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Electronic state studies of a mono-boron-doped giant heterofullerene
PII: S0022-3697(97)00047-4
Pergamon
J. Phys. Chera Solids Vo158, No. I 1, pp. 1657-1660, 1997 O 1997 Elsevier Science Ltd Printed in Great Britain. All rights t~eserved 0022-3697/97 $17.00+ 0.00
ELECTRONIC STATE STUDIES OF A MONO-BORON-DOPED GIANT HETEROFULLERENE Y I N G Z O U , Z H I J I A N W A N G and W E N Z H O U LI Department of Physics, Zhejiang University, Hangzhou 310027, P.R. China Abstract--With the establishment of a succinct geometrical description of a giant fuilerene (GF), a built-in golden ratio has been discovered. The geometrical description serves as a key start for electronic state studies on large scale fullerenes and also heterofullerenes. Utilizating an extended Su-Schrieffer-Heeger model we mainly investigate one-boron substitution in fuUerenesCn (n = 60, 180, 240, 420, 540, 720, 780). A mid-gap state can be found intruding into the gap of pristine fullerenes. The wave function amplitude spreads over the whole fullerene but has a stronger localization at the corresponding site for a larger fullerene. © 1997 Elsevier Science Ltd. Keywords: fuUerenes, boron, SSH model, golden ratio
1. INTRODUCTION Fullerenes CA have been intensively investigated. In particular, the occurrence of superconductivity in alkali-ion doped C60 [1] has attracted much interest in doped systems. Electron-doping in C60 was achieved with alkali-metal atoms inserted at the interstitial sites. Theoretical studies within the local-density approximation (LDA) have revealed [2] that an electron transfer occurs from alkali-metal s orbitals to a conduction band of solid C60, and that injected electrons in the conduction bands play an important role in the superconductivity. However, the next hole doping in which halogen is chosen as an acceptor in solid C60 has been hindered on account of the large electronegativity of C60 [3]. Very recently, Guo et al. [4] reported the gas-phase preparation of molecular clusters mainly consisting of Cto-n - B n. Later, CnNm, fullerenes were also reported by several groups [5-7]. A viable route set by Hummelen [8] made the isolation and characterization of biazafullerenyl in solution available. More recently, BxCyN z nanotubules, analogs of carbon nanotubules, have also been successfully synthesized via arc-discharge methods [9]. The boron-doped C 60fullerene is expected to be a promising new way of hole doping in solid fullerenes, and has stimulated a great interest in researchers to investigate its structural and electronic properties [10-13], as well as the band structure and cohesive energy of solid C 59B [ 14]. In this new progress, we notice a striking fact that, in the reported cluster mass spectra, the Smalley group [4] also specified that the even-numbered clusters were evident throughout the 44-200 atom size range. This caused the necessity of theoretical studies on the electronic properties of a giant heterofullerene, to which adequate attention, to our knowledge, has not been paid.
Pcs5s.-lt-,
In this paper, we report our theoretical investigation of the properties of heterofullerenes C~_lB(n -< 780). We have followed an extended Su-Schrieffer-Heeger model which has been successfully applied on C59B [12], in which the consistency with a self-consistent-field molecular-orbital method (SCF-MO) has been confirmed. We find in all the other boron-doped giant fullerenes, a localized distortion appears as in C59B. A mid-gap state is put into the original gap of pristine fullerenes. Relative to LUMO and those states beyond LUMO, the wave function amplitude on the dopant site turns out to be intensified in larger heterofullerenes.
2. CONSTRUCTION AND MODEL We propose a very convenient method to build an icosahedral polygon. Firstly, we nest together three rectangles with a length-width ratio l:r. These rectangles are set along three perpendicular axes as illustrated in Fig. 1. After connecting the nearestneighbored vertices of these rectangles, we obtain a total of 20 triangles which encapsulate a polygon. The three rectangles act as a skeleton to span the polygon. An icosahedral symmetry of the polygon is guaranteed only when the condition: V/r2 + (r - 1)2 + 1 = 2r is satisfied. What amazes us is that the reasonable value for r turns out to be
v/~-I 2
'
exactly the magic number for the golden section ratio. This latent feature of aesthetics contributes a graceful and
1657
1658
YING ZOU et al.
