NANO LETTERS
Formation of Fullerene Molecules from Carbon Nanotubes: A Quantum Chemical Molecular Dynamics Study
2003 Vol. 3, No. 4 465-470
Stephan Irle,† Guishan Zheng,† Marcus Elstner,‡,§ and Keiji Morokuma*,† Cherry L. Emerson Center for Scientific Computation and Department of Chemistry, Emory UniVersity, Atlanta, Georgia 30322, UniVersita¨ t Paderborn, Fachbereich Physik, 33095 Paderborn, Germany, and Deutsches Krebsforschungszentrum, Abteilung Molekulare Biophysik, Im Neuenheimer Feld 280, 69120 Heidelberg, Germany Received January 13, 2003; Revised Manuscript Received February 14, 2003
ABSTRACT The first quantum chemical molecular dynamics calculations for the formation of fullerene molecules from carbon nanotubes are presented. The use of quantum chemical potential is shown to be essential to describe important effects of π-conjugation in fullerene chemistry. Trajectories for open-ended carbon nanotubes with various tube lengths were run at 1000−5000 K, using the density functional tight-binding potential. At temperatures around 3000 K, extremely fast fullerene formation was observed in about 14 ps and shorter.
Although fullerenes have been around for some time, the mechanism of their formation still remains unknown and constitutes one of the most challenging topics in fullerene chemistry. The conditions under which fullerene molecules are formed are very harsh and involve either vaporization of graphite by laser1 or combustion of hydrocarbon molecules in oxygen-rich diffusion flames under low pressure.2,3 In the process only reaction products have been identified, and intermediate species with potentially helpful information for understanding of the formation mechanism have not been detected. The abundance of closed carbon cage structures in the products (up to 40%) clearly indicates that there must exist some mechanisms of building highly organized fullerenes and nanotubes from small carbon fragments. The most important structural requirement is known to be the introduction of pentagons into the hexagon lattice for graphite structures to develop curvature. Over the years, a plethora of fullerene growth mechanisms have appeared in the literature to rationalize how highly structured, chemically almost inert species such as fullerene molecules can emerge from a chaotic mixture of small carbon fragments in surprising abundance. Among the most prominent are the “pentagon road,”4 the “fullerene road,”5 the “ring-stacking” mechanism,6 and the “ring fusion spiral zipper” mechanism.7,8 While these mechanisms are more or less guesswork and rely on different assumptions, they all * Corresponding author: E-mail
[email protected]. † Emory University. ‡ Universita ¨ t Paderborn. § Abteilung Molekulare Biophysik. 10.1021/nl034023y CCC: $25.00 Published on Web 03/13/2003
© 2003 American Chemical Society
share an underlying principal of order by which fullerene molecules are either constructed stepwise from well-defined smaller carbon fragments or spontaneously formed by the collapse of a highly preorganized structure. Quantum mechanical (QM) electronic structure calculations have been performed on numerous hypothetical intermediate structures,9-12 and even an attempt has been made to locate transition states connecting intermediate structures and describing entire pathways for the formation of the C28 fullerene molecule starting from small rings such as C9 and C13.13 It is, however, more than questionable whether an orderly growth process along a single or multiple reaction pathways with well-defined intermediate species can be assumed to take place under the high-temperature nonequilibrium conditions during which fullerene molecules are produced. The high-temperature conditions of the formation processes allow the carbon clusters to climb upward on hills of the potential energy surface, and let rapidly fluctuating structures play a key role in the formation mechanism. Although molecular dynamical (MD) studies for energetics of intermediate structures along a proposed reaction pathway have been performed,14 direct insight into the formation mechanism cannot be gained from such studies. Reactive dynamical approaches allowing bond formation and breaking are required for this purpose. Monte Carlo15 as well as MD studies on the formation mechanism of fullerene molecules from atomic carbon and small carbon clusters16-18 have been reported in the literature. Most of these studies use semiclassical reactive empirical
