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Molecular structures, binding energies and electronic properties of dopyballs C59X (X=B, N and S)
Volume 198, number 1,2
CHEMICAL PHYSICS LETTERS
2 October 1992
Molecular structures, binding energies and electronic properties of dopyballs C59X (X=B, N and S) Noriyuki Kurita, Kinya Kobayashi, Hiroki Kumahora, Kazutami Tago and Kunio Ozawa Energ~ Research Laboratory, Hitachi Ltd., 1168 Moriyamacho. Hitachi-shi, Ibaraki 316, Japan
Received 10 February 1992; in final form 16 July 1992
When optimized by a molecular orbital method with Harris functional and spin-restricted approximations, the molecular structures of CsgBand C59Nare found to be almost the same as that of C60,while that ofC59S is different from that of C6o.The binding energies calculated self-consistently are 6.05 (C6o), 6.03 (CsgB), 6.00 (C59N) and 5.91 (C59S) eV/atom. The energy gaps between the LUMO and the HOMO or the half-occupied molecular orbital are 1.50 (C6o), 1.06 (C59B), 0.30 (C59N) and 0.63 eV (C59S), and the Mulliken charges of the doped B, N and S atoms are 4.5, 7.2 and 15.5, respectively, meaning the N atom exists as an acceptor, while the B and S atoms exist as donors in these dopyballs.
1. Introduction In semiconductor technology and the solid-state physics of silicon, vital electronic properties are given by doping boron or phosphorous atoms into a pure silicon crystal. It was found that the cage-shaped carbon c o m p o u n d Coo, which is an insulator in pure solid state, becomes a superconductor by doping alkali metals in the interstitial vacant sites of fcc C6o crystal [ 1 ]. This has led to systematic searches for high-To superconductors by doping m a n y kinds of atoms into the C6o lattice [2,3 ]. There are two other ways o f doping Coo: ( 1 ) doping on the inside of the C6o molecule, and (2) replacing one or more carbon atoms o f the C6o molecule with other atoms. Smalley's group has carried out successful dopings in both ways, which have led to many kinds of modified Coo molecules [4]. It was proposed that these molecules may be the building blocks of an array o f new nanometer-engineered materials. However, their structures and physical properties have not yet been clarified. In this work, we have calculated stable molecular structures o f dopyballs C59X (X = B, N and S), by using a molecular orbital method with Harris functional and spin-reCorrespondence to: N. Kurita, Energy Research Laboratory, Hitachi Ltd., 1168 Moriyamacho,Hitachi-shi, Ibaraki 316, Japan.
stricted approximations. Moreover, their binding energies and electronic properties have been calculated self-consistently.
2. Computational method For structure optimizations we use the Harris approximation [ 5 ], in which the total electron density o f the system can be approximated by a superposition of electron densities of the isolated atoms with a first-order energy correction of the density error, and in which quadratic errors in the electron Coulomb repulsion and exchange-correlation ener•gies are partially cancelled and can be ignored. This assumption makes calculations of the electrostatic potential and Coulomb energy easier and eliminates the self-consistent-field (SCF) iteration. The calculated results of the Harris approximation were compared with the results o f the SCF molecular orbital (SCF-MO) method in refs. [ 5 - 7 ] . In each step of the optimizations, atomic forces are calculated from the energy gradients, whose detailed formulations were shown in ref. [ 6 ]. And then, in order not to search local energy-minimum structures, the atoms are allowed to move according to the forces acting on them, and their velocities at a given m o m e n t [ 8 ]. The velocity of an atom is ap-
0009-2614/92/$ 05.00 © 1992 Elsevier Science Publishers B.V. All rights reserved.
