- Email: [email protected]
A bucky onion from C20 and C60—an AM1 treatment
Journal of Molecular Structure (Theochem) 545 (2001) 207±214
www.elsevier.nl/locate/theochem
A bucky onion from C20 and C60 Ðan AM1 treatment Lemi TuÈrker* Middle East Technical University, Department of Chemistry, 06531, Ankara, Turkey Received 8 January 2001; accepted 12 February 2001
Abstract A bucky onion-like composite system of C20 in C60 structure was subjected to semiempirical quantum chemical treatment at the level of AM1-RHF type calculations. The composite system was found to be a highly endothermic but stable structure. Strong ` through-space' type interaction between C20 and C60 shells should exist resulting a dipole moment originating from C60 shell to C20 shell. Thus, the composite system should have anisotropic polarizability. q 2001 Elsevier Science B.V. All rights reserved. Keywords: Bucky onions; Fullerenes; C20; C60; AM1 treatment
1. Introduction In recent years, a great deal of achievement has been done in the ®eld of nanometric carbon particles. The unexpected and overwhelming development is of course parallel to the improvement of techniques for the synthesis [1,2]. Various nanometric graphitic systems have been obtained by making slight modi®cations to the electric arc experiments, such as nanotubes [3,4], nanoparticles [5±7], metal-®lled nanoparticles [8±10] etc. It has been shown that carbonaceous materials transform themselves into quasispherical onionlike graphitic particles under the effect of intense electron irradiation [11]. Fullerenes are characterized by 12 ®vemembered and a varying number of six-membered rings. For example, the ground state structure of C60 is a closed 3-dimensional cage with 12 ®vemembered and 20 six-membered rings [12]. C20 is * Tel.: 190-312-210-3244; fax: 190-312-210-1280. E-mail address: [email protected] (L. TuÈrker).
the smallest fullerene [13] which has no sixmembered rings. Many theoretical reports have appeared in the literature dealing with C20 [14± 19]. Ab initio calculations at the correlated level predicts fullerene structure for C20 as the ground state conformer among the other C20 isomers [13]. It has been argued that the C20 structure might be anticipated as a regular dodecahedron of the Ih point group. However, due to the possibility of Jahn±Teller distortion of the molecular geometry, a lower symmetry than Ih is expected [13]. On the other hand, C60, which has real existence, is one of the profoundly studied carbon clusters in the last few decades [20]. C20 structure, encapsulated by C60 should constitute one of the simplest bucky-onions. However, buckyonions even having only 2±4 shells were shown to be stable under electron bombardment [21]. In the present study, the bucky onion-like composite system of C20 in C60 (C20@C60) (Fig.1) is investigated structurally and electronically by using the semiempirical treatment at the level of AM1 calculations [22].
0166-1280/01/$ - see front matter q 2001 Elsevier Science B.V. All rights reserved. PII: S 0166-128 0(01)00421-3
L. TuÈrker / Journal of Molecular Structure (Theochem) 545 (2001) 207±214
208
restricted Hartree±Fock (RHF) level and consecutive applications of the various optimization methods. For this purpose, the steepest descent method followed by conjugate gradient minimizations, Fletcher±Rieves and Polak±Ribiere techniques were applied. The global energy minima were sought by using the simulated annealing technique [23]. For that purpose, a simulation protocol involving a heating time of 0.1 ps, followed by a 1 ps. simulation at 3000 K and cooling to 298 K within 200 ps was applied on the initially geometry optimized structures. The time step of 0.5 fs was used for molecular dynamic studies. The ®nal optimizations were obtained by the application of a conjugate gradient method, Polak±Ribiere (convergence limit of 4.18 £ 10 ±4 kJ/ mol (0.0001 kcal/mol) and RMS gradient of 4.18 £ 107 kJ/(m.mol), (0.001 kcal/(A 0 mol)). All these calculations were performed by using the Hyperchem (release 5.1) and ChemPlus (2.0) package programs.
Fig. 1. Structure of the C20@C60 composite system.