bond-order (REBO) interatomic carbon-carbon molecular mechanics (MM) force field developed by Brenner for studying vapor deposition of diamond.19 Unlike classical MM force fields, the REBO potential allows for the formation and dissociation of covalent chemical bonds during a simulation by determination of next neighbors and switching bond functions. Fullerene formation was observed in MM/ MD studies17,18 on a nanosecond time scale at a temperature of 3000 K. However, because fullerenes and carbon nanotubes are all made from sp2 hybridized atoms where π-conjugational effects are important, we strongly feel that classical or semiclassical MM force field methods are inappropriate for reaction dynamics of all-carbon clusters. Concepts such as aromaticity and delocalization stabilization are crucial for a realistic description of conjugated carbon clusters and absent in such force fields. The influence of the electronic structure on relative stabilities and locations of bond formation or breaking cannot be taken into account by the very nature of the atomic force field approach. Therefore, MD studies based on such MM force fields cannot be even qualitatively correct. Thus for the study of the mechanism of fullerene formation, it is essential to use QM electronic structure methods and perform molecular dynamics (QM/MD) calculations. Spontaneous capping on single ends of carbon nanotubes has been observed in Car-Parinello type QM/MD calculations;20 however, except for a discussion of relative stabilities, no analysis was attempted as to how the closure occurred and what the role of electronic structure is for individual steps. Here we report for the first time results of QM/MD simulations of carbon nanotubes leading to completely closed cage fullerene structures and identify key steps during these dynamics. We believe that, even though using carbon nanotubes as initial structures is certainly somewhat artificial for the study of fullerene formation, the knowledge of “major players” emerging from our QM/MD simulations will lead to deeper understanding of general growth mechanisms in carbon nanochemistry. We ran trajectories for a canonical ensemble with a velocity Verlet integrator, using 1.2 fs as for time step unless otherwise noted. Temperature was kept constant by scaling of atomic velocities at random intervals plus regular intervals of 12 fs with an overall probability of 20%. (In the case of a (5,5) tube with 7.5 Å length at 3000 K we tested scaling of temperature at a lower rate (5%) and actually observed faster closing of both ends, indicating that a scaling probability of 20% does not artificially speed up the dynamics simulation.) All calculations were carried out using a 30 Å cubic periodic cell. Random velocities are applied at the first step of each trajectory, making the choice of initial geometries irrelevant to the dynamics. To obtain energies and gradients, all-valence electronic structure calculations were carried out using the computationally inexpensive density functional tight binding (DFTB) method.21,22 DFTB is a method approximating density functional theory (DFT) utilizing an optimized minimal LCAO basis set in combination with a two-center approximation for the Hamilton matrix elements. All parameters of the method are calculated from 466
DFT, and no fitting to experimental data is involved. DFTB has been successfully used in the past to explain relative stabilities of fullerene isomers and aggregates.23-27 Orbital occupation numbers were determined for each time step; when energy differences are smaller than 10-4 a.u., orbitals are considered to be degenerate and electrons are distributed based on the Hund rule. While total energies are not affected by the way that electrons are distributed among degenerate orbitals, gradients depend on the spatial distribution of the wave function. It is well known that neutral carbon clusters adapt different configurations upon cluster growth. Cn clusters with n e 5 prefer linear cumulene-type structures, and in the intermediate regime of 6 e n < 18, monocyclic isomers are preferred, before fullerenoid structures