,o,
Fig. 2. The graphitic honeycomb plane. Two basis vectors, a and b, at the center of a hexagon are each labeled with an arrow. A vector OM from (0,0) to (re,n) is defined, from which an equilateral triangle can be built. The equilateral triangle as the generator of fullerene C6o is labeled as A'B'C'.
G Fig. 1. An icosahedron (thin line), together with the three skeleton rectangles ABCD, EFGH, and PQRS (thick line), the rear of which is plotted with dotted lines for clarity. A shadowed triangle EBQ connecting with vertexes E, B and Q is illustrated.
A ' B ' C ' is the corresponding generator of fullerene C60. In this way, we are able to construct any size of fullerenes
attractive appearance to the icosahedron, which may be
electron-phonon coupling would significantly deviate
the reason that icosahedral symmetry not only occurs on
from the above idealized configuration, while for specific
the molecular level but also pervasively exists in the
types of fullerenes the icosahedral symmetry survives
capsids of many virions [15]. We initiate with a graphitic honeycomb plane to build
[17, 18]. In this paper, we adopt an extended version of the SSH
the lattice structure of fullerenes [16]. Two basis vectors
model proposed in Ref. [12] to study the electronic
a and b can be defined at the center of a hexagon to reflect the translational invariance of such a plane. The position
properties of giant heterofullerenes to the advantage of our convenient structure description method. We
of any hexagon can be indicated by a vector which is the combination of shifted basis vectors. So a vector O M in
briefly note here that the original SSH Hamiltonian applied successfully in C60 [19] is modified to take the
the plane can be expressed as ma 4. nb, or simply as an index pair (m,n). Taking the vector O M as an edge, we can build up an equilateral triangle on the plane. Then we paste such a equilateral triangle on one of the surfaces of
consideration of the perturbation Hi caused by dopant
above constructed polygon. Regarding it as a generator,
which have a rigid icosahedral symmetry. However, it should be noted that a dynamic dimerization caused by
boron as H = H0 4- Hi, with Cn) r KO 2] H, = ~ / ( - t n - otnyij)(ci + Cjs 4- H ' C ) 4 . --j-'Yijl ( n = 0 , 1) ".t j (i,1), s 1.
we consecutively make I symmetry operations on it, which results in an icosahedral fullerene with atom number N = 20(m 2 + mn 4. n2), where (m,n) is the index of vector OM. In Fig. 2, the labeled triangle
where the sum with 0 or 1 is taken over the nearestneighbor pairs for the C - C bonds and C - B bonds, respectively. Details about this model are referred to in
Table 1. Calculated values of energy gap (or the energy difference between the single occupied state and LUMO state), excess electron on dopant site (only for heterofullerens), maximum difference of bond-variables, and the average total energy per electron for heterofullerens C,_tB (n = 60, 180, 240, 420, 540, 720, 780) compared with those values for pristine fullerens Cn (n = 60, 180, 240, 420, 540) Cluster
Eg (eV)
Pristine fullerenes C~ 2.2553 C]so 1.6323 C2~ 1.3882 C420 1.1150 C54o 0.9731 Boron-doped he~rofullerenes C59B 1.0604 CI79B 0.8778 C239B 0.6998 C419B 0.7474 C539B 0.5503 C719B 0.6692 C~9B 0.5014
Excess electron on dopant site n
m
-
0.565 0.538 0.478 0.447 0.400 0.353 0.354
Average total energy per electron Etot (eV)
Maximum difference of bond-variable
(Yij)max (m)
-
3.9156 3.9262 3.9282 3.9311 3.9321
0.0500 0.0278 0.0263 0.0209 0.0198
-
3.9033 3.9225 3.9265 3.9295 3.9316 3.9321 3.9328
0.1373 0.1186 0.1125 0.1094 0.1087 0.1003 0.0956
Electronic state studies of a mono-boron-doped giant heterofullerene Ref. [12]. In our numerical calculation, we have used the same parameter set as that in Ref. [12]: to=2.5eV tl = 1.025 eV
c~0=6.31 eV/,~
Ko=49.7eV/A 2
otI = 5 . 8 eV/,g, K t =49.0eV/.~ 2
Actually we reproduce similar results for the smallest heterofullerene C59B as those in Ref. [12].
