd.., Diradicals, Wiley, New York, 1982, pp. 1–72. w31x H. Muller, C. Opitz, Croatia Chem. Acta 68 Ž1995. 721. ¨ w32x H.W. Kroto, D.R.M. Walton, Chem. Phys. Lett. 214 Ž1993. 353. w33x C. Milani, C. Giambelli, H.E. Roman, F. Alasia, G. Benedek, R.A. Broglia, S. Sanguinetti, K. Yabana, Chem. Phys. Lett. 258 Ž1996. 554. w34x T. Heine, P.W. Fowler, K.M. Rogers, G. Seifert, J. Chem. Soc., Perkin Trans. 2 Ž1999. 707.
Chemical Physics Letters 328 Ž2000. 32–38 www.elsevier.nlrlocatercplett
Do C 36 and C 36 H 6 molecules have w36-D6h xfullerene structure? Akihiro Ito, Tae Monobe, Takao Yoshii, Kazuyoshi Tanaka) Department of Molecular Engineering, Graduate School of Engineering, Kyoto UniÕersity, Sakyo-ku, Kyoto 606-8501, Japan Received 19 June 2000; in final form 10 August 2000
Abstract In order to clarify whether C 36 has a fullerene structure with D6h symmetry, B3LYP calculations were performed for hydrogenated species of the putative w36-D6h xfullerene ŽC 36 H n ; n s 1, 2, 4, and 6. as well as mono- and dianions of C 36 H 6 . Contrary to the experimental results, it appears that the hydrogenated w36-D6h xfullerene no longer has a diradical character corroborating the high reactivity. If the long-lived C 36 H 6 is derived from w36-D6h xfullerene, the first electron affinity is predicted to be 0.60 eV, lower than that of intact C 36 , 2.5 eV, and, furthermore, the 13 C-NMR spectrum for C 36 H 6 would show a signal in the extremely low field region. q 2000 Elsevier Science B.V. All rights reserved.
1. Introduction The cage-like molecules containing carbon atoms less than 60 are classified into the ‘lower’ fullerene family. It has been well known that the general lower fullerenes built up only from pentagons and hexagons such as in the conventional fullerenes inevitably contain fused pentagon rings, that is, they violate the ‘isolated pentagon rule’ w1,2x and, therefore, are considered to be highly strained w3x. Thus the lower fullerenes enjoy much less popularity except for being regarded as an intermediate in the formation of C 60 , C 70 , and the higher fullerenes w4x since separation of macroscopic quantities of lower fullerenes was quite far from expectation. However, in 1998, Zettl and co-workers reported preparation of a C 36 -based solid material and identified that the constituent C 36 has a cage-like structure ) Corresponding author. Fax: q81-75-771-0172; e-mail: [email protected]
with D6h symmetry from the solid state 13 C-NMR spectrum w5x. Moreover, they also observed a large increase in electrical conductivity of the C 36 solid upon doping with alkali metals like sodium and potassium. After this discovery, several theoretical investigations were launched simultaneously w6–15x. In particular, Cohen and co-workers have indicated that a trigonal D6h –C 36 crystal is a possible candidate for high-temperature superconductor w7x. This prediction suggests that C 36 could be an interesting material next to C 60 w16,17x. It should be noted, however, that the more detailed experimental investigations on its geometrical structure have not yet appeared since the first report by Zettl’s group. This strongly indicates that C 36 is too reactive to accept the conventional structural analyses. In fact, Zettl and co-workers observed a C 36 derivative with mrz s 438, which is 6 atomic mass units Ža.m.u.. higher than that of C 36 from the time-of-flight ŽTOF. mass spectrum of the purified film sample. This indicates that reactions of the C 36 clusters with moisture takes
0009-2614r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 0 0 . 0 0 9 1 1 - 8
A. Ito et al.r Chemical Physics Letters 328 (2000) 32–38
place through the purifying process. Therefore, independent confirmation of reproduction is clearly of great importance to the fullerene science community. After a two year interval, however, Shinohara and co-workers have reported successful production of C 36 -related compounds, i.e. C 36 H 6 and C 36 H 6 O w18x. In particular, they succeeded in isolating C 36 H 6 by using a high-performance liquid chromatography ŽHPLC. technique. More importantly, from the TOF mass spectrum of the as-produced soot, rather than the signal corresponding to the intact C 36 , they found two at mrz s 436 and 452 assigned to C 36 H 4 and C 36 H 4 O. According to ‘An Atlas of Fullerenes’ w3x, 15 different isomers are possible for the C 36 fullerene molecule. Theoretically, there is no disagreement on the point that isomer 15 Žor w36-D6h xfullerene after the IUPAC nomenclature w19x. is the most probable of all the isomers Žisomer numbers are according to Ref. w3x.. Energetic stability of the lower fullerenes well correlates with the minimum possible numbers of the shared pentagon–pentagon bonds w3,20x. Of the C 36 fullerenes, isomers 14 and 15 have that minimal value of 12; isomers 9, 11, and 12 have 13 w3x. However, the issue of the relative stability of these C 36 isomers is still open to debate. Moreover, as a result of future investigations of the isolated C 36 H 6 molecule, structures other than conventional fullerenes might be established. In this Letter, some clues have been given in order to confirm whether the isolated C 36 H 6 has a w36-D6h xfullerene structure on the basis of hybrid HFrDF calculations. In particular, we focus on the reactivity of intact C 36 and its partially hydrogenated species ŽC 36 H n ; n - 6. and the magnetic properties related to the future high-resolution NMR experiment.