2. Method In the preset study all the energy minima were achieved by using AM1 (Austin model 1) self-consistent ®elds molecular orbital (SCF MO) [22] method at the
3. Results and discussion The bucky-onion-like system consisted of C20
Table 1 Some calculated properties of bucky-onion like C20@C60 composite
Surface area (m 2) Volume (m 3) log P Refractivity (m 3) Polarizability (m 3)
C20@C60
C20
C60
582 £ 10 220 1335 £ 10 230 12.80 3.10 £ 10 228 1.52 £ 10 228
314 £ 10 220 539 £ 10 230 3.20 0.78 £ 10 228 0.38 £ 10 228
546 £ 10 220 1202 £ 10 230 9.60 2.33 £ 10 228 0.71 £ 10 228
Table 2 Some energies of the bucky-onion like C20@C60 composite system and its components Energy (kJ/mol)
C20@C60
C20
C60
Total Binding Isolated atomic Electronic Core±core repulsion Heat of formation LUMO a HOMO a DE b
2975,263 242,687 2932,576 217,507,897 16,532,634 14,514 25.9024 A 212.8399 A 6.9375
2243,780 210,636 2233,144 21,711,132 1,467,352 3664 25.2393 B2 214.6489 B3 9.4096
2738,263 238,831 2699,432 27,802,155 9,063,891 4069 24.7210 215.4508 10.7298
a b
Energies on the order of 10 219 J. The symmetries of the orbitals are after the numeric data. DE: LUMO±HOMO energy difference.
L. TuÈrker / Journal of Molecular Structure (Theochem) 545 (2001) 207±214
Fig. 2. The HOMO and LUMO orbitals of the composite system (dashed lines stand for axes of inertia).
209
210
L. TuÈrker / Journal of Molecular Structure (Theochem) 545 (2001) 207±214
Fig. 3. Molecular orbital energy diagrams for C20, C60 and their composite onion.
and C60 should be one of the simplest representatives of its kind. However, the formation mechanism of fullerenes and the related structures is not well understood. The formation of multi-shell graphitic particles from the gas phase by a spiral growth mechanism has been suggested [24,25]. It has also been proposed that the onion like particles are generated by the graphitization of a liquid carbon drop [5,6]. Whatever the prevailing mechanism is, the formation of a particular molecular structure is governed by the energetics of the system, that is the stability at the molecular level. Thus, the present treatment is intended to shed
some light on the onion-like composite system of C20 and C60 at the molecular level. The results of AM1 geometry optimization (carried out without any imposed symmetry restriction) indicate that individually C20 and C60 shells in the composite system belongs to C1 molecular point group. Also the whole composite system is characterized with C1 symmetry. The bond lengths between any two hexagons or any two pentagons vary from hexagon to hexagon or pentagon to pentagon. Table 1 shows some calculated properties of the composite system. The area and the volume for C20@C60 are 6.5% and 11.0% larger,
L. TuÈrker / Journal of Molecular Structure (Theochem) 545 (2001) 207±214
Fig. 4. The 3-dimensional electrostatic potential contours for C20, C60 and C20@C60 (dashed lines stand for axes of inertia).
211
212
L. TuÈrker / Journal of Molecular Structure (Theochem) 545 (2001) 207±214
Fig. 5. The 3-dimensional charge density contours for C20, C60 and C20@C60 (dashed lines stand for axes of inertia).