3. RESULTS AND DISCUSSIONS We summarize our calculated results for heterofullerenes C,_IB (n = 60, 180, 240, 420, 540, 720, 780) along with those of pristine fullerenes Cn (n = 60, 180, 240, 420, 540) in Table 1. It can be seen from the table that, as the value of the energy gap decreases continuously for a much larger fullerene, the declination tendency of the energy differences between a singleoccupied orbit and a LUMO state for heterofullerenes can be fit as Eg(N) = ( - 2 . 9 3 × 10 -6 N 2 + 3.58 X 10 -3 N + 0.739) (-~/, of which the total atom number, N, satisfies N = 60m 2 (m defined as topological factor in Section 2). But the values for C179B, C419B, C719B and C779B are distinctively deviated from the above relationship. This can be ascribed to the effect of the topology of corresponding pristine fullerenes, because the symmetric group for these fullerenes are actually I rather than lb. The negative excess electron number on the dopant site indicates its acceptor role. Its absolute value decreases with the increasing size of the heterofullerene. It may be evidence of the more obvious "filling" on the dopant site by the delocalized electrons on the larger cage structure. A comparison of the average total energy for each electron between pristine and doped fullerenes reveals less stability in the latter ones. While the difference of average total energy per
1659
electron varies from 0.0123 eV (/~tot- C,gn -/~tot- c60) to 0.0005 eW (Etot-Cs39B-Etot-C~4o), reflecting that the perturbation effect of dopant on the matrix cage tends to become much weaker as the size of the fullerene turns smaller. It can also be found that heterofullerenes share a much larger bond-variable difference between the maximal and the minimal bondlengths than pristine fullerenes. We plot energy levels of C59B, C179B and C779B in Fig. 3 with the upper panel simultaneously illustrating the probability amplitude of different energy levels at the dopant site. It is clear that in these heterofullerenes, all wave functions of the mid-gap state (MS) have a large amplitude on the dopant site, reflecting its local characteristics. However, we note that only in C59B does the LUMO state also contribute a large part, which indicates that the electron occupying the MS state easily moves around through channels of the LUMO state and those states beyond. As to larger heterofullerenes, we find a decrease of the probability of the occupation of LUMO and states beyond LUMO. This decrease in the mobility of the electron thus also leads to a stronger bound state. We can expect from the above study that it is more feasible to form a narrow metallic band in crystal C59B than in the other crystal, C,_IB (n > 60), which is a critical factor for superconductivity. For larger heterofullerenes, it may be quite interesting to investigate the effects of dipole moment resulting from localized charge on the crystal structure as well as on the dielectric properties.
4. CONCLUSION In this paper, we report our theoretical investigations of the properties of heterofullerenes Cn-lB (n -< 780). With regard to the establishment of a succinct geometrical description of a giant fullerene (GF), we have been able to
0.4 0.2 0.0
q
I II II IIII I II I IIII I IIIII II 11
0
iiI(b)
M.~ i ~ 0
~'
I,I
0.4 g 0.0
G) C (D
8' o~
0.0 Q.
1
011 -8.0
•6,0
-4.0
-2.0
0.0
2.0
4.0
6.0
8.0
Energy (eV) Fig. 3. Energy levels (lower panel) and probability amplitude of the dopant on corresponding level (upper panel) in (a) C59B,(b) C 179B and (c) C719B.The probabilities of the mid-gap state (MS) and LUMO are indicated.