become the most stable species for n e 18.11,28 In contrast to the semiempirical AM129 and PM330 methods, DFTB is capable of reproducing these crucial configuration preferences for carbon clusters and more in line with the full DFT calculations such as B3LYP/631G(d).31 We chose to run MD trajectories starting with open-ended carbon nanotubes of different chirality and lengths at various temperatures. In total, we ran more than 70 trajectories, most of them for at least 12 ps. The low temperature 1000 K regime was nonreactive and the high-temperature regime above 4000 K led to fragmentation. Three different types of (n,m) nanotubes were chosen with about the same diameter d: armchair (5,5), d ) 6.88 Å, chiral (7,3), d ) 7.15 Å, and zigzag (9,0), d ) 7.06 Å. In addition, a (10,5) nanotube with a much larger diameter of d ) 10.5 Å was studied. Three different tube lengths (7.5, 10, and 20 Å) were adopted for each species. An important finding is that the diameter of the (10,5) nanotube appears to be too large to allow its openings to be closed within 12 ps, regardless of the tube length. Table 1 gives an overview of trajectories at 2000, 3000, and 4000 K (omitting our 2500 and 3500 K simulations for brevity) for (5,5), (7,3), and (9,0) open nanotubes. We call the end of a tube “closed” when the largest rings present in the opening involve not more than 8 carbon atoms. A measure of 1.8 Å was used as a threshold for bonded interaction. Since only one or a few trajectories were run for each case, we make no claims on the statistical validity of the findings. However, we want to extract important dynamic events common to many of these trajectories. The most striking finding of the present study is that many trajectories at 3000 and 4000 K closed both ends and formed fullerene structures within 14 ps. The time required for closure does not seem to depend on the length of the tube. As will be described in detail later, the key dynamics is an interplay between wobbling C2 fragments, which are formed at the ends of the tube and occasionally catch neighboring hexagons to form pentagons, and creation, migration, and isomerization of pentagons. Trajectories at 4000 K, compared to 3000 K, show higher C2 formation activities and tend to close faster, accompanied with loss of C1 to C3 fragments. Trajectories at 2000 K also formed wobbling bonds at lower Nano Lett., Vol. 3, No. 4, 2003
Table 1. Selected Trajectories of (5,5), (7,3), and (9,0) Cn Nanotubes at Temperatures T ) 2000, 3000, and 4000 K with Various Lengthsa type (n,m)
length [Å]
Cn n
T [K]
〈V〉/n [kcal/mol]
sim. time [ps]
(5,5)
7.5
70
2000 3000 3000 4000 2000 3000 4000 2000 3000 4000 2000 3000 4000 2000 3000 4000 2000 3000 4000 2000 3000 4000 2000 3000 4000 2000 3000 4000
-66.8 -62.3 -63.7 -40.1 -69.7 -64.4 -51.7 -74.4 -69.4 -59.7 -65.0 -60.3 -39.9 -70.4 -64.8 -62.8 -74.6 -68.9 -59.8 -68.5 -62.0 -46.7 -69.3 -64.3 -47.5 -74.9 -67.9 -60.6
11.89 23.78 23.78 11.89 11.89 11.89 5.37 9.46 5.35 14.21 11.90 11.90 11.90 11.89 11.89 11.89 7.92 7.92 8.26 11.89 11.90 11.90 9.98 11.66 11.90 7.99 15.86 10.14
10.0
20.0
(7,3)
7.5
10.0
20.0
(9,0)
7.5
10.0
20.0
90
170
70
98
182
90
108
180
τ1 [ps]
τ2 [ps]
11.69 1.64
14.22 4.93
6.60 3.77
10.55 5.44
1.48 1.28
3.39
7.73
11.84
8.58 7.62
11.01
3.89 1.63
7.48 5.75
10.50
7.22
12.89 5.59
13.88 10.29
# of lost C1|C2|C3 units
# of final 4/5/6/7 rings
0|0|0 0|1|0 2|0|0 destroyed 0|0|0 0|0|0 0|4|0 0|0|0 0|0|0 3|5|0 0|0|0 0|0|0 destroyed 0|0|0 0|1|0 destroyed 0|0|0 0|4|0 2|5|1 0|0|0 0|1|0 destroyed 0|0|0 0|1|0 destroyed 0|0|0 0|1|0 3|4|0
1/4/21/1 1/12/17/4 1/11/23/1 0/0/0/0 1/8/29/1 1/11/34/1 0/7/19/1 0/0/71/0 0/8/66/2 0/14/53/1 0/3/20/0 1/12/16/3 0/0/0/0 1/6/35/1 0/14/33/0 0/0/0/0 0/0/77/0 1/11/74/1 0/12/63/5 0/1/34/1 0/11/23/2 0/0/0/0 0/2/41/2 0/9/27/4 0/0/0/0 0/2/77/2 0/10/74/0 0/12/57/2
a T is the target temperature and 〈V〉/n is the average potential energy per C atom relative to one half of C energy. τ is the time of closing of the first 2 1 end and τ2 that of the other end; no entry here means that no closing occurred within the given simulation time. The numbers of C1, C2, and C3 fragments lost and the numbers of 4-, 5-, 6-, and 7-membered rings at the end of trajectory are also given. The italic trajectory was carried out using only a 5% velocity scaling rate.