L. TuÈrker / Journal of Molecular Structure (Theochem) 545 (2001) 207±214
respectively, than the corresponding values for C60.Note that log P is a measure of the hydrophobicity of the system and it is greater for C20@C60 as compared to its components. Table 2 shows some energies of C20@C60, the onion-like composite system. As it is seen the structure is characterized with negative total and binding energies but positive heat of formation value which collectively implies that it should be a stable but highly endothermic structure. On the other hand, when the total energy per carbon and the binding energy per carbon values are calculated for C20@C60, C20 and C60 (212,190.8, 212,189.0 and ± 12,304.3 kJ/carbon for the total energy and ±533.5, 2531.8 and ±647.2 kJ/carbon for the binding energy, respectively) the stability order should be in the order of C60 . C20@C60 . C20. The highest occupied and the lowest unoccupied molecular orbitals (HOMO and LUMO, respectively) of C20@C60 both have the A-type symmetry (Fig.2). The HOMO level is characterized with the energy value of 212.8399 £ 10 219 J, whereas the LUMO energy level is 25.9024 £ 10 219 J. Fig.3 shows molecular orbital energy levels of C20, C60 and their composite system, respectively. The interfrontier molecular orbital energy gap (DE) values follow the order of C60 . C20 . C20@C60 (see Table 2). It is known that DE generally decreases as the conjugation increases [26,27]. Hence, the above order of DE values imply that C20 and C60 layers strongly in¯uence each other's p-system in the direction of narrowing of the interfrontier energy gap in the composite onion-like system as compared to its components. Although, the nature of this interlayer interaction is `throughspace' as it is in cyclophanes [28±30] it needs to be investigated further in other onion-like systems. Figs. 4 and 5 show the 3-dimensional electrostatic potential and charge density contours of the composite system and its components, respectively. As seen in Fig. 4, C20 and C60 possess evenly distributed spherical-like electrostatic potential ®eld, whereas C20@C60, the onion-like composite structure has positive (outside) and negative (inside) unevenly spread potential ®elds. Hence, although, C20 and C60 have zero dipole moment individually, when they construct C20@C60 structure the resultant composite system possesses a dipole moment oriented from C60 shell to C20 shell and having the magnitude of
213
230
7.808 £ 10 cm (2.327 D). The direction and the magnitude of the dipole moment also support the likely occurrence of through-space interaction in C20@C60 system, the outer layer, C60, being the electron donor and C20 core, the electron acceptor. Most probably, some of the pentagonal rings of C20 acquire negative charge in the direction of forming 4m type psystems (which are aromatic and stable, whereas the nonalternant rings [31] in C20 normally should be less stable than their anionic forms). Thus, the composite system should have anisotropic polarizability [32]. 4. Conclusion The bucky-onion-like system, C20@C60 considered presently, is one of the simplest model of its kind. However, the AM1 type semiempirical quantum chemical calculations have revealed some interesting properties. The most striking is the ` through-space' interaction between the C20 and C60 shells in the composite anion-like system, C20@C60. The enlargement of C60 structure in C20@C60 as compared to the isolated C60 molecule, the narrowing of the interfrontier molecular orbital energy gap, DE, in C20@C60, the arousal of a new pattern of electrostatic contour diagram for C20@C60 as compared to the respective pattern of its components and the existence of a dipole moment in C20@C60 while its components have nil, are all the indications of strong inter-shell interaction operative through space in this onion-like system. References [1] H.W. Kroto, J.R. Health, S.C. O'Brien, R.F. Curl, R.E. Smaley, Nature 318 (1985) 162. [2] W. Kratschmer, L.D. Lamb, K. Foristopoulos, D.R. Huffman, Nature 347 (1990) 354. [3] S. Iijima, Nature 354 (1991) 56. [4] T.W. Ebbesen, P.M. Ajayan, Nature 358 (1992) 220. [5] S. Iijima, J. of, Cryst.Growth 50 (1980) 675. [6] D. Ugarte, Chem. Phys. Lett. 198 (1992) 596. [7] Y. Saito, T. Yoshikawa, M. Inagaki, M. Tomita, T. Hayashi, Chem. Phys. Lett. 204 (1993) 277. [8] R.S. Ruoff, D.C. Lorentz, B. Chan, R. Malhotra, S. Subramoney, Science 259 (1993) 346. [9] M. Tomita, Y. Saito, T. Hayashi, Jpn. J. Appl. Phys. 32 (28) (1993) L280. [10] D. Ugarte, Chem. Phys. Lett. 209 (1993) 99. [11] D. Ugarte, Nature 359 (1992) 707.