2. Method of calculations The geometries described in this study were fully optimized using a hybrid HFrDF method ŽB3LYP. that combines Becke’s three-parameter non-local exchange functional w21x with the non-local correlation functional of Parr and co-workers w22x using the 6-31G ) basis set w23x. Single polarization function was added for hydrogens of hydrogenated species.
33
For the species with spin multiplicity, the unrestricted B3LYP ŽUB3LYP. methods were employed. Magnetic shieldings and nuclear independent chemical shifts ŽNICS. w24x were also evaluated using the gauge-independent atomic orbital ŽGIAO. method w25x with the 6-311G ) basis set w23x at B3LYPr631G ) optimized geometries. The magnetic shielding of tetramethylsilane ŽTMS. as a standard was computed at the same level of theory in order to calibrate the isotropic chemical shifts Ž d .. All calculations were performed with the GAUSSIAN 94 package of ab initio MO programs w26x.
3. Results and discussion 3.1. Importance of open-shell structures: C36 as highly reactiÕe species Although the electronic structures of w36-D6h xfullerene have been reported repeatedly in preceding papers w8,10,11,13,14x, we would like again to review the electronic structures of the isomer. The most important point is that w36-D6h xfullerene can be regarded as acene-based cage-like molecules in a geometrical sense w14x. In fact, the frontier orbitals show the corresponding features with a small HOMO–LUMO gap w10x. It is possible that this situation causes the second-order Žor pseudo-. Jahn–Teller distortion w27x. As a matter of fact, the preceding calculations result in the D6h C 6v symmetry breaking w8,10x. However, at the B3LYPr631G ) level, an energetically favored C 6v structure could not be found and, furthermore, the D6h -symmetrical structure was confirmed to be a local minimum by frequency analysis, suggesting that w36D6h xfullerene corresponds to a weak pseudo-Jahn– Teller system. As is well-known in the pseudoJahn–Teller effect, the system concerned remains stable with respect to this displacement, unless the energy gain due to the displacement surpasses the loss of energy due to elastic distortion of other bonds. In highly strained molecules such as C 36 , the loss of energy by this elastic distortion is expected to be large. Moreover, vibronic coupling is anticipated to be small when the mixing states involve nonbonding orbitals w27x. In addition, Choi and Kim also
™
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A. Ito et al.r Chemical Physics Letters 328 (2000) 32–38
reported that w6xcyclacene has D6h symmetry at the B3LYPr6-31G ) level w28x. According to the above arguments, we conclude that w36-D6h xfullerene maintains its D6h symmetrical structure owing to a weak pseudo-Jahn–Teller effect. More importantly, the HOMO Ž5b1u . and LUMO Ž5b 2g . are localized over the rims of the hexacene belt w10,13,14x, similar to those of polyacene andror oligoacenes w29x. These MOs have a non-bonding character and overlap each other in their spatial distributions, suggesting a strong exchange repulsion energy, which favors the triplet state. Hence a triplet diradical state of w36-D6h xfullerene is worthy of consideration as inferred from the well-known guiding principle in the chemistry of high-spin organic molecules w30x. In fact, the 3A 2u state is predicted to lie 3.7 kcal moly1 below the 1A 1g state 1 at the B3LYPr6-31G ) level w14x. On the other hand, as pointed out by Fowler and co-workers w11x, the singlet diradical state should also be considered as a plausible ground state of w36-D6h xfullerene with the small HOMO–LUMO gap. In the usual DFT scheme, it is difficult to investigate the singlet states from multi-configurational point of view. Therefore, we performed CASŽ6,6.rSTO-3G calculations of w36D6h xfullerene by using B3LYPr6-31G ) optimized geometry. As a result, it was found that the singlet state also has a diradical character Žthe fractional occupation numbers of the 1A 1g state; 9e 1g Ž0.40., 5b1u Ž0.99., 5b 2g Ž1.01., 10e 2g Ž0.05.x and furthermore, the 1A 1g state lies 0.13 kcal moly1 below the 3A 2u state. This suggests that the more reliable level of calculations should also predict the singlet ground state of w36-D6h xfullerene, although even the CASŽ6,6.r6-31G ) rrCASŽ6,6.r6-31G ) calculations are prohibitively time-consuming. In the field of cluster physics and chemistry, reactivity or stability of clusters in question is often argued in terms of valency w31–33x. In the present case, a hypervalent state of C 36 might be realized in
1 To check the closed-shell instability, we performed unrestricted B3LYP calculations for the singlet state of C 36 . However, the resulting 50:50 singlet–triplet state is found to be rather high above the closed-shell state, indicating stability of the restricted wavefunction.