rate but did not close at either end; slow activity is likely to require longer time to close than the present length of simulation. We observe a trend that the potential energy V increases initially as dangling bonds develop from the nanotube structure and later decreases substantially when dangling bonds are saturated and open ends are closed. Not surprisingly, for each system, the average per-atom relative potential energy 〈V〉/n rises as temperature is increased, allowing the system to sample higher energetic structures. At each temperature, 〈V〉/n is almost identical (within 10 kcal/mol) for different (n,m) types. While temperature was observed to fluctuate by as much as 500 K around the target temperature T, the average temperature (not shown in Table 1) for each trajectory stayed within 30 K from T. To discuss detailed structural events occurring during tube closing trajectories, we will focus on two very different systems: armchair (5,5) and zigzag (9,0) nanotubes with a relatively short length of 7.5 Å at 3000 K. Both of them closed at least at one end of the tube within 14 ps but showed very different dynamic behaviors at least at the beginning of trajectories. Nevertheless, the number of pentagons created at the end of most 12 ps simulations is almost the same for all the trajectories, between 10 and 14, with only one Nano Lett., Vol. 3, No. 4, 2003
exception in Table 1. As to the fragments lost (and sometimes reattached) during the trajectory, we find a prevalent dominance of C2 units over atomic C and C3 with a ratio of about 3:2:0.1. Some trajectories at 4000 K lead to complete destruction of the tube structure, and when this happens, only long, sometimes branched cumulene chains and large macrocyclic Cn rings with n > 20 remain. Although we picked two trajectories, many of the individual events occurring during the simulation are found to be common and representative for all trajectories (the two trajectories are available at http://euch4m.chem.emory.edu/nano). Figure 1 shows snapshots of a trajectory of an armchair (5,5) tube. Top and bottom ends are called T and B, respectively. Almost as soon as the trajectory starts, one cisoid bond at B breaks at 0.12 ps, leading to a wobbling C2 unit. Immediately following this event, another cisoid bond breaks also at B and at the same hexagon of which the first C2 unit broke off. This neighboring “double wobbling” is seen frequently in all trajectories. After this event, it takes quite some time for anything else interesting to happen. The wobbling C2 units stick out straight and refuse to reattach to the main tube structure. This is due to the fact that their local electronic structure is now acetylene-like with linear sp hybridized carbon atoms, as indicated by a very short average 467
Figure 1. Twelve representative snapshots of a trajectory for a (5,5) tube with 7.5 Å at 3000 K. Carbon-carbon bonds are drawn with a threshold of 1.8 Å.
