- Email: [email protected]
Models of the stable dumbbell-like C120 cluster and crimped nanotubes constructed from C60 fullerenes
25 April1997
CHEMICAL PHYSICS LETTERS ELSEVIER
Chemical Physics Letters 269 (1997) 85-87
Models of the stable dumbbell-like C 120 cluster and crimped nanotubes constructed from C 6o fullerenes E.G. Gal'pern a, I.V. Stankevich a, A.L. Chistyakov a, L.A. Chernozatonskii b a Institute of Organoelement Compounds, Russian Academy of Science, 28 Vacilot,a St., Moscow I 17813, Russian Federation h Institute Of Chemical Physics, Russian Academy of Science, 4 Kosygin St., Moscow 117334, Russian Federation
Received 14 January 1997
Abstract
A new dumbbell-shaped structure of a C6o fullerene dimer which is substantially advantageous from an energy point of view as compared to dumbbell-shaped C J2o clusters is proposed. The geometry and electronic structure of such a fullerene is calculated by the MM2, MNDO/PM3 and MNDO/AM 1 methods. This dimer is shown to be approximately twice as stable as known ones. The results obtained are applied to modeling a quasi one-dimensional crimped nanotube structure. The crystal orbital method has shown the crimped nanotube electron spectrum to have a gap equal to 0.5 eV.
The synthesis of C60 fullerenes in macroscopic quantities has opened prospects in creating new types of materials made of C6o clusters attached to each other. Such compounds are obtained by photopolymerization and plasma polymerization [1,2] and also by the application of high pressure to C6o crystals
[3-5]. Ref. [6] reports the results of the chemical structure analysis of films obtained as a result of C60 plasma polymerization. The presence of oligomers containing up to ten C6o monomers has been found out by means of laser desorption time-of-flight and field desorption mass-analysis. The most intensive peaks in mass-spectra correspond to CII 6 and Ci20 clusters. Several models of such systems have been proposed [6-8]. The formation of a C120 cluster has been interpreted as the product of cycloaddition of cyclohexatrienyl units of two C60 fullerenes. Dimers formed by (1,2 + 1,2)-, (1,4 + 1,4)- and (1,2 + 1,4)-additions were consid-
ered. However, these dimers contain highly strained fragments which connect sphere-like C6o clusters. It was supposed that such dimers are further transformed and a dumbbell-like Cl20 or Cjl 6 cluster can appear as a result. The Cl~ 6 cluster is formed by the elimination of four atoms from Cl20 (two from each monomer). The present work shows that there exists at least one more dumbbell-shaped Cl2 o isomer (I), Fig. la, besides the clusters analyzed in Refs. [7,8], Fig. lb and c. Ref. [8] shows by the quantum mechanical M N D O / A M 1 method [9] that the two stable C120 clusters have a dumbbell-like form. One of them (II) consists of only sp2-atoms and its sphere-like fragments are attached to each other by a frame-like C28 cluster consisting of four six-membered and two ten-membered cycles, Fig. lb. There are four sp 3 atoms and 116 spZ-atoms in the other cluster (III), Fig. lc. The sp3-atoms form a planar cyclobutane cycle which is a part of the frame-like C28 cluster
0009-2614/97/$1%00 Copyright © 1997 Published by Elsevier Science B.V. All rights reserved. PII S0009-26 14(97)0022 I-2
86
E.G. Gal 'pern et al. / Chemical Physics Letters 269 (1997) 85-87
,b,
(e)
discussed for C108 clusters). Such compounds have been proposed to describe the transformation of a fullerene chain into a crimped nanotube [11] which becomes possible under high pressures with a shear [3-5]. It is possible that such clusters were formed in a C6o fullerite under the influence of strong electron beams (see region ' B ' , containing elongated fullerenes, in Fig. 2 [12]). The CI20 cluster is optimized by the molecular mechanics (MM2), M N D O / P M 3 [13] and M N D O / A M 1 methods [9]. The C 120 cluster consists of 62 polygons (38 hexagons, 18 pentagons, 6 heptagons) and 174 bonds (114 pseudo-single (1) bonds, 60 pseudo-double (2) bonds). The following lengths of these bonds (in (,~,) according to the M N D O / PM3 calculation are: bl = 1.384 (2-6), b2 = 1.459 (1-6), b3 = 1.457 (1-12), b4 = 1.386 (2-12), b5 = 1.458 (1-12), b6 = 1.452 (1-6), b7 = 1.458 (1-12), b8 = 1.380 (2-6), b9 = 1.455 (1-12), bl0 = 1.376 (2-12), b l l = t.1.454 (1-12), b 1 2 = 1.405 (2-6), b 1 3 = 1.444 (1-12), b 1 4 = 1.1.455 (1-6), b 1 5 = 1.457 (1-6), b16 = 1.392 (2-12), b17 = 1.448 ( 1 12), b 1 8 = 1.376 (2-6), b 1 9 = 1 . 4 6 2 (1-6). Here the bond type and number of bonds are given in
Fig. 1. Structures of three dumbbell-like Ci20 clusters: (a) cluster I containing a belt of seven-membered cycles, (b) and (c) clusters !i and Ill taken from Ref. [8].