214 [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23]
L. TuÈrker / Journal of Molecular Structure (Theochem) 545 (2001) 207±214 G.E. Scuseria, Chem. Phys. Lett. 176 (Suppl.) (1991) 423. V. Parasuk, Chem. Phys. Lett. 184 (1±3) (1991) 187. K. Balasubramanian, Chem. Phys. Lett. 224 (3±4) (1994) 325. K. Balasubramanian,, J. Chem. Inf. and Comp. Sciences 32 (2) (1994) 421. R. Piccito, R. Pucci, Clusters, J. Chem. Phys. 98 (1) (1993) 502. K. Balasubramanian, J. Phys. Chem. 97 (27) (1993) 6990. K. Balasubramanian, J. Phys. Chem. 97 (18) (1993) 4647. F. Varga, L. Nemes, G.I. Csanka, J. of, Molecular Structure 376 (1996) 513. M.S. Dresselhause, Science of Fullerenes and Carbon Nanotubes, New York, Academic Press., 1995. D. Ugarte, Lett. 22 (1) (1993) 45. M.J.S. Dewar, E.G. Zoebisch, E.F. Healey, J.J.P. Stewart, J. Am. Chem. Soc 107 (1985) 3902. S.J. Weiner, P.A. Kollman, D.A. Case, U.C. Singh, C. Ghio,
[24] [25] [26] [27] [28] [29] [30] [31] [32]
G. Alagona, S. Profeta Jr., Weiner, J. Am. Chem. Soc. 106 (3) (1984) 765. Q.L. Zhang, S.C. O'Brien, J.R. Heath, Y. Liu, R. Curl, H.W. Kroto, R.E. Smalley, J. Phys. Chem. 90 (4) (1986) 525. H.W. Kroto, K. McKay, Nature 331 (1988) 328. I. Fleming, Frontier Orbitals and Organic Chemical Reactions, Wiley, London, 1996. E. Heilbronner, E. Bock, The HMO-Model and Its Application, Verlag, Weinheim, 1976. V. Boekelheide, in: F.L. Boschke (Ed.), Cyclophanes I, Topics in Curr. Chem. 113Springer-Verlag, Berlin, 1983, p. 117. L. TuÈrker, J. of, Molecular Structure (Theochem) 497 (2000) 11. L. TuÈrker, Ind. J. Chemistry 38B (1999) 152. M.J.S. Dewar, R.C. Dougherty, The PMO Theory of Organic Chemistry, Plenum-Rosetta, New York, 1975. A. Hinchliffe, R.W. Munn, Molecular Electromagnetism, Wiley, New York, 1985.
www.elsevier.nl/locate/theochem
A bucky onion from C20 and C60 Ðan AM1 treatment Lemi TuÈrker* Middle East Technical University, Department of Chemistry, 06531, Ankara, Turkey Received 8 January 2001; accepted 12 February 2001
Abstract A bucky onion-like composite system of C20 in C60 structure was subjected to semiempirical quantum chemical treatment at the level of AM1-RHF type calculations. The composite system was found to be a highly endothermic but stable structure. Strong ` through-space' type interaction between C20 and C60 shells should exist resulting a dipole moment originating from C60 shell to C20 shell. Thus, the composite system should have anisotropic polarizability. q 2001 Elsevier Science B.V. All rights reserved. Keywords: Bucky onions; Fullerenes; C20; C60; AM1 treatment
1. Introduction In recent years, a great deal of achievement has been done in the ®eld of nanometric carbon particles. The unexpected and overwhelming development is of course parallel to the improvement of techniques for the synthesis [1,2]. Various nanometric graphitic systems have been obtained by making slight modi®cations to the electric arc experiments, such as nanotubes [3,4], nanoparticles [5±7], metal-®lled nanoparticles [8±10] etc. It has been shown that carbonaceous materials transform themselves into quasispherical onionlike graphitic particles under the effect of intense electron irradiation [11]. Fullerenes are characterized by 12 ®vemembered and a varying number of six-membered rings. For example, the ground state structure of C60 is a closed 3-dimensional cage with 12 ®vemembered and 20 six-membered rings [12]. C20 is * Tel.: 190-312-210-3244; fax: 190-312-210-1280. E-mail address: [email protected] (L. TuÈrker).
the smallest fullerene [13] which has no sixmembered rings. Many theoretical reports have appeared in the literature dealing with C20 [14± 19]. Ab initio calculations at the correlated level predicts fullerene structure for C20 as the ground state conformer among the other C20 isomers [13]. It has been argued that the C20 structure might be anticipated as a regular dodecahedron of the Ih point group. However, due to the possibility of Jahn±Teller distortion of the molecular geometry, a lower symmetry than Ih is expected [13]. On the other hand, C60, which has real existence, is one of the profoundly studied carbon clusters in the last few decades [20]. C20 structure, encapsulated by C60 should constitute one of the simplest bucky-onions. However, buckyonions even having only 2±4 shells were shown to be stable under electron bombardment [21]. In the present study, the bucky onion-like composite system of C20 in C60 (C20@C60) (Fig.1) is investigated structurally and electronically by using the semiempirical treatment at the level of AM1 calculations [22].