95
Volume 198, number 1,2
CHEMICAL PHYSICS LETTERS
proximated as the product of the discrete time interval (St) and the vector displacement since the previous step, r(t)-r(t-St). This optimization process is iterated until the maximum atomic force becomes smaller than 0.01 hartree/ao (ao is the Bohr radius). For the optimized structure, its binding energy and electronic properties are calculated by the SCF-MO method based on the local density functional formalism. Details of formulations will appear in a future paper [7]. In the present calculations, the spin-restricted molecular orbitals are expanded in terms of Slater-type atomic orbitals and single-zeta functions [ 9 ] are used as basis functions, because of the computational time for the calculation of C59S. We use the Xot (or=0.7) exchange-correlation potential and the integral method developed by Becke [ 10] for calculating Fock and overlap matrix elements. A fine mesh Of points (1720 points per atom) is required for calculating the force acting on each atom from the energy gradients. The numerical error of integrations in the atomic force for C2 is less than 10 - 4 hartree/ ao, and the optimized bond length of C2 evaluated by the above method coincides with that calculated from total energy differentials to within 0.005 A (0.5%).
3. Results and discussion
To check the suitability of our calculation method, we first calculated the molecular structures and electronic properties of corannulene (C20Hl0) which is composed of one pentagonal and five hexagonal rings. The optimized structure is shown in fig. l, and its I-I
H
H--- c3 H
H
Fig. 1. Optimal structure of corannulene C2oH 1o.
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2 October 1992
Table 1 Optimized bond lengths (A), bond angles (deg) and Mulliken charges of corannulene C2oH~o Calc. bond lengths C 1-C 1 C 1-C2 C2-C3 C3-C3 C3-H
1.49 1.47 1.53 1.49 1.20
bond angles CI-C1-C1 CI-C1-C2 C 1-C2-C3 C3-C2-C3 C2-C3-C3 C2-C3-H C3-C3-H
107-108 121-123 116-117 125-126 120-122 117-123 116-123
Mulliken charges C2 C2 C3 H
Exp. a
1.413 1.391 1.44 1.402
108 123 114.3 130.9 122
6.04 6.02 6.24 0.73
") From ref. [ 11 ].
bond lengths, bond angles and Mulliken charges are listed in table 1. The calculated results are almost the same as the experimental values [ 11 ], except for the 6% overestimation of bond lengths, which may be due to the incompleteness of the basis set and the Harris approximation. Therefore, the present method is expected to yield stable shapes of carbon fullerenes, although the bond length is somewhat overestimated. We started our structure optimization calculations for C59X with the structure of C60 optimized by the above-mentioned computational method; i.e. a truncated icosahedral with the two types of bond lengths 1.43 and 1.49 A. For C6o, C59 B, C59 N and C59S, the optimized bond lengths, binding energies, energy gaps befween LUMO (lowest unoccupied molecular orbitals) and HOMO (highest occupied molecular orbitals) or half-occupied molecular orbitals and atomic charges estimated from a Mulliken analysis are listed in table 2. Although the Mulliken analysis cannot estimate the atomic charges quantitatively, their signs can be estimated [ 12 ]. The energy levels near the Fermi level are shown in fig. 2.
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CHEMICAL PHYSICS LETTERS
Table 2 Optimized bond lengths (~,), binding energies (eV/atom), HOMO-LUMO energy gaps (eV), and atomic charges estimated from the Mulliken analysis for C6o and dopyballs C59B, C59N and C59S C60
C59 B
C59N
bond lengths C-dopant (min.) ~) C-dopant (max.) bl C-C (min.) C-C (max.)
_ 1.43 1.49
1.49 1.56 1.43 1.54
binding energy
6.05
6.03
6.00
HOMO-LUMO gap
1.50
1.06 ~)
0.30
atomic charges dopant C (min.) C (max.)
0.0 0.0
+0.5 -0.2 +0.1
CsgS
1.47 1.52 1.43 1.52
2.01 2.16 1.43 1.54 5.91 0.63
~)
-0.2 0.0 +0.1
+0.5 -0.1 0.0
a) Minimal value of bond lengths between a dopant and its nearest-neighbor carbon atoms. b) Maximal value of bond lengths between a dopant and its nearest-neighbor carbon atoms. ¢) Energy gaps between the half-occupied and the lowest unoccupied orbitals. Coo
C5~ B
C59N
C59S
-4£
--
N
__--
~-L U M O ~ -- *
=~-L-UMO
-6.[ - t~u L U M O ~ L U M O
-8.[
--~HOMO
hu HOMO =
oJ -10.{
L ~E - 12.(} ILl - 14.(} -
-
-16.0
-18.0 - -
m
=-
~
~
Z
-
~
~
Orbital (a)
(b)
_-
-
~
•
degeneracy (c)
(d)
Fig. 2. Energy levels near the Fermi level for Cso, C59B, C59N and C59S. The half-occupied, the highest occupied and the lowest unoccupied molecular orbitals are marked with #, HOMO and LUMO, respectively.