connection with the fact that only the C 36 H 6 species can be isolated. Although we explored the electronic states with quintet Žtetravalent. and septet Žhexavalent. spin multiplicity, no quintet state was found in the present study and, furthermore, it was predicted that the septet state lies 31.8 kcal moly1 above the singlet state. Hence, w36-D6h xfullerene can be regarded as a divalent ’pseudoatom’. The most important point is that w36-D6h xfullerene is a very reactive species due to its diradical character. Actually, Koshio et al. could not detect the intact C 36 throughout their production process of C 36 -related compounds w18x. 3.2. Hydrogenated C36 : Is it a still reactiÕe species? As a result of an exhaustive computational search of C 36 H 6 on the assumption of the D6h carbon skeleton, Heine et al. found that thermodynamically favored structure has D 3h symmetry w34x. That structure corresponds to the highest symmetrical one in numerous possible structures. Herein, we must go a step further and clarify the point: why does the hydrogenation reaction stop at the C 36 H 6 stage? In Section 3.2, we examine the reactivity of w36D6h xfullerene by making inspection of electronic structures for some hypothetical fractionally hydrogenated C 36 derivatives; C 36 H, C 36 H 2 , C 36 H 4 , and C 36 H 6 . First, we briefly mention the geometrical features of these derivatives. 3.2.1. C36 H As described in Section 3.2, the first hydrogenation reaction is predicted to occur at the edge of the hexacene belt. The optimized structure for the C 36 H is shown in Fig. 1a. By this hydrogenation, the molecule is transformed into a C s-symmetric structure with doublet multiplicity. The bond lengthening is observed only in the vicinity of the methine carbon. Bond alternation takes place along the hydrogenated acene edge. Interestingly, the Mulliken spin density is localized over the non-hydrogenated edge of the hexacene belt ŽC1; 0.25, C2; 0.28, C3; 0.32, C4; 0.32.. This suggests that if the hydrogenation reaction occurs stepwise, the second hydrogen atom can attack any carbon atom on that edge. When
A. Ito et al.r Chemical Physics Letters 328 (2000) 32–38
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Fig. 1. Optimized geometries for Ža. C 36 H 1 , Žb. C 36 H 2 , Žc. C 36 H 4 , and Žd. C 36 H 6 at the B3LYPr6-31G ) ) level of theory. Bond lengths ˚ . are shown only for the symmetry-independent fragments and those for the competing triplet state are in italics. Hydrogen atoms are Žin A shown in black. Atom numbering except for C 36 H 6 indicates a carbon atom having a Mulliken spin density larger than 0.2.
the hydrogenation is not regiospecific, the isolated C 36 H 6 results in a mixture of many isomers. 3.2.2. C36 H2 According to the conjecture by Heine et al., the thermodynamically favored structure in C 36 H 2 n can be accounted for by a simple chemical rule of 1,4addition w33x. In the case of C 36 H 2 , the C 2v-symmetric structure is promising, as shown in Fig. 1b. As for the singlet state Ž1A 1 ., the geometrical features
are similar to those for the hydrogenated hemisphere of C 36 H 1 and, consequently, bond alternation takes place on the both edges of the cyclic hexacene belt. On the other hand, the optimized geometry with triplet multiplicity Ž3 B 2 . shows that the bond alternation is dissolved. Associated with this geometrical change, the Mulliken spin density is localized on the non-hydrogenated hemisphere ŽC1; 0.25, C2; 0.24, C3; 0.20.. Moreover, the 1A 1 state is stable by 8.0 kcal moly1 compared with the 3 B 2 state.