0166-1280/01/$ - see front matter q 2001 Elsevier Science B.V. All rights reserved. PII: S 0166-128 0(01)00421-3
L. TuÈrker / Journal of Molecular Structure (Theochem) 545 (2001) 207±214
208
restricted Hartree±Fock (RHF) level and consecutive applications of the various optimization methods. For this purpose, the steepest descent method followed by conjugate gradient minimizations, Fletcher±Rieves and Polak±Ribiere techniques were applied. The global energy minima were sought by using the simulated annealing technique [23]. For that purpose, a simulation protocol involving a heating time of 0.1 ps, followed by a 1 ps. simulation at 3000 K and cooling to 298 K within 200 ps was applied on the initially geometry optimized structures. The time step of 0.5 fs was used for molecular dynamic studies. The ®nal optimizations were obtained by the application of a conjugate gradient method, Polak±Ribiere (convergence limit of 4.18 £ 10 ±4 kJ/ mol (0.0001 kcal/mol) and RMS gradient of 4.18 £ 107 kJ/(m.mol), (0.001 kcal/(A 0 mol)). All these calculations were performed by using the Hyperchem (release 5.1) and ChemPlus (2.0) package programs.
Fig. 1. Structure of the C20@C60 composite system.
2. Method In the preset study all the energy minima were achieved by using AM1 (Austin model 1) self-consistent ®elds molecular orbital (SCF MO) [22] method at the
3. Results and discussion The bucky-onion-like system consisted of C20
Table 1 Some calculated properties of bucky-onion like C20@C60 composite
Surface area (m 2) Volume (m 3) log P Refractivity (m 3) Polarizability (m 3)
C20@C60
C20
C60
582 £ 10 220 1335 £ 10 230 12.80 3.10 £ 10 228 1.52 £ 10 228
314 £ 10 220 539 £ 10 230 3.20 0.78 £ 10 228 0.38 £ 10 228
546 £ 10 220 1202 £ 10 230 9.60 2.33 £ 10 228 0.71 £ 10 228
Table 2 Some energies of the bucky-onion like C20@C60 composite system and its components Energy (kJ/mol)
C20@C60
C20
C60
Total Binding Isolated atomic Electronic Core±core repulsion Heat of formation LUMO a HOMO a DE b
2975,263 242,687 2932,576 217,507,897 16,532,634 14,514 25.9024 A 212.8399 A 6.9375
2243,780 210,636 2233,144 21,711,132 1,467,352 3664 25.2393 B2 214.6489 B3 9.4096
2738,263 238,831 2699,432 27,802,155 9,063,891 4069 24.7210 215.4508 10.7298
a b
Energies on the order of 10 219 J. The symmetries of the orbitals are after the numeric data. DE: LUMO±HOMO energy difference.
L. TuÈrker / Journal of Molecular Structure (Theochem) 545 (2001) 207±214
Fig. 2. The HOMO and LUMO orbitals of the composite system (dashed lines stand for axes of inertia).