1660
YING ZOU et al.
study not only the structural but also the electronic properties of GFs using a successfully extended Su-Schrieffer-Heeger model. We found a mid-gap state (MS) within the gap of pristine fullerenes. Relative to LUMO and those states beyond LUMO, the wave function amplitude on the dopant site turns out to be intensified in larger heterofullerenes, which suggests the emergence of a bound state. For the fullerene C59B, the MS state is more delocated and indicates the possibility of the existence of a narrow metallic band in its solid form. Acknowledgements--This work has been supported by National Science Foundationand National Doctorate Foundation of China.
REFERENCES
1. Hebard, A.F., Rosseinsky, M.J., Haddon, R.C., Murphy, D.W., Glarum, S.H., Palstra, T.T.M., Ramirez, A.P. and Kortan, A.R., Nature, 1991, 350, 600. 2. Saito. S., Oshiyamam, A., Phys. Rev. Lett. 66 (1991) 2637; Hamada, N., Saito, S., Miyamoto, Y., Oshiyama, A., Jpn. J. Appl. Phys. 30 (1991) L2036. 3. Miyamoto, Y., Oshiyama, O. and Saito, S., Solid State Commun., 1992, 82, 437.
4. Guo, T., Jin, C. and Smalley, R.E., J. Phys. Chem., 1991,95, 4948. 5. Pardeep, T., Vijayakrishnan, U., Santra, A.K. and Rao, C.N.R., J. Phys. Chem., 1991, 95, 10564. 6. Yu, R. et al., Phys. Chem., 1995, 99, 1818. 7. Mattau, J. et al., Tetrahedron, 1995, 51, 6977. 8. Hummelen, J.C., Knight, B., Pavlovich, J., Gonzalez, X. and Wudl, F., Science, 1995, 269, 1554. 9. Weng-Sieh, Z. et al., Phys. Rev. B, 1995, 51, 11229. 10. Andreoni, W., Gygi, F. and Parrinello, M., Chem. Phys. Lett., 1992, 190, 159. 11. Kurita, N., Kobayashi, K., Kumahora, H., Tago, K. and Ozawa, K., Chem. Phys. Lett., 1992, 198, 95. 12. Dong, J.M., Jiang, J., Wang, Z.D. and Xing, D.Y., Phys. Rev. B, 1995, 51, 1977. 13. Kurita, N., Kobayashi, K., Kumahora, H. and Tago, K., Phys. Rev. B, 1993, 48, 4850. 14. Miyamoto, Y., Hamada, N., Oshiyama, A. and Saito, S., Phys. Rev. B, 1992, 46, 1749. 15. Harter, W.G., J. Stat. Phys, 36 (1984) 749; Pine, A.S., Maid, A.G., Robielte, A.G., Krohn, B.J., Watson, J.K.G., Urbanek, Th., J. Am. Chem. Soc. 106 (1984) 891. 16. Wang, Z.J., Li, W.Z., Cao, Z.L. and Han, R.S., Sci. China, 1995, A38, 47. 17. Harigaya, K., Phys. Rev. B, 1993, 47, 16563. 18. Wang, Z.J., Han, R.S., Cao, Z.L., Wang, Y. and Li, W.Z., Sci. China (in Chinese), 1995, 25, 719. 19. Harigaya, K., J. Phys. Soc. Jpn., 1991, 60, 4001.