C-C bond distance of only about 1.22 Å. Their linear configuration prevents them from coming close to the rims of the tube opening, and therefore they wobble relatively independent with a long lifetime. At 0.49 ps another cisoid bond breaks at the opposite T end of the tube, and at 0.94 ps the very same pattern of neighboring bond breaking occurs here as was observed previously at the B end. At 1.11 ps, a wobbling C2 unit at T bridges to a next neighbored hexagon, giving rise to a pentagon structure with one carbon atom attached to its top. However, this kind of five-membered ring is relatively short-lived for just 0.36 ps before it breaks again and the C2 unit reappears. Creation and destruction of this pentagon in this way occurs repeatedly afterward, and at 2.52 ps we notice pentagon formation with one carbon atom attached at the top at the B end. Both hexagons adjacent to this pentagon have wobbling C2 units attached to them (“double wobbling”), making the formation of a heptagon possible with the atom on top of the pentagon in the center. At 2.64 ps, one of them catches the carbon atom at the top of a pentagon, and a fused 5- and 7-membered rings (hereafter called a 5/7 fused ring) is formed which proves to be relatively stable. The 5/7 ring combination produced in this way continues to occur frequently, and one of their characteristics is that the 5/7 fused bond separating pentagon and heptagon is long and weak, giving this structure a larger flexibility than a regular hexagon lattice. Reisomerization of the 5/7 fused ring system to two hexagons (often called Stones-Wales32 isomerization) is observed especially at temperatures 3000 K or below. At 5.35 ps, the T end has four wobbling C2 units, while the B end is completely healed back to that of a regular armchair tube. Shortly after, at 5.98 ps, two independent T-C2 units reattach to the opening rim, and again a pentagon with a single wobbling carbon atom at its top is formed. This time, this carbon atom bends over the next-neighbored four carbon atoms to its left, and two 468
adjacent pentagons are formed in a very short time at 6.11 ps. Almost immediately, the pentagon on the right side of the figure separates itself from its pentagon neighbor by migration through a hexagon, as shown in the structure at 6.23 ps. Three 5/7 combinations appear at 6.88 ps, one at T and two at B, with two of them displaying a stretched carbon-carbon bond at their 5/7 junctions, making them more look like a 10-membered ring. The tube has been rotated in the figure to indicate how far the 5/7, 10-membered cyclic structure reached inside the tube opening, with wobbling C2 units around it. At 9.48 ps, a C2 unit attaches to a nearby 7-membered ring, leading to a new heptagon and the first 7/7 junction of this simulation. This effectively reduces the number of members in the macrocyclic opening, which is consequently reduced in size to a 12-membered ring. The structure at 11.39 ps shows a system which only contains three 12-membered rings as openings, and two fused 12membered rings are visible in the front of the picture which were created shortly before by a wobbling C2 unit acting as a “bridge”. Another C2 unit seemingly acts as a bystander while being attached to one of the 12-membered rings. The snapshot taken at 11.42 shows how simultaneous collapse of a 12-membered ring into a 5/6/5 combination occurs by a [2+4] cycloaddition-like formation of two σ bonds. This ring collapse causes the adjacent 12-membered ring to adapt, and very shortly afterward at 11.60 ps, two carbon atoms on opposite sides of the macrocycle come close to each other, leading to the formation of a pentagon and heptagon with the C2 unit now wobbling outside the cage structure. This constitutes end closure, which occurred within 0.2 ps from the simultaneous collapse of two fused 12-membered rings. Subsequently, it takes about 1.4 ps before the wobbling C2 unit is lost. The other end closes at 13.74 ps, when the 12membered ring structure reemerges from a 14-macrocycle plus wobbling C2 unit and repeating the [2+4] cycloaddition style collapse into a 5/6/5 combination of the other end, leaving an almost perfect C68 fullerene molecule with 12 pentagons, 4 heptagons, and 1 four-membered ring. Figure 2 illustrates a trajectory of a 7.5 Å long (9,0) zigzag tube also at 3000 K. In contrast to the armchair case where the first C2 unit was created within 0.12 ps, it takes 1.70 ps for the zigzag tube to develop a wobbling C2 unit. StoneWales type 5/7 pair formation and reisomerization is the dominant pattern generally observed for the first 2 ps of zigzag tubes at 3000 K, indicating that the polyacetylenic rim of the zigzag tube openings is much more stable against bond cleavage than the armchair tube openings. The wobbling C2 unit is created by bond cleavage of a 5/7 heptagon at the T end. Once the rim of a zigzag tube has been broken open at a heptagon, next-neighbored hexagons become more likely to break because of lack of π-conjugational stabilization. The structure at 2.04 ps depicts such a situation. Occasionally it is observed that wobbling C2 units break off, here after 2.66 ps. Upon loss of C2, a next-neighbored wobbling C2 unit attacks at the break-off point, giving rise to a hexagon and a pentagon at 2.93 ps. Two fused pentagons are created at 3.72 ps at B as a result of heptagon isomerization toward a pentagon with wobbling C2 formation. Nano Lett., Vol. 3, No. 4, 2003
Figure 2. Twelve representative snapshots of a trajectory for a (9,0) tube with 7.5 Å at 3000 K. Only one end closed. Carboncarbon bonds are drawn with a threshold of 1.8 Å.