209
210
L. TuÈrker / Journal of Molecular Structure (Theochem) 545 (2001) 207±214
Fig. 3. Molecular orbital energy diagrams for C20, C60 and their composite onion.
and C60 should be one of the simplest representatives of its kind. However, the formation mechanism of fullerenes and the related structures is not well understood. The formation of multi-shell graphitic particles from the gas phase by a spiral growth mechanism has been suggested [24,25]. It has also been proposed that the onion like particles are generated by the graphitization of a liquid carbon drop [5,6]. Whatever the prevailing mechanism is, the formation of a particular molecular structure is governed by the energetics of the system, that is the stability at the molecular level. Thus, the present treatment is intended to shed
some light on the onion-like composite system of C20 and C60 at the molecular level. The results of AM1 geometry optimization (carried out without any imposed symmetry restriction) indicate that individually C20 and C60 shells in the composite system belongs to C1 molecular point group. Also the whole composite system is characterized with C1 symmetry. The bond lengths between any two hexagons or any two pentagons vary from hexagon to hexagon or pentagon to pentagon. Table 1 shows some calculated properties of the composite system. The area and the volume for C20@C60 are 6.5% and 11.0% larger,
L. TuÈrker / Journal of Molecular Structure (Theochem) 545 (2001) 207±214
Fig. 4. The 3-dimensional electrostatic potential contours for C20, C60 and C20@C60 (dashed lines stand for axes of inertia).
211
212
L. TuÈrker / Journal of Molecular Structure (Theochem) 545 (2001) 207±214
Fig. 5. The 3-dimensional charge density contours for C20, C60 and C20@C60 (dashed lines stand for axes of inertia).
L. TuÈrker / Journal of Molecular Structure (Theochem) 545 (2001) 207±214
respectively, than the corresponding values for C60.Note that log P is a measure of the hydrophobicity of the system and it is greater for C20@C60 as compared to its components. Table 2 shows some energies of C20@C60, the onion-like composite system. As it is seen the structure is characterized with negative total and binding energies but positive heat of formation value which collectively implies that it should be a stable but highly endothermic structure. On the other hand, when the total energy per carbon and the binding energy per carbon values are calculated for C20@C60, C20 and C60 (212,190.8, 212,189.0 and ± 12,304.3 kJ/carbon for the total energy and ±533.5, 2531.8 and ±647.2 kJ/carbon for the binding energy, respectively) the stability order should be in the order of C60 . C20@C60 . C20. The highest occupied and the lowest unoccupied molecular orbitals (HOMO and LUMO, respectively) of C20@C60 both have the A-type symmetry (Fig.2). The HOMO level is characterized with the energy value of 212.8399 £ 10 219 J, whereas the LUMO energy level is 25.9024 £ 10 219 J. Fig.3 shows molecular orbital energy levels of C20, C60 and their composite system, respectively. The interfrontier molecular orbital energy gap (DE) values follow the order of C60 . C20 . C20@C60 (see Table 2). It is known that DE generally decreases as the conjugation increases [26,27]. Hence, the above order of DE values imply that C20 and C60 layers strongly in¯uence each other's p-system in the direction of narrowing of the interfrontier energy gap in the composite onion-like system as compared to its components. Although, the nature of this interlayer interaction is `throughspace' as it is in cyclophanes [28±30] it needs to be investigated further in other onion-like systems. Figs. 4 and 5 show the 3-dimensional electrostatic potential and charge density contours of the composite system and its components, respectively. As seen in Fig. 4, C20 and C60 possess evenly distributed spherical-like electrostatic potential ®eld, whereas C20@C60, the onion-like composite structure has positive (outside) and negative (inside) unevenly spread potential ®elds. Hence, although, C20 and C60 have zero dipole moment individually, when they construct C20@C60 structure the resultant composite system possesses a dipole moment oriented from C60 shell to C20 shell and having the magnitude of