(a)
/f
......
/
containing eight polycondensed six-membered cycles. According to the M N D O / A M I calculation, the dissociation energies of clusters II and III into two isolated C60 molecules are equal to 73.0 and 81.6 kcal/mol [8]. We have found such a structure (I) which is much more advantageous in energy than those mentioned earlier. Cluster I can be described as follows. When all three bonds shared with pentagons in a C6o fullerene hexagon are broken, a fifteenmembered cycle in C60 is formed. Six atoms of this cycle have only two neighbours. We take two such transformed C6o clusters (Fig. 2a) and bind in pairs bi-coordinated atoms of one cluster with analogous atoms of the other one so that a structure of C~20 with 3-order axis rotation symmetry is formed (Fig. 2b). Thus cluster I is formed with a belt of six sevenmembered cycles connecting two sphere-like C6o clusters (see also Ref. [10] where a similar belt is
~
(b) x
/,
!,
Ceo
C6o
I
?',
,
'/
/
k
/ \
/// x
~
1
/
Fig. 2. Schemes of CK2o formation out of two C6o when 6 single bonds in neighboring C6o hexagons are broken (a), and displacement of single and double bonds in the dumbbell-like cluster (b). Calculated bond lengths designated by 1-19 numbers are presented in the text; L t is the crimped nanotube translation period.
E.G. Gal'pern et al. / Chemical Physics Letters 269 (1997) 85-87
brackets. Bond lengths calculated by the M N D O / A M 1 method differ from those given above by _0.005 A. Cage displacement of these bonds is shown in Fig. 2b. The length of the C 120 cluster cage is 15.6 ,~. The transformation reaction of a C 120 cluster I to two C60 has been proven to be an endothermic one. The energy effect of the cluster I formation out of two C6o is equal to 131.6 k c a l / m o l (according to the PM3 calculation) and 166 k c a l / m o l (according to AM1 calculation). Thus cluster I is approximately twice as stable as known ones. A model of a crimped nanotube formed from a C6o chain has been built on the basis of PM3 calculations on a similar trimer of C6o fullerenesporecursor of the tube: its large cage diameter is 7.0 A, the belt diameter is 4.2 A, and the length of translation is 8.6 A, Fig. 2b. A program complex from Ref. [14] has been used. The following lengths of repeated fragment bonds have been found: b4(bl6) = !.39, b 5 ( b l 5 ) = 1.46, b 6 ( b 1 4 ) = 1.45, b7(bl3) = 1.45, b 8 ( b l 2 ) - - 1.39, b 9 ( b l l ) - - 1.45, b l 0 = 1.38, b l 7 = 1.45, b l 8 = 1.38, b 1 9 = 1.46 ((0.005 ,~). Calculations of the nanotube electron structure were performed by the Huckel method in the topological approximation and by the EHT in the valence approximation using the program from Ref. [15]. In the topological approach such a crimped macromolecule, which can be regarded as a carbon nanotube superlattice, has a semimetallic spectrum, while there appears a g a p o f 0.5 eV as we proceed to the valence approximation. The last value is three times smaller than the energy gap of a C6o fullerite. Thus the presence of the crimped oligomers of C6o formed in a fullerite, influenced by a high pressure [3,4] or strong electron beams [13] can increase its electronic conductivity. We suppose the crimped oligomers of C60 will also be stable, and they could be observed in ultrahard phases of a fullerite, which could be conductive [3-5]. Thus we have described new models of a dumbbell-like C12o cluster and a crimped nanotube, constructed from C60 fullerenes. Our calculations o
87
demonstrate a high stability of the C 120 cluster and a semiconductor-like character of the tube's electron energy spectrum with a narrow gap.
Acknowledgements The work has been supported by the Russian Basic Research Foundation (grant N 96-02-18445-a), ISTC (project N 079) and Russian Program 'Actual Direction in Condensed Matter Physics', direction 'Fullerenes and Atomic Clusters'.