For C59 B and C59N , the optimized bond lengths between a doped atom and its nearest-neighbor carbon atoms are 1.49-1.56 and 1.47-1.52/1., respec-
2 October 1992
tively. The bond lengths between adjacent carbon atoms are 1.43-1.54 (C59B) and 1.43-1.52 A (C59N), which are similar to the bond lengths of C60 ( 1.43 and 1.49 A). The maximum atomic distortions from the C6o structure are 0.07 and 0.06 ]L respectively, for C59B and C~9N. These small values (about 5% of the bond lengths) can be related to the similarity of the B-C (1.56/k) and N-C (1.47 A) bond lengths to that o f C - C ( 1.54 ]k for a single bond and 1.34 A for a double bond) [ 13 ]. The binding energies, the difference in the total energies of the whole system and the fragments, were calculated self-consistently by the SCF-MO method. The results for C59B (6.03 eV/atom) and C59N (6.00 eV/atom) are almost the same as that for C6o (6.05 eV/atom). Therefore, it is expected that C59B and C59N molecules would be stable, if a B or N atom is doped during the formation process of a cage molecule. Smalley et al. [4] found that it was more difficult to obtain C59N than C59B. This result is attributed to the much larger binding energy of diatomic N2 (9.9 eV) than those of C2 (6.355 eV) and B2 (3.0 eV) [ 14 ]. The electronic properties of C59B and C59N are different from each other, because of the difference in valency of the doped atoms. Since the icosahedral symmetry of C6o is lost by doping, each energy level of C59X splits. In fig. 2, the molecular orbitals whose energies agree with each other to within 0.05 eV are regarded as degenerate, and the length of each horizontal bar gives the orbital degeneracy. Since the structures of Cs9B and C59N are almost the same as that of C6o, there are many approximately degenerate orbitals. Replacing one C by a B atom, one hole is doped in the HOMO (hu symmetry) of C6o, and the half-occupied level with one hole is in about a 0.4 eV higher energy region than the other four levels, so that the energy gap between this level and the LUMO level is 1.06 eV. On the other hand, by doping with an N atom, one electron is doped in the LUMO (tlu symmetry) of C6o, and it splits into three nondegenerate levels. One of these levels is half-occupied with one electron and in about a 0.3 eV lower-energy region, so that the energy gap between this level and the LUMO level of C59N is 0.30 eV. These results indicate the possibility that C6o_2nl2n and C60_2nN2n can be the components of various band-gap semiconductors. 97
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CHEMICALPHYSICSLETTERS
The MO levels, which contain the 2s (2p,,) character of the doped B atom, are in the 7.7-9.7 (3.55.0) eV lower-energy region than the half-occupied MO level, while those with the 2p~ character are in the 0.0-3.5 eV higher-energy region. The atomic charge estimated from a Mulliken analysis of B is +0.5, so that the doped B donates electronic charge to its neighbor carbons and exists as a donor. On the other hand, the, MO levels containing the 2s (2p,) character of the doped N atoms are in the 17-20 (9.0-11 ) eV lower-energy region than the half-occupied MO level, while those with the 2p~ character are in the energy region from 6.0 eV lower to 1.5 eV higher than the half-occupied MO level. The doped N atom exists as an acceptor, whose atomic charge is - 0 . 