213
230
7.808 £ 10 cm (2.327 D). The direction and the magnitude of the dipole moment also support the likely occurrence of through-space interaction in C20@C60 system, the outer layer, C60, being the electron donor and C20 core, the electron acceptor. Most probably, some of the pentagonal rings of C20 acquire negative charge in the direction of forming 4m type psystems (which are aromatic and stable, whereas the nonalternant rings [31] in C20 normally should be less stable than their anionic forms). Thus, the composite system should have anisotropic polarizability [32]. 4. Conclusion The bucky-onion-like system, C20@C60 considered presently, is one of the simplest model of its kind. However, the AM1 type semiempirical quantum chemical calculations have revealed some interesting properties. The most striking is the ` through-space' interaction between the C20 and C60 shells in the composite anion-like system, C20@C60. The enlargement of C60 structure in C20@C60 as compared to the isolated C60 molecule, the narrowing of the interfrontier molecular orbital energy gap, DE, in C20@C60, the arousal of a new pattern of electrostatic contour diagram for C20@C60 as compared to the respective pattern of its components and the existence of a dipole moment in C20@C60 while its components have nil, are all the indications of strong inter-shell interaction operative through space in this onion-like system. References [1] H.W. Kroto, J.R. Health, S.C. O'Brien, R.F. Curl, R.E. Smaley, Nature 318 (1985) 162. [2] W. Kratschmer, L.D. Lamb, K. Foristopoulos, D.R. Huffman, Nature 347 (1990) 354. [3] S. Iijima, Nature 354 (1991) 56. [4] T.W. Ebbesen, P.M. Ajayan, Nature 358 (1992) 220. [5] S. Iijima, J. of, Cryst.Growth 50 (1980) 675. [6] D. Ugarte, Chem. Phys. Lett. 198 (1992) 596. [7] Y. Saito, T. Yoshikawa, M. Inagaki, M. Tomita, T. Hayashi, Chem. Phys. Lett. 204 (1993) 277. [8] R.S. Ruoff, D.C. Lorentz, B. Chan, R. Malhotra, S. Subramoney, Science 259 (1993) 346. [9] M. Tomita, Y. Saito, T. Hayashi, Jpn. J. Appl. Phys. 32 (28) (1993) L280. [10] D. Ugarte, Chem. Phys. Lett. 209 (1993) 99. [11] D. Ugarte, Nature 359 (1992) 707.
214 [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23]
L. TuÈrker / Journal of Molecular Structure (Theochem) 545 (2001) 207±214 G.E. Scuseria, Chem. Phys. Lett. 176 (Suppl.) (1991) 423. V. Parasuk, Chem. Phys. Lett. 184 (1±3) (1991) 187. K. Balasubramanian, Chem. Phys. Lett. 224 (3±4) (1994) 325. K. Balasubramanian,, J. Chem. Inf. and Comp. Sciences 32 (2) (1994) 421. R. Piccito, R. Pucci, Clusters, J. Chem. Phys. 98 (1) (1993) 502. K. Balasubramanian, J. Phys. Chem. 97 (27) (1993) 6990. K. Balasubramanian, J. Phys. Chem. 97 (18) (1993) 4647. F. Varga, L. Nemes, G.I. Csanka, J. of, Molecular Structure 376 (1996) 513. M.S. Dresselhause, Science of Fullerenes and Carbon Nanotubes, New York, Academic Press., 1995. D. Ugarte, Lett. 22 (1) (1993) 45. M.J.S. Dewar, E.G. Zoebisch, E.F. Healey, J.J.P. Stewart, J. Am. Chem. Soc 107 (1985) 3902. S.J. Weiner, P.A. Kollman, D.A. Case, U.C. Singh, C. Ghio,
[24] [25] [26] [27] [28] [29] [30] [31] [32]
G. Alagona, S. Profeta Jr., Weiner, J. Am. Chem. Soc. 106 (3) (1984) 765. Q.L. Zhang, S.C. O'Brien, J.R. Heath, Y. Liu, R. Curl, H.W. Kroto, R.E. Smalley, J. Phys. Chem. 90 (4) (1986) 525. H.W. Kroto, K. McKay, Nature 331 (1988) 328. I. Fleming, Frontier Orbitals and Organic Chemical Reactions, Wiley, London, 1996. E. Heilbronner, E. Bock, The HMO-Model and Its Application, Verlag, Weinheim, 1976. V. Boekelheide, in: F.L. Boschke (Ed.), Cyclophanes I, Topics in Curr. Chem. 113Springer-Verlag, Berlin, 1983, p. 117. L. TuÈrker, J. of, Molecular Structure (Theochem) 497 (2000) 11. L. TuÈrker, Ind. J. Chemistry 38B (1999) 152. M.J.S. Dewar, R.C. Dougherty, The PMO Theory of Organic Chemistry, Plenum-Rosetta, New York, 1975. A. Hinchliffe, R.W. Munn, Molecular Electromagnetism, Wiley, New York, 1985.