References [1] D.C. Cornett, l.J. Amster, M.A. Duncan, A.M. Rao, P.C. Eklund, J. Phys. Chem. 97 (1993) 5036. [2] N. Takahashi, H. Dock, N. Matsuzawa, M. Ata, J. Appl. Phys. 74 (1993) 5790. [3] VD. Blank, S.G. Buga, G.A. Dubitskii, M.Yu. Popov, Workshop Fullerenes and atomic clusters-95, St. Petersburg, Russia, Abstracts of Invited Lectures and Contributed Papers, 1995, p. 131 [4] V.D. Blank, S.G. Buga, G.A. Dubitskii, M.Yu. Popov, J. Mol. Mat. C 7 (1996) 251. [5] V.D. Blank, S.G. Buga, N.R. Serebryanaya, V.N. Denisov, G.A. Dubitskii, A.N. Ivlev, B.N. Mavrin, M.Yu. Popov, Phys. Lett. A. 205 (1995) 208. [6] N. Matsuzawa, M. Ata, D.A. Dixon, G. Fitzgerald, J. Phys. Chem. 98 (1994) 2555. [7] M. Ata, N. Takahashi, K. Nojima, J. Phys. Chem. 98 (1994) 9960. [8] S. Osawa, E. Osawa, Y. Hirose, Fullerene Sci. Technol. 3 (1995) 565. [9] M.J.S. Dewar, E.G. Zoebish, E.F. Healy, J.J.P. Stewart, J. Am. Chem. Soc. 107 (1985) 3902. [10] J.L. Aragon, H. Terrones, D. Romeu, Phys. Rev. B 48 (1993) 8409. [11] L.A. Chernozatonskii, J. Mol. Mat. C 7 (1996) 41. [12] S. Wang, P.R. Buseck, Chem. Phys. Lett. 182 (1991) I. [13] J.J.P. Stewart, J. Comp. Chem. 10 (1989) 209. [14] M.W. Schmidt, K.K. Baldridge, J.A. Boatz, S.T. Elbert, M.S. Gordon, J.H. Jensen, S. Koseki, N. Matsunaga, K.A. Nguyen, S.J. Su, T.L. Windus, M. Dupuis, J.A. Montgomery, J. Comp. Chem. 14 (1993) 1347. [15] D.A. Bochvar, E.G. Hal'pern, I.V. Stankevich, Zu. Struk. Khim. (in Russian) 29 (1988) 26.
CHEMICAL PHYSICS LETTERS ELSEVIER
Chemical Physics Letters 269 (1997) 85-87
Models of the stable dumbbell-like C 120 cluster and crimped nanotubes constructed from C 6o fullerenes E.G. Gal'pern a, I.V. Stankevich a, A.L. Chistyakov a, L.A. Chernozatonskii b a Institute of Organoelement Compounds, Russian Academy of Science, 28 Vacilot,a St., Moscow I 17813, Russian Federation h Institute Of Chemical Physics, Russian Academy of Science, 4 Kosygin St., Moscow 117334, Russian Federation
Received 14 January 1997
Abstract
A new dumbbell-shaped structure of a C6o fullerene dimer which is substantially advantageous from an energy point of view as compared to dumbbell-shaped C J2o clusters is proposed. The geometry and electronic structure of such a fullerene is calculated by the MM2, MNDO/PM3 and MNDO/AM 1 methods. This dimer is shown to be approximately twice as stable as known ones. The results obtained are applied to modeling a quasi one-dimensional crimped nanotube structure. The crystal orbital method has shown the crimped nanotube electron spectrum to have a gap equal to 0.5 eV.