2 . Therefore, C59B and C59N have opposite electronic polarizations, while the C6o molecule is isotropic. The calculated atomic charge of B is consistent with the experimental result [ 4 ] that an electron-deficient site was produced at the B position on the cage. In the case of doping into silicon (the IV family in the periodic table), doped boron (the III family) exists as an acceptor, while doped phosphorous (the V family) exists as a donor. Thus, the present results for C59B and C59N differ greatly from that for silicon. This difference is expected to be related to the uniqueness of C6o in its electronic properties; large electron affinity, electronic band structure etc. Our final goal is to predict the existence of other stable dopyballs C6o-nXn (X is neither B nor N) and to investigate their electronic properties. Smalley's group chose boron and nitrogen as a replacement for carbon in C6o, considering the bond strength, size and valency [ 4 ]. In order to check ifa spherical structure is maintained or not when a large-size atom is doped in the C6o cage, we chose a sulfur atom as a replacement candidate, since its electronegativity (2.58 ) is similar to that of carbon (2.55) [13]. To obtain a stable structure of C59S, it took about five times as many structure optimization steps as for C59B and C59N. A large force (about 0.2 hartree/ao) acted on the replaced S atom in the C6o cage, and S was pushed outward from the cage, so that the distance between S and its nearest-neighbor carbon atoms was 2.012.16 ,~, for the optimized structure shown in fig. 3. The binding energy calculated by the SCF-MO method is 5.91 eV/atom and is much smaller than those of C59B and Cs9N. Therefore, when a large-size 98
2 October 1992
Fig. 3. Optimized structure of C59S.The black circle is the doped S atom, and two atoms whosedistance is lessthan 2.0/k are joined by bonds. The distances between S and its nearest-neighborcarbons are 2.01-2.16 A. atom such as S is doped in the C6ocage, the spherical structure of C6o can be distorted. As shown in fig. 2 and table 2, the energy gap between the H O M O and LUMO of C59S is 0.63 eV, and both H O M O and LUMO have the character of the carbon atoms. The MO levels containing the 3s character of the doped S atom are in the 15-17 eV lower-energy region than the H O M O level, while those with the 3p character split into two, whose MO levels are in the 5.1-6.3 eV lower-energy region than the H O M O level and the 0.1-1.5 eV higher-energy region than the LUMO level, respectively. The atomic charge of S estimated from a Mulliken analysis is +0.5, so that the doped S exists as a donor in the cage.
4. Conclusion To investigate the molecular structures and physical properties of dopyballs C59B and C59N, and to search for new dopybaUs, we optimized the structures ofC59x (X=B, N and S) by using a molecular orbital method with Harris functional and spin-restricted approximations. For C59Band C59N, the optimized structures and binding energies were almost the same as those for C60, so that they would be stable if a B or N atom is doped in the C60 cage. On the
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CHEMICAL PHYSICS LETTERS
other hand, the optimized structure of C59S was different from that of C60, because of the larger force acting on the replaced S atom in the C60 cage. The energy levels near the Fermi level were remarkably changed by doping. Doping with a B atom gave one hole doped in the H O M O of C60, so that the energy gap between the half-occupied orbital and the LUMO of C59 B w a s 1.06 eV. Doping with a N atom gave one electron doped in the LUMO of C60 and the energy gap between the half-occupied orbital and the LUMO of C59 N w a s 0.30 eV. For C59S, the energy gap between the HOMO and LUMO was 0.63 eV. The atomic charges estimated from a Mulliken analysis of doped B, N and S atoms were + 0.5, - 0 . 2 and +0.5, respectively, so that the N atom exists as an acceptor, while the B and S atoms exist as donors in C59x. From these results, we propose that C6o_2nX2ndopyballs may be important components of semiconductors with various band gaps and electronic polarizations.
Acknowledgement We thank Dr. S. Maruyama of the University of Tokyo for helpful discussions about dopyballs.