In this case, they isomerize and reisomerize into a 5/7 combination by incorporation of the attached C2 unit repeatedly as shown for 6.05 ps. At this time, no hexagon survived at either tube opening, which is now completely dominated by 5/7 ring combinations. Eventually, at 8.04 ps, three fused pentagons with a heptagon attached are developed at the same end, now rotated in the figure for better clarity. Here, the 5/7 combination develops into a 10-membered cyclic structure reaching into the opening similar as in the armchair tube case. The three fused pentagons are responsible for a greater curvature in the opening, and at 8.95 ps a heptagon is created in the opening by attaching a C2 unit across the strongly curved polypentagon system. Eventually restructuring and separation of the pentagons by hexagons occur, and two pentagons with attached hexagons enforce a curvature strong enough to form a bond over the opening. This leads finally to a 6-membered ring with an 8-membered ring attached to it, closing this end at 10.50 ps. The DFTB MD simulations described above give an excellent insight into key elements involved in converting a three-dimensionally curved hexagon cluster of carbon atoms to closed cage structures with a high pentagon-to-hexagon ratio at the open ends. To summarize, the key dynamic steps are: 1. Armchair-type openings show a high tendency toward breaking of cisoid bonds, forming many wobbling C2 units, whereas C2 units are formed an order of magnitude slower for zigzag type openings as a result of bond breaking in heptagons, preceded by a large number of 6/6 to 5/7 ring isomerizations. 2. Wobbling C2 units have a high lifetime and have a tendency to be created pairwise at same hexagons (“double wobbling”). They show acetylene-type electronic structures and stand out upright from the rim of the opening, with occasional approach of next neighbored rings to form pentagons or other rings. 3. Once a structural defect such as C2 creation occurs, π-delocalization in that region of the opening is decreased, Nano Lett., Vol. 3, No. 4, 2003
and more bonds are likely to break, giving rise to more C2 units and subsequent reorganization steps. 4. The 5/7 fused 10-membered ring systems show a high flexibility; especially the 5/7 fused bond is fragile and often breaks in high-temperature conditions. This gives rise to large bridge-like structures, reaching into the openings and providing a chance for attack of C2 units and other defects from the opposite side of the opening. 5. [2+4] cycloaddition “zipper” type reactions occur in final stages of closing when the opening size has been reduced and only consists of 12-membered rings. The cycloaddition reaction in this case leads spontaneously to the creation of 2 pentagons and 1 hexagon. 6. Pentagons are often formed by 5/7 ring conversions into 5/5 + C2. When multiple fused pentagons are created, a strongly deformed region is created at the opening and stabilizes itself by bond formation across the two furthermost ends, which gives rise to a hexagon in the opening that can then attach itself to the opposite side of the opening, leading to closing. The MD calculations described above represent simulations in the context of fullerene formation in which for the first time quantum mechanical potential is used. Open-ended nanotubes were successfully converted to fullerene molecules within 10 to 14 ps. We started with (5,5), (7,3), (9,0), and (10,5) open-ended nanotubes of different lengths. Temperature is the most