Pergamon
J. Phys. Chera Solids Vo158, No. I 1, pp. 1657-1660, 1997 O 1997 Elsevier Science Ltd Printed in Great Britain. All rights t~eserved 0022-3697/97 $17.00+ 0.00
ELECTRONIC STATE STUDIES OF A MONO-BORON-DOPED GIANT HETEROFULLERENE Y I N G Z O U , Z H I J I A N W A N G and W E N Z H O U LI Department of Physics, Zhejiang University, Hangzhou 310027, P.R. China Abstract--With the establishment of a succinct geometrical description of a giant fuilerene (GF), a built-in golden ratio has been discovered. The geometrical description serves as a key start for electronic state studies on large scale fullerenes and also heterofullerenes. Utilizating an extended Su-Schrieffer-Heeger model we mainly investigate one-boron substitution in fuUerenesCn (n = 60, 180, 240, 420, 540, 720, 780). A mid-gap state can be found intruding into the gap of pristine fullerenes. The wave function amplitude spreads over the whole fullerene but has a stronger localization at the corresponding site for a larger fullerene. © 1997 Elsevier Science Ltd. Keywords: fuUerenes, boron, SSH model, golden ratio
1. INTRODUCTION Fullerenes CA have been intensively investigated. In particular, the occurrence of superconductivity in alkali-ion doped C60 [1] has attracted much interest in doped systems. Electron-doping in C60 was achieved with alkali-metal atoms inserted at the interstitial sites. Theoretical studies within the local-density approximation (LDA) have revealed [2] that an electron transfer occurs from alkali-metal s orbitals to a conduction band of solid C60, and that injected electrons in the conduction bands play an important role in the superconductivity. However, the next hole doping in which halogen is chosen as an acceptor in solid C60 has been hindered on account of the large electronegativity of C60 [3]. Very recently, Guo et al. [4] reported the gas-phase preparation of molecular clusters mainly consisting of Cto-n - B n. Later, CnNm, fullerenes were also reported by several groups [5-7]. A viable route set by Hummelen [8] made the isolation and characterization of biazafullerenyl in solution available. More recently, BxCyN z nanotubules, analogs of carbon nanotubules, have also been successfully synthesized via arc-discharge methods [9]. The boron-doped C 60fullerene is expected to be a promising new way of hole doping in solid fullerenes, and has stimulated a great interest in researchers to investigate its structural and electronic properties [10-13], as well as the band structure and cohesive energy of solid C 59B [ 14]. In this new progress, we notice a striking fact that, in the reported cluster mass spectra, the Smalley group [4] also specified that the even-numbered clusters were evident throughout the 44-200 atom size range. This caused the necessity of theoretical studies on the electronic properties of a giant heterofullerene, to which adequate attention, to our knowledge, has not been paid.
Pcs5s.-lt-,
In this paper, we report our theoretical investigation of the properties of heterofullerenes C~_lB(n -< 780). We have followed an extended Su-Schrieffer-Heeger model which has been successfully applied on C59B [12], in which the consistency with a self-consistent-field molecular-orbital method (SCF-MO) has been confirmed. We find in all the other boron-doped giant fullerenes, a localized distortion appears as in C59B. A mid-gap state is put into the original gap of pristine fullerenes. Relative to LUMO and those states beyond LUMO, the wave function amplitude on the dopant site turns out to be intensified in larger heterofullerenes.
2. CONSTRUCTION AND MODEL We propose a very convenient method to build an icosahedral polygon. Firstly, we nest together three rectangles with a length-width ratio l:r. These rectangles are set along three perpendicular axes as illustrated in Fig. 1. After connecting the nearestneighbored vertices of these rectangles, we obtain a total of 20 triangles which encapsulate a polygon. The three rectangles act as a skeleton to span the polygon. An icosahedral symmetry of the polygon is guaranteed only when the condition: V/r2 + (r - 1)2 + 1 = 2r is satisfied. What amazes us is that the reasonable value for r turns out to be
v/~-I 2
'
exactly the magic number for the golden section ratio. This latent feature of aesthetics contributes a graceful and
1657
1658
YING ZOU et al.
,o,
Fig. 2. The graphitic honeycomb plane. Two basis vectors, a and b, at the center of a hexagon are each labeled with an arrow. A vector OM from (0,0) to (re,n) is defined, from which an equilateral triangle can be built. The equilateral triangle as the generator of fullerene C6o is labeled as A'B'C'.
G Fig. 1. An icosahedron (thin line), together with the three skeleton rectangles ABCD, EFGH, and PQRS (thick line), the rear of which is plotted with dotted lines for clarity. A shadowed triangle EBQ connecting with vertexes E, B and Q is illustrated.