2 October 1992
References [ 1 ] A.F. Hebard, M.J. Rosseinsky, R.C. Haddon, D.W. Murphy, S.H. Glarum, T.T.M. Palstra, A.P. Ramirez and A.R. Kortan, Nature 350 ( 1991 ) 600. [2] K. Holczer, O. Klein, S.-M. Huang, R.B. Kaner, K.-J. Fu, R.L. Whetten and F. Diederich, Science 252 ( 1991 ) 1154. [ 3 ] K. Tanigaki, T.W. Ebbesen, S. Saito, J. Mizuki, J.S. Tsai, Y. Kubo and S. Kuroshima, Nature 352 ( 1991 ) 222. [4] T. Guo, C. Jin and R.E. Smalley, J. Phys. Chem. 95 ( 1991 ) 4948; Y. Chai, T. Guo, C. Jin, R.E. Haufler, L.P.F. Chibante, J. Fure, L. Wang, J.M. Alford and R.E. Smalley, J. Phys. Chem. 95 (1991) 7564. [ 5 ] J. Harris, Phys. Rev. B 31 ( 1985 ) 1770. [6] F.W. Averill and G.S. Painter, Phys. Rev. B 41 (1990) 10344. [ 7 ] K. Kobayashi, N. Kurita, H. Kumahora and K. Tago, to be submitted for publication. [8] L. Goodwin, Phys. Rev. B 44 ( 1991 ) 11432. [9] E. Clementi and C. Roetti, Atomic data and nuclear data tables 14 (1974) 445. [ 10] A.D. Becke, J. Chem. Phys. 88 (1988) 2547. [ 11 ] W.E. Barth and R.G. Lawton, J. Am. Chem. Soc. 93 ( 1971 ) 1730. [ 12] A. Szabo and N.S. Ostlund, Modem quantum chemistry (Macmillan, New York, 1982). [ 13 ] J. Emsley, The elements (Clarendon Press, Oxford, 1991 ). [14]K.P. Huber and G. Herzberg, Molecular structure and molecular spectra, Vol. 4 (Van Nostrand Reinhold, New York, 1979).
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Molecular structures, binding energies and electronic properties of dopyballs C59X (X=B, N and S) Noriyuki Kurita, Kinya Kobayashi, Hiroki Kumahora, Kazutami Tago and Kunio Ozawa Energ~ Research Laboratory, Hitachi Ltd., 1168 Moriyamacho. Hitachi-shi, Ibaraki 316, Japan
Received 10 February 1992; in final form 16 July 1992
When optimized by a molecular orbital method with Harris functional and spin-restricted approximations, the molecular structures of CsgBand C59Nare found to be almost the same as that of C60,while that ofC59S is different from that of C6o.The binding energies calculated self-consistently are 6.05 (C6o), 6.03 (CsgB), 6.00 (C59N) and 5.91 (C59S) eV/atom. The energy gaps between the LUMO and the HOMO or the half-occupied molecular orbital are 1.50 (C6o), 1.06 (C59B), 0.30 (C59N) and 0.63 eV (C59S), and the Mulliken charges of the doped B, N and S atoms are 4.5, 7.2 and 15.5, respectively, meaning the N atom exists as an acceptor, while the B and S atoms exist as donors in these dopyballs.
1. Introduction In semiconductor technology and the solid-state physics of silicon, vital electronic properties are given by doping boron or phosphorous atoms into a pure silicon crystal. It was found that the cage-shaped carbon c o m p o u n d Coo, which is an insulator in pure solid state, becomes a superconductor by doping alkali metals in the interstitial vacant sites of fcc C6o crystal [ 1 ]. This has led to systematic searches for high-To superconductors by doping m a n y kinds of atoms into the C6o lattice [2,3 ]. There are two other ways o f doping Coo: ( 1 ) doping on the inside of the C6o molecule, and (2) replacing one or more carbon atoms o f the C6o molecule with other atoms. Smalley's group has carried out successful dopings in both ways, which have led to many kinds of modified Coo molecules [4]. It was proposed that these molecules may be the building blocks of an array o f new nanometer-engineered materials. However, their structures and physical properties have not yet been clarified. In this work, we have calculated stable molecular structures o f dopyballs C59X (X = B, N and S), by using a molecular orbital method with Harris functional and spin-reCorrespondence to: N. Kurita, Energy Research Laboratory, Hitachi Ltd., 1168 Moriyamacho,Hitachi-shi, Ibaraki 316, Japan.
stricted approximations. Moreover, their binding energies and electronic properties have been calculated self-consistently.
2. Computational method For structure optimizations we use the Harris approximation [ 5 ], in which the total electron density o f the system can be approximated by a superposition of electron densities of the isolated atoms with a first-order energy correction of the density error, and in which quadratic errors in the electron Coulomb repulsion and exchange-correlation ener•gies are partially cancelled and can be ignored. This assumption makes calculations of the electrostatic potential and Coulomb energy easier and eliminates the self-consistent-field (SCF) iteration. The calculated results of the Harris approximation were compared with the results o f the SCF molecular orbital (SCF-MO) method in refs. [ 5 - 7 ] . In each step of the optimizations, atomic forces are calculated from the energy gradients, whose detailed formulations were shown in ref. [ 6 ]. And then, in order not to search local energy-minimum structures, the atoms are allowed to move according to the forces acting on them, and their velocities at a given m o m e n t [ 8 ]. The velocity of an atom is ap-
0009-2614/92/$ 05.00 © 1992 Elsevier Science Publishers B.V. All rights reserved.