important factor. Above 4000 K, the systems fall apart into fragments. At around 3000 K, the hexagons of the nanotube ends open and create acetylenic C2 units that wobble at the end of the openings. Such wobbling C2 units have never been observed in MM simulations (see, e.g., refs 17 and 18) but are the most essential building tool in restructuring of the tube opening. Some of them recombine and form pentagons which cause the open ends to curl inside. At the curled end, a wobbling C2 chain suddenly binds to the other side of curl and forms a new ring, narrowing the opening. This occurs repeatedly and preferably at 5/7 ring combinations with broken fused inter-ring bonds, forming a bridge-like structure in the opening. Eventually the openings will close by systematically reducing the opening size by bridging with C2 units, leaving octagons as the largest cyclic structures observable at the ends. When this happens at both ends of the nanotubes, the tube is fully closed and a fullerene molecule is formed. Between 2000 and 3000 K we observed some, however, less frequent C2 wobbling chain formation, and the tube opening cannot be closed within the given simulation time. Presumably it takes much longer to close the nanotubes at this temperature. Around 1000 K, C2 wobbling chain formation and 5/7 isomerization at the open ends are very rare, and the nanotube seems to be stable against deformations of the hexagonal lattice in the time frame of several picoseconds. Under experimental conditions, however, fullerene formation occurs typically between 1000 and 1500 K, indicating that a simulation time of several picoseconds is not sufficient to follow rearrangement processes in this temperature region. In conclusion, we expect our findings to be applicable for general carbon clusters with a high degree of curvature, 469
which is a prerequisite for the final stages of fullerene formation. How such preorganized systems are created is still an open question, which we are confident to demystify by future DFTB MD simulations. Acknowledgment. This work was partially supported by a grant from the Mitsubishi Chemical Corporation and from the Petroleum Research Fund, the American Chemical Society. Acknowledgment is made to the Cherry L. Emerson Center of Emory University for the use of its resources, which is in part supported by a National Science Foundation grant (CHE-0079627) and an IBM Shared University Research Award. We also thank the National Center for Supercomputing Applications (NCSA) for valuable computer time. References (1) Kra¨tschmer, W.; Lamb, L. D.; Fostiropoulos, K.; Huffman, D. R. Nature 1990, 347, 354-358. (2) Gerhardt, P.; Lo¨ffler, S.; Homann, K.-H. Chem. Phys. Lett. 1987, 137, 306-310. (3) Howard, J. B.; McKinnon, J. T.; Makarovsky, Y.; Lafleur, A. L.; Johnson, M. E. Nature 1991, 352, 139-141. (4) Haufler, R. E.; Chai, Y.; Chibante, L. P. F.; Conceicao, J.; Jin, C.; Wang, L.-S.; Maruyama, S.; Smalley, R. E. Mater. Res. Soc. Symp. Proc. 1991, 206, 627-637. (5) Heath, J. R. ACS Symp. Ser. 1991, 481, 1-23. (6) Wakabayashi, T.; Shiromaru, H.; Kikuchi, K.; Achiba, Y. Chem. Phys. Lett. 1993, 201, 470-474. (7) Helden, G. Nature 1993, 363, 60-63. (8) Hunter, X. Science 1993, 260, 784-786. (9) Strout, D. L.; Scuseria, G. E. J. Phys. Chem. 1996, 100, 64926498. (10) Bates, K. R.; Scuseria, G. E. J. Phys. Chem. A 1997, 101, 30383042. (11) Jones, R. O. J. Chem. Phys. 1999, 110, 5189-5200.
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Nano Lett., Vol. 3, No. 4, 2003