A ' B ' C ' is the corresponding generator of fullerene C60. In this way, we are able to construct any size of fullerenes
attractive appearance to the icosahedron, which may be
electron-phonon coupling would significantly deviate
the reason that icosahedral symmetry not only occurs on
from the above idealized configuration, while for specific
the molecular level but also pervasively exists in the
types of fullerenes the icosahedral symmetry survives
capsids of many virions [15]. We initiate with a graphitic honeycomb plane to build
[17, 18]. In this paper, we adopt an extended version of the SSH
the lattice structure of fullerenes [16]. Two basis vectors
model proposed in Ref. [12] to study the electronic
a and b can be defined at the center of a hexagon to reflect the translational invariance of such a plane. The position
properties of giant heterofullerenes to the advantage of our convenient structure description method. We
of any hexagon can be indicated by a vector which is the combination of shifted basis vectors. So a vector O M in
briefly note here that the original SSH Hamiltonian applied successfully in C60 [19] is modified to take the
the plane can be expressed as ma 4. nb, or simply as an index pair (m,n). Taking the vector O M as an edge, we can build up an equilateral triangle on the plane. Then we paste such a equilateral triangle on one of the surfaces of
consideration of the perturbation Hi caused by dopant
above constructed polygon. Regarding it as a generator,
which have a rigid icosahedral symmetry. However, it should be noted that a dynamic dimerization caused by
boron as H = H0 4- Hi, with Cn) r KO 2] H, = ~ / ( - t n - otnyij)(ci + Cjs 4- H ' C ) 4 . --j-'Yijl ( n = 0 , 1) ".t j (i,1), s 1.
we consecutively make I symmetry operations on it, which results in an icosahedral fullerene with atom number N = 20(m 2 + mn 4. n2), where (m,n) is the index of vector OM. In Fig. 2, the labeled triangle
where the sum with 0 or 1 is taken over the nearestneighbor pairs for the C - C bonds and C - B bonds, respectively. Details about this model are referred to in
Table 1. Calculated values of energy gap (or the energy difference between the single occupied state and LUMO state), excess electron on dopant site (only for heterofullerens), maximum difference of bond-variables, and the average total energy per electron for heterofullerens C,_tB (n = 60, 180, 240, 420, 540, 720, 780) compared with those values for pristine fullerens Cn (n = 60, 180, 240, 420, 540) Cluster
Eg (eV)
Pristine fullerenes C~ 2.2553 C]so 1.6323 C2~ 1.3882 C420 1.1150 C54o 0.9731 Boron-doped he~rofullerenes C59B 1.0604 CI79B 0.8778 C239B 0.6998 C419B 0.7474 C539B 0.5503 C719B 0.6692 C~9B 0.5014
Excess electron on dopant site n
m
-
0.565 0.538 0.478 0.447 0.400 0.353 0.354
Average total energy per electron Etot (eV)
Maximum difference of bond-variable
(Yij)max (m)
-
3.9156 3.9262 3.9282 3.9311 3.9321
0.0500 0.0278 0.0263 0.0209 0.0198
-
3.9033 3.9225 3.9265 3.9295 3.9316 3.9321 3.9328
0.1373 0.1186 0.1125 0.1094 0.1087 0.1003 0.0956
Electronic state studies of a mono-boron-doped giant heterofullerene Ref. [12]. In our numerical calculation, we have used the same parameter set as that in Ref. [12]: to=2.5eV tl = 1.025 eV
c~0=6.31 eV/,~
Ko=49.7eV/A 2
otI = 5 . 8 eV/,g, K t =49.0eV/.~ 2
Actually we reproduce similar results for the smallest heterofullerene C59B as those in Ref. [12].