The synthesis of C60 fullerenes in macroscopic quantities has opened prospects in creating new types of materials made of C6o clusters attached to each other. Such compounds are obtained by photopolymerization and plasma polymerization [1,2] and also by the application of high pressure to C6o crystals
[3-5]. Ref. [6] reports the results of the chemical structure analysis of films obtained as a result of C60 plasma polymerization. The presence of oligomers containing up to ten C6o monomers has been found out by means of laser desorption time-of-flight and field desorption mass-analysis. The most intensive peaks in mass-spectra correspond to CII 6 and Ci20 clusters. Several models of such systems have been proposed [6-8]. The formation of a C120 cluster has been interpreted as the product of cycloaddition of cyclohexatrienyl units of two C60 fullerenes. Dimers formed by (1,2 + 1,2)-, (1,4 + 1,4)- and (1,2 + 1,4)-additions were consid-
ered. However, these dimers contain highly strained fragments which connect sphere-like C6o clusters. It was supposed that such dimers are further transformed and a dumbbell-like Cl20 or Cjl 6 cluster can appear as a result. The Cl~ 6 cluster is formed by the elimination of four atoms from Cl20 (two from each monomer). The present work shows that there exists at least one more dumbbell-shaped Cl2 o isomer (I), Fig. la, besides the clusters analyzed in Refs. [7,8], Fig. lb and c. Ref. [8] shows by the quantum mechanical M N D O / A M 1 method [9] that the two stable C120 clusters have a dumbbell-like form. One of them (II) consists of only sp2-atoms and its sphere-like fragments are attached to each other by a frame-like C28 cluster consisting of four six-membered and two ten-membered cycles, Fig. lb. There are four sp 3 atoms and 116 spZ-atoms in the other cluster (III), Fig. lc. The sp3-atoms form a planar cyclobutane cycle which is a part of the frame-like C28 cluster
0009-2614/97/$1%00 Copyright © 1997 Published by Elsevier Science B.V. All rights reserved. PII S0009-26 14(97)0022 I-2
86
E.G. Gal 'pern et al. / Chemical Physics Letters 269 (1997) 85-87
,b,
(e)
discussed for C108 clusters). Such compounds have been proposed to describe the transformation of a fullerene chain into a crimped nanotube [11] which becomes possible under high pressures with a shear [3-5]. It is possible that such clusters were formed in a C6o fullerite under the influence of strong electron beams (see region ' B ' , containing elongated fullerenes, in Fig. 2 [12]). The CI20 cluster is optimized by the molecular mechanics (MM2), M N D O / P M 3 [13] and M N D O / A M 1 methods [9]. The C 120 cluster consists of 62 polygons (38 hexagons, 18 pentagons, 6 heptagons) and 174 bonds (114 pseudo-single (1) bonds, 60 pseudo-double (2) bonds). The following lengths of these bonds (in (,~,) according to the M N D O / PM3 calculation are: bl = 1.384 (2-6), b2 = 1.459 (1-6), b3 = 1.457 (1-12), b4 = 1.386 (2-12), b5 = 1.458 (1-12), b6 = 1.452 (1-6), b7 = 1.458 (1-12), b8 = 1.380 (2-6), b9 = 1.455 (1-12), bl0 = 1.376 (2-12), b l l = t.1.454 (1-12), b 1 2 = 1.405 (2-6), b 1 3 = 1.444 (1-12), b 1 4 = 1.1.455 (1-6), b 1 5 = 1.457 (1-6), b16 = 1.392 (2-12), b17 = 1.448 ( 1 12), b 1 8 = 1.376 (2-6), b 1 9 = 1 . 4 6 2 (1-6). Here the bond type and number of bonds are given in
Fig. 1. Structures of three dumbbell-like Ci20 clusters: (a) cluster I containing a belt of seven-membered cycles, (b) and (c) clusters !i and Ill taken from Ref. [8].
(a)
/f
......
/
containing eight polycondensed six-membered cycles. According to the M N D O / A M I calculation, the dissociation energies of clusters II and III into two isolated C60 molecules are equal to 73.0 and 81.6 kcal/mol [8]. We have found such a structure (I) which is much more advantageous in energy than those mentioned earlier. Cluster I can be described as follows. When all three bonds shared with pentagons in a C6o fullerene hexagon are broken, a fifteenmembered cycle in C60 is formed. Six atoms of this cycle have only two neighbours. We take two such transformed C6o clusters (Fig. 2a) and bind in pairs bi-coordinated atoms of one cluster with analogous atoms of the other one so that a structure of C~20 with 3-order axis rotation symmetry is formed (Fig. 2b). Thus cluster I is formed with a belt of six sevenmembered cycles connecting two sphere-like C6o clusters (see also Ref. [10] where a similar belt is
~
(b) x
/,
!,
Ceo
C6o
I
?',
,
'/
/
k
/ \
/// x
~
1
/
Fig. 2. Schemes of CK2o formation out of two C6o when 6 single bonds in neighboring C6o hexagons are broken (a), and displacement of single and double bonds in the dumbbell-like cluster (b). Calculated bond lengths designated by 1-19 numbers are presented in the text; L t is the crimped nanotube translation period.