95
Volume 198, number 1,2
CHEMICAL PHYSICS LETTERS
proximated as the product of the discrete time interval (St) and the vector displacement since the previous step, r(t)-r(t-St). This optimization process is iterated until the maximum atomic force becomes smaller than 0.01 hartree/ao (ao is the Bohr radius). For the optimized structure, its binding energy and electronic properties are calculated by the SCF-MO method based on the local density functional formalism. Details of formulations will appear in a future paper [7]. In the present calculations, the spin-restricted molecular orbitals are expanded in terms of Slater-type atomic orbitals and single-zeta functions [ 9 ] are used as basis functions, because of the computational time for the calculation of C59S. We use the Xot (or=0.7) exchange-correlation potential and the integral method developed by Becke [ 10] for calculating Fock and overlap matrix elements. A fine mesh Of points (1720 points per atom) is required for calculating the force acting on each atom from the energy gradients. The numerical error of integrations in the atomic force for C2 is less than 10 - 4 hartree/ ao, and the optimized bond length of C2 evaluated by the above method coincides with that calculated from total energy differentials to within 0.005 A (0.5%).
3. Results and discussion
To check the suitability of our calculation method, we first calculated the molecular structures and electronic properties of corannulene (C20Hl0) which is composed of one pentagonal and five hexagonal rings. The optimized structure is shown in fig. l, and its I-I
H
H--- c3 H
H
Fig. 1. Optimal structure of corannulene C2oH 1o.
96
2 October 1992
Table 1 Optimized bond lengths (A), bond angles (deg) and Mulliken charges of corannulene C2oH~o Calc. bond lengths C 1-C 1 C 1-C2 C2-C3 C3-C3 C3-H
1.49 1.47 1.53 1.49 1.20
bond angles CI-C1-C1 CI-C1-C2 C 1-C2-C3 C3-C2-C3 C2-C3-C3 C2-C3-H C3-C3-H
107-108 121-123 116-117 125-126 120-122 117-123 116-123
Mulliken charges C2 C2 C3 H
Exp. a
1.413 1.391 1.44 1.402
108 123 114.3 130.9 122
6.04 6.02 6.24 0.73
") From ref. [ 11 ].
bond lengths, bond angles and Mulliken charges are listed in table 1. The calculated results are almost the same as the experimental values [ 11 ], except for the 6% overestimation of bond lengths, which may be due to the incompleteness of the basis set and the Harris approximation. Therefore, the present method is expected to yield stable shapes of carbon fullerenes, although the bond length is somewhat overestimated. We started our structure optimization calculations for C59X with the structure of C60 optimized by the above-mentioned computational method; i.e. a truncated icosahedral with the two types of bond lengths 1.43 and 1.49 A. For C6o, C59 B, C59 N and C59S, the optimized bond lengths, binding energies, energy gaps befween LUMO (lowest unoccupied molecular orbitals) and HOMO (highest occupied molecular orbitals) or half-occupied molecular orbitals and atomic charges estimated from a Mulliken analysis are listed in table 2. Although the Mulliken analysis cannot estimate the atomic charges quantitatively, their signs can be estimated [ 12 ]. The energy levels near the Fermi level are shown in fig. 2.
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CHEMICAL PHYSICS LETTERS
Table 2 Optimized bond lengths (~,), binding energies (eV/atom), HOMO-LUMO energy gaps (eV), and atomic charges estimated from the Mulliken analysis for C6o and dopyballs C59B, C59N and C59S C60
C59 B
C59N
bond lengths C-dopant (min.) ~) C-dopant (max.) bl C-C (min.) C-C (max.)
_ 1.43 1.49
1.49 1.56 1.43 1.54
binding energy
6.05
6.03
6.00
HOMO-LUMO gap
1.50
1.06 ~)
0.30
atomic charges dopant C (min.) C (max.)