3. RESULTS AND DISCUSSIONS We summarize our calculated results for heterofullerenes C,_IB (n = 60, 180, 240, 420, 540, 720, 780) along with those of pristine fullerenes Cn (n = 60, 180, 240, 420, 540) in Table 1. It can be seen from the table that, as the value of the energy gap decreases continuously for a much larger fullerene, the declination tendency of the energy differences between a singleoccupied orbit and a LUMO state for heterofullerenes can be fit as Eg(N) = ( - 2 . 9 3 × 10 -6 N 2 + 3.58 X 10 -3 N + 0.739) (-~/, of which the total atom number, N, satisfies N = 60m 2 (m defined as topological factor in Section 2). But the values for C179B, C419B, C719B and C779B are distinctively deviated from the above relationship. This can be ascribed to the effect of the topology of corresponding pristine fullerenes, because the symmetric group for these fullerenes are actually I rather than lb. The negative excess electron number on the dopant site indicates its acceptor role. Its absolute value decreases with the increasing size of the heterofullerene. It may be evidence of the more obvious "filling" on the dopant site by the delocalized electrons on the larger cage structure. A comparison of the average total energy for each electron between pristine and doped fullerenes reveals less stability in the latter ones. While the difference of average total energy per
1659
electron varies from 0.0123 eV (/~tot- C,gn -/~tot- c60) to 0.0005 eW (Etot-Cs39B-Etot-C~4o), reflecting that the perturbation effect of dopant on the matrix cage tends to become much weaker as the size of the fullerene turns smaller. It can also be found that heterofullerenes share a much larger bond-variable difference between the maximal and the minimal bondlengths than pristine fullerenes. We plot energy levels of C59B, C179B and C779B in Fig. 3 with the upper panel simultaneously illustrating the probability amplitude of different energy levels at the dopant site. It is clear that in these heterofullerenes, all wave functions of the mid-gap state (MS) have a large amplitude on the dopant site, reflecting its local characteristics. However, we note that only in C59B does the LUMO state also contribute a large part, which indicates that the electron occupying the MS state easily moves around through channels of the LUMO state and those states beyond. As to larger heterofullerenes, we find a decrease of the probability of the occupation of LUMO and states beyond LUMO. This decrease in the mobility of the electron thus also leads to a stronger bound state. We can expect from the above study that it is more feasible to form a narrow metallic band in crystal C59B than in the other crystal, C,_IB (n > 60), which is a critical factor for superconductivity. For larger heterofullerenes, it may be quite interesting to investigate the effects of dipole moment resulting from localized charge on the crystal structure as well as on the dielectric properties.
4. CONCLUSION In this paper, we report our theoretical investigations of the properties of heterofullerenes Cn-lB (n -< 780). With regard to the establishment of a succinct geometrical description of a giant fullerene (GF), we have been able to
0.4 0.2 0.0
q
I II II IIII I II I IIII I IIIII II 11
0
iiI(b)
M.~ i ~ 0
~'
I,I
0.4 g 0.0
G) C (D
8' o~
0.0 Q.
1
011 -8.0
•6,0
-4.0
-2.0
0.0
2.0
4.0
6.0
8.0
Energy (eV) Fig. 3. Energy levels (lower panel) and probability amplitude of the dopant on corresponding level (upper panel) in (a) C59B,(b) C 179B and (c) C719B.The probabilities of the mid-gap state (MS) and LUMO are indicated.
1660
YING ZOU et al.
study not only the structural but also the electronic properties of GFs using a successfully extended Su-Schrieffer-Heeger model. We found a mid-gap state (MS) within the gap of pristine fullerenes. Relative to LUMO and those states beyond LUMO, the wave function amplitude on the dopant site turns out to be intensified in larger heterofullerenes, which suggests the emergence of a bound state. For the fullerene C59B, the MS state is more delocated and indicates the possibility of the existence of a narrow metallic band in its solid form. Acknowledgements--This work has been supported by National Science Foundationand National Doctorate Foundation of China.
REFERENCES
1. Hebard, A.F., Rosseinsky, M.J., Haddon, R.C., Murphy, D.W., Glarum, S.H., Palstra, T.T.M., Ramirez, A.P. and Kortan, A.R., Nature, 1991, 350, 600. 2. Saito. S., Oshiyamam, A., Phys. Rev. Lett. 66 (1991) 2637; Hamada, N., Saito, S., Miyamoto, Y., Oshiyama, A., Jpn. J. Appl. Phys. 30 (1991) L2036. 3. Miyamoto, Y., Oshiyama, O. and Saito, S., Solid State Commun., 1992, 82, 437.
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