36
A. Ito et al.r Chemical Physics Letters 328 (2000) 32–38
3.2.3. C36 H4 Based on the assumption that the additional dihydrogenation of C 36 H 4 produces the D 3h-symmetric isomer of C 36 H 6 , the C 2v-symmetric structure shown in Fig. 1c is indispensable for C 36 H 4 , although the calculated spin density distribution for the abovementioned C 36 H 2 does not support the proposed structure. Moreover, a species corresponding to C 36 H 2 was not observed by Koshio et al. w18x, suggesting that tetrahydrogenation occurs all at once. As shown in Fig. 1c, the bond lengths remain virtually unchanged for both the singlet Ž1A 1 . and triplet Ž3 B 2 . states. In the 3 B 2 state, the Mulliken spin density concentrates on the expected two carbons ŽC1 and C1X ; 0.34., to which two more hydrogen atoms are attached to generate the D 3h -symmetric C 36 H 6 . However, the 3 B 2 state lies 17.2 kcal moly1 above the 1A 1 state.
3.2.4. C35 H6 The optimized geometry of the D 3h -symmetric C 36 H 6 is shown in Fig. 1d. As a result of hexahydrogenation, this molecule can be regarded as 30electron p-system analogous to the so-called spheriphane as pointed out by Fowler and co-workers w10x. This can be clearly seen also from magnetic point of view, as described in the later section. Although calculation results of the 1,4-addition isomers of C 36 H 2 and C 36 H 4 show that the triplet state is far above the corresponding closed-shell singlet state, the possibility of existence of openshell singlet state is not abandoned. Therefore, we performed CASSCFŽ6,6.rSTO-3GrrB3LYPr631G ) ) level of calculation for these species. However, both C 36 H 2 and C 36 H 4 has no mixing configuration in contrast to the intact C 36 . To understand the reason, we examined the HOMO–LUMO gaps for C 36 , C 36 H 2 , C 36 H 4 , and C 36 H 6 . As is well known, density functional calculations often underestimate the HOMO–LUMO gap. Therefore, at the RHFr6-31G )rrB3LYPr6-31G ) Ž ) . level, we recalculated the HOMO–LUMO gap: C 36 Ž3.7 eV.; C 36 H 2 Ž5.7 eV.; C 36 H 4 Ž6.7 eV.; C 36 H 6 Ž8.4 eV.. In C 36 , the energy level of the HOMO is relatively high, whereas that of the LUMO is around -2 eV and, thus the HOMO–LUMO gap of 3.7 eV is small. Hence the configuration corresponding to the excita-
tion of two electrons from the HOMO to the LUMO can be expected to be an important contributor as well to the ground-state wavefunction. However, the HOMO–LUMO gap increases with increasing the number of attached hydrogens, indicating the difficulty of configuration-mixing, that is, having no diradical character. It is thus expected that the reactivity of the observed C 36 H 4 and C 36 H 6 is not so high when compared with the intact C 36 . This might suggest that the entity of C 36 H 6 is beyond the expectation by the previous theoretical considerations. Finally, it may be worth mentioning, incidentally, the electronic structures for mono- and dianionic species of C 36 H 6 with D 3h symmetry. In contrast to C 36 , C 36 H 6 has degenerate LUMOs and, hence, the mono- and dianion of C 36 H 6 are expected to have a Jahn–Teller-distorted structure. In fact, we found the C 2v -deformed structure for these anionic species. Relative energies for the mono- and dianion of C 36 H 6 are listed in Table 1. In the dianion, the competing triplet state with C 2v symmetry lies 3.0 kcal moly1 below the singlet state. However, these two states must be considered to be essentially isoenergetic. More importantly, DSCF adiabatic first electron affinity for C 36 H 6 is predicted to be 0.60 eV. This indicates that C 36 H 6-based material is still pertinent
Table 1 Relative energies, D Er e l , Žkcal moly1 . for some electronic states of w36-D6h xfullerene and its hydrogenated species at the ŽU.B3LYPr6-31G ) Ž ) . level Symmetry
Electronic state
D Er e l
C 36
D6h
1
C 36 H 2
C 2v C 2v C 2v C 2v D 3h C 2v C 2v C 2v
0.0 y3.7 31.8 0.0 8.0 0.0 17.2 0.0 y16.2 53.0 50.0
C 36 H 4 C 36 H 6 C 36 Hy 6 C 36 H 62y
A 1g A 2u 7 A 2u 1 A1 3 B2 1 A1 3 B2 1 X A1 2 B2 1 A1 3 B2 3
a
a Energy relative to the neutral singlet state of each hydrogenated form, where the positive value stands for the stabilization; C 36 Ž1A 1g .: y1371.2567 hartree, C 36 H 2 Ž1A 1 .: y1372.5355 X hartree, C 36 H 4 Ž1A 1 .: y1373.8098 hartree, C 36 H 6 Ž1A 1 .: y1375.0737 hartree.