0.0 0.0
+0.5 -0.2 +0.1
CsgS
1.47 1.52 1.43 1.52
2.01 2.16 1.43 1.54 5.91 0.63
~)
-0.2 0.0 +0.1
+0.5 -0.1 0.0
a) Minimal value of bond lengths between a dopant and its nearest-neighbor carbon atoms. b) Maximal value of bond lengths between a dopant and its nearest-neighbor carbon atoms. ¢) Energy gaps between the half-occupied and the lowest unoccupied orbitals. Coo
C5~ B
C59N
C59S
-4£
--
N
__--
~-L U M O ~ -- *
=~-L-UMO
-6.[ - t~u L U M O ~ L U M O
-8.[
--~HOMO
hu HOMO =
oJ -10.{
L ~E - 12.(} ILl - 14.(} -
-
-16.0
-18.0 - -
m
=-
~
~
Z
-
~
~
Orbital (a)
(b)
_-
-
~
•
degeneracy (c)
(d)
Fig. 2. Energy levels near the Fermi level for Cso, C59B, C59N and C59S. The half-occupied, the highest occupied and the lowest unoccupied molecular orbitals are marked with #, HOMO and LUMO, respectively.
For C59 B and C59N , the optimized bond lengths between a doped atom and its nearest-neighbor carbon atoms are 1.49-1.56 and 1.47-1.52/1., respec-
2 October 1992
tively. The bond lengths between adjacent carbon atoms are 1.43-1.54 (C59B) and 1.43-1.52 A (C59N), which are similar to the bond lengths of C60 ( 1.43 and 1.49 A). The maximum atomic distortions from the C6o structure are 0.07 and 0.06 ]L respectively, for C59B and C~9N. These small values (about 5% of the bond lengths) can be related to the similarity of the B-C (1.56/k) and N-C (1.47 A) bond lengths to that o f C - C ( 1.54 ]k for a single bond and 1.34 A for a double bond) [ 13 ]. The binding energies, the difference in the total energies of the whole system and the fragments, were calculated self-consistently by the SCF-MO method. The results for C59B (6.03 eV/atom) and C59N (6.00 eV/atom) are almost the same as that for C6o (6.05 eV/atom). Therefore, it is expected that C59B and C59N molecules would be stable, if a B or N atom is doped during the formation process of a cage molecule. Smalley et al. [4] found that it was more difficult to obtain C59N than C59B. This result is attributed to the much larger binding energy of diatomic N2 (9.9 eV) than those of C2 (6.355 eV) and B2 (3.0 eV) [ 14 ]. The electronic properties of C59B and C59N are different from each other, because of the difference in valency of the doped atoms. Since the icosahedral symmetry of C6o is lost by doping, each energy level of C59X splits. In fig. 2, the molecular orbitals whose energies agree with each other to within 0.05 eV are regarded as degenerate, and the length of each horizontal bar gives the orbital degeneracy. Since the structures of Cs9B and C59N are almost the same as that of C6o, there are many approximately degenerate orbitals. Replacing one C by a B atom, one hole is doped in the HOMO (hu symmetry) of C6o, and the half-occupied level with one hole is in about a 0.4 eV higher energy region than the other four levels, so that the energy gap between this level and the LUMO level is 1.06 eV. On the other hand, by doping with an N atom, one electron is doped in the LUMO (tlu symmetry) of C6o, and it splits into three nondegenerate levels. One of these levels is half-occupied with one electron and in about a 0.3 eV lower-energy region, so that the energy gap between this level and the LUMO level of C59N is 0.30 eV. These results indicate the possibility that C6o_2nl2n and C60_2nN2n can be the components of various band-gap semiconductors. 97
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The MO levels, which contain the 2s (2p,,) character of the doped B atom, are in the 7.7-9.7 (3.55.0) eV lower-energy region than the half-occupied MO level, while those with the 2p~ character are in the 0.0-3.5 eV higher-energy region. The atomic charge estimated from a Mulliken analysis of B is +0.5, so that the doped B donates electronic charge to its neighbor carbons and exists as a donor. On the other hand, the, MO levels containing the 2s (2p,) character of the doped N atoms are in the 17-20 (9.0-11 ) eV lower-energy region than the half-occupied MO level, while those with the 2p~ character are in the energy region from 6.0 eV lower to 1.5 eV higher than the half-occupied MO level. The doped N atom exists as an acceptor, whose atomic charge is - 0 . 