E.G. Gal'pern et al. / Chemical Physics Letters 269 (1997) 85-87
brackets. Bond lengths calculated by the M N D O / A M 1 method differ from those given above by _0.005 A. Cage displacement of these bonds is shown in Fig. 2b. The length of the C 120 cluster cage is 15.6 ,~. The transformation reaction of a C 120 cluster I to two C60 has been proven to be an endothermic one. The energy effect of the cluster I formation out of two C6o is equal to 131.6 k c a l / m o l (according to the PM3 calculation) and 166 k c a l / m o l (according to AM1 calculation). Thus cluster I is approximately twice as stable as known ones. A model of a crimped nanotube formed from a C6o chain has been built on the basis of PM3 calculations on a similar trimer of C6o fullerenesporecursor of the tube: its large cage diameter is 7.0 A, the belt diameter is 4.2 A, and the length of translation is 8.6 A, Fig. 2b. A program complex from Ref. [14] has been used. The following lengths of repeated fragment bonds have been found: b4(bl6) = !.39, b 5 ( b l 5 ) = 1.46, b 6 ( b 1 4 ) = 1.45, b7(bl3) = 1.45, b 8 ( b l 2 ) - - 1.39, b 9 ( b l l ) - - 1.45, b l 0 = 1.38, b l 7 = 1.45, b l 8 = 1.38, b 1 9 = 1.46 ((0.005 ,~). Calculations of the nanotube electron structure were performed by the Huckel method in the topological approximation and by the EHT in the valence approximation using the program from Ref. [15]. In the topological approach such a crimped macromolecule, which can be regarded as a carbon nanotube superlattice, has a semimetallic spectrum, while there appears a g a p o f 0.5 eV as we proceed to the valence approximation. The last value is three times smaller than the energy gap of a C6o fullerite. Thus the presence of the crimped oligomers of C6o formed in a fullerite, influenced by a high pressure [3,4] or strong electron beams [13] can increase its electronic conductivity. We suppose the crimped oligomers of C60 will also be stable, and they could be observed in ultrahard phases of a fullerite, which could be conductive [3-5]. Thus we have described new models of a dumbbell-like C12o cluster and a crimped nanotube, constructed from C60 fullerenes. Our calculations o
87
demonstrate a high stability of the C 120 cluster and a semiconductor-like character of the tube's electron energy spectrum with a narrow gap.
Acknowledgements The work has been supported by the Russian Basic Research Foundation (grant N 96-02-18445-a), ISTC (project N 079) and Russian Program 'Actual Direction in Condensed Matter Physics', direction 'Fullerenes and Atomic Clusters'.
References [1] D.C. Cornett, l.J. Amster, M.A. Duncan, A.M. Rao, P.C. Eklund, J. Phys. Chem. 97 (1993) 5036. [2] N. Takahashi, H. Dock, N. Matsuzawa, M. Ata, J. Appl. Phys. 74 (1993) 5790. [3] VD. Blank, S.G. Buga, G.A. Dubitskii, M.Yu. Popov, Workshop Fullerenes and atomic clusters-95, St. Petersburg, Russia, Abstracts of Invited Lectures and Contributed Papers, 1995, p. 131 [4] V.D. Blank, S.G. Buga, G.A. Dubitskii, M.Yu. Popov, J. Mol. Mat. C 7 (1996) 251. [5] V.D. Blank, S.G. Buga, N.R. Serebryanaya, V.N. Denisov, G.A. Dubitskii, A.N. Ivlev, B.N. Mavrin, M.Yu. Popov, Phys. Lett. A. 205 (1995) 208. [6] N. Matsuzawa, M. Ata, D.A. Dixon, G. Fitzgerald, J. Phys. Chem. 98 (1994) 2555. [7] M. Ata, N. Takahashi, K. Nojima, J. Phys. Chem. 98 (1994) 9960. [8] S. Osawa, E. Osawa, Y. Hirose, Fullerene Sci. Technol. 3 (1995) 565. [9] M.J.S. Dewar, E.G. Zoebish, E.F. Healy, J.J.P. Stewart, J. Am. Chem. Soc. 107 (1985) 3902. [10] J.L. Aragon, H. Terrones, D. Romeu, Phys. Rev. B 48 (1993) 8409. [11] L.A. Chernozatonskii, J. Mol. Mat. C 7 (1996) 41. [12] S. Wang, P.R. Buseck, Chem. Phys. Lett. 182 (1991) I. [13] J.J.P. Stewart, J. Comp. Chem. 10 (1989) 209. [14] M.W. Schmidt, K.K. Baldridge, J.A. Boatz, S.T. Elbert, M.S. Gordon, J.H. Jensen, S. Koseki, N. Matsunaga, K.A. Nguyen, S.J. Su, T.L. Windus, M. Dupuis, J.A. Montgomery, J. Comp. Chem. 14 (1993) 1347. [15] D.A. Bochvar, E.G. Hal'pern, I.V. Stankevich, Zu. Struk. Khim. (in Russian) 29 (1988) 26.