A. Ito et al.r Chemical Physics Letters 328 (2000) 32–38 Table 2 Calculated 1 H-, 13 C-NMR chemical shifts Ž d , ppm. a , and NICS of C 36 H 6 at the GIAO-HFr6-311G ) ) rrB3LYPr6-31G ) ) level Atom b Žor ring center.
Intensity
d Žor NICS.
C1 C2 C3 C4 C5 H6 a b c d
1r6 1r6 1r3 1r6 1r6
214.7 181.6 178.1 80.4 171.7 5.1 y10.7 y3.2 y13.5 y6.1
a
The magnetic shielding of tetramethylsilane ŽTMS. as a standard was computed at the same level of theory in order to calibrate the isotropic chemical shifts Ž d .. b Atom numbering Žor ring center designation. corresponds to that in Fig. 1d.
to n-type doping. However, its electron-accepting ability is not so strong as that of C 36 -based one Ž DSCF adiabatic first electron affinity for w36D6h xfullerenes 2.3 eV w14x.. 3.3. NMR chemical shifts and local aromaticities for C36 H6 with D 3h symmetry It is well known that the NMR measurement directly gives the important clues to identify the structure and symmetry of isolated C 36 H 6 molecules. Here we have calculated the 1 H- and 13 C-NMR chemical shifts within the GIAO approach using the B3LYPr6-31G ) ) optimized structure. As can be seen in Table 2, the calculated chemical shifts have some notable points. First, C 36 H 6 has a magnetically and chemically independent methine carbon. The corresponding chemical shifts for its 1 H and 13 C is predicted to be 5.1 and 80.4 ppm respectively. More importantly, the most downfield chemical shift exceeds 200 ppm. As is well known in 13 C-NMR for hydrocarbons, those containing carbonyl groups or allene moieties are the only compounds that give a signal with chemical shift larger than 200 ppm, and furthermore, to the best of our knowledge, for all the isolated fullerenes, no signals have been observed in such a region. Therefore, the existence of signal
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around 200 ppm will give a strong evidence for w36-D6h xfullerene structure. On the other hand, as listed in Table 2, the calculated NICS values for C 36 H 6 show the picture that C 36 H 6 can be regarded as a kind of spheriphane, as suggested by Fowler et al. w10x; 5- and 6-membered rings having methine carbon show non-aromaticity, while the other 6-membered rings have negative large NICS values comparable with that of benzene. 4. Conclusion In order to answer the title question, we carried out quantum chemical calculations for the putative hydrogenated w36-D6h xfullerenes. Contrary to the current experimental consensus, all the hydrogenated species studied here are predicted not to have diradicaloid electronic structure, while the intact w36D6h xfullerene can be regarded as a diradical. This suggests that the hydrogenation reactions do not reach C 36 H 6 stage. Besides, judging from the spin density for C 36 H 1 , further hydrogenation reactions do not necessarily proceeds via 1,4-addition intermediates. Moreover, thermodynamically stable C 36 H 6 with D 3h symmetry has unusual carbon atoms showing 13 C-NMR chemical shift exceeding 200 ppm, giving a strong evidence for w36-D6h xfullerene structure. Acknowledgements We are grateful to Professor H. Shinohara and Mr. A. Koshio for providing preprints ŽRef. w18x. prior to publication and valuable discussion. Numerical calculations were partly carried out at the Supercomputer Laboratory of the Institute for Chemical Research of Kyoto University. References w1x T.G. Schmalz, W.A. Zeitz, D.J. Klein, G.E. Hite, J. Am. Chem. Soc. 110 Ž1988. 111. w2x H.W. Kroto, Nature ŽLondon. 329 Ž1987. 529. w3x P.W. Fowler, D.E. Manolopoulos, An Atlas of Fullerenes, Oxford University Press, New York, 1995. w4x G. von Helden, N.G. Gotts, M.T. Bowers, Nature ŽLondon. 363 Ž1993. 60.
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