2 . Therefore, C59B and C59N have opposite electronic polarizations, while the C6o molecule is isotropic. The calculated atomic charge of B is consistent with the experimental result [ 4 ] that an electron-deficient site was produced at the B position on the cage. In the case of doping into silicon (the IV family in the periodic table), doped boron (the III family) exists as an acceptor, while doped phosphorous (the V family) exists as a donor. Thus, the present results for C59B and C59N differ greatly from that for silicon. This difference is expected to be related to the uniqueness of C6o in its electronic properties; large electron affinity, electronic band structure etc. Our final goal is to predict the existence of other stable dopyballs C6o-nXn (X is neither B nor N) and to investigate their electronic properties. Smalley's group chose boron and nitrogen as a replacement for carbon in C6o, considering the bond strength, size and valency [ 4 ]. In order to check ifa spherical structure is maintained or not when a large-size atom is doped in the C6o cage, we chose a sulfur atom as a replacement candidate, since its electronegativity (2.58 ) is similar to that of carbon (2.55) [13]. To obtain a stable structure of C59S, it took about five times as many structure optimization steps as for C59B and C59N. A large force (about 0.2 hartree/ao) acted on the replaced S atom in the C6o cage, and S was pushed outward from the cage, so that the distance between S and its nearest-neighbor carbon atoms was 2.012.16 ,~, for the optimized structure shown in fig. 3. The binding energy calculated by the SCF-MO method is 5.91 eV/atom and is much smaller than those of C59B and Cs9N. Therefore, when a large-size 98
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Fig. 3. Optimized structure of C59S.The black circle is the doped S atom, and two atoms whosedistance is lessthan 2.0/k are joined by bonds. The distances between S and its nearest-neighborcarbons are 2.01-2.16 A. atom such as S is doped in the C6ocage, the spherical structure of C6o can be distorted. As shown in fig. 2 and table 2, the energy gap between the H O M O and LUMO of C59S is 0.63 eV, and both H O M O and LUMO have the character of the carbon atoms. The MO levels containing the 3s character of the doped S atom are in the 15-17 eV lower-energy region than the H O M O level, while those with the 3p character split into two, whose MO levels are in the 5.1-6.3 eV lower-energy region than the H O M O level and the 0.1-1.5 eV higher-energy region than the LUMO level, respectively. The atomic charge of S estimated from a Mulliken analysis is +0.5, so that the doped S exists as a donor in the cage.
4. Conclusion To investigate the molecular structures and physical properties of dopyballs C59B and C59N, and to search for new dopybaUs, we optimized the structures ofC59x (X=B, N and S) by using a molecular orbital method with Harris functional and spin-restricted approximations. For C59Band C59N, the optimized structures and binding energies were almost the same as those for C60, so that they would be stable if a B or N atom is doped in the C60 cage. On the
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CHEMICAL PHYSICS LETTERS
other hand, the optimized structure of C59S was different from that of C60, because of the larger force acting on the replaced S atom in the C60 cage. The energy levels near the Fermi level were remarkably changed by doping. Doping with a B atom gave one hole doped in the H O M O of C60, so that the energy gap between the half-occupied orbital and the LUMO of C59 B w a s 1.06 eV. Doping with a N atom gave one electron doped in the LUMO of C60 and the energy gap between the half-occupied orbital and the LUMO of C59 N w a s 0.30 eV. For C59S, the energy gap between the HOMO and LUMO was 0.63 eV. The atomic charges estimated from a Mulliken analysis of doped B, N and S atoms were + 0.5, - 0 . 2 and +0.5, respectively, so that the N atom exists as an acceptor, while the B and S atoms exist as donors in C59x. From these results, we propose that C6o_2nX2ndopyballs may be important components of semiconductors with various band gaps and electronic polarizations.
Acknowledgement We thank Dr. S. Maruyama of the University of Tokyo for helpful discussions about dopyballs.
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