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An extensive first-principles study of fully exo-hydrogenated zigzag (n,0) and armchair (n,n) single wall carbon nanotubes (CnHn), polyhedral molecules including cubane, dodecahedrane, and C60H60 points to crucial differences in the electronic and atomic structures relevant to hydrogen storage and device applications. CnHn's are estimated to be stable up to the radius of a (8,8) nanotube, with binding energies proportional to 1/R. Attaching a single hydrogen to any nanotube is always exothermic. Hydrogenation of zigzag nanotubes is found to be more likely than armchair nanotubes with similar radius. Our findings may have important implications for selective functionalization and finding a way of separating similar radius nanotubes from each other.


Carbon nanotubes exhibit very unusual structural and electronic properties, suggesting a wide variety of technological applications, including the storage of hydrogen where the large effective surface area promises a large absorption capacity. Unfortunately, the studies to date report conflicting results. While some labs report hydrogen storage densities up to 10 wt\% other labs report only 0.4 wt\% on the same system. Theories based on physisorption have failed to predict such high uptake. To the best of our knowledge, studies of hydrogen chemisorption in nanotubes are very limited and are clearly needed to have a better understanding of hydrogen and nanotube system.

A single-wall exohydrogenated carbon nanotube
FIGURE 1) Three different polyhedra of carbon and hydrogen; (a) cubane, (b) dodecahedrane, and (c) a side and top view of a single-wall exohydrogenated carbon nanotube.

Hydrogen-carbon interactions have been studied extensively both theoretically and experimentally for many interesting polyhedral molecules, such as cubane (C8H8), dodecahedrane (C20H20), and various isomers of C60Hn (see Fig.~1). Despite its very strained 90o CCC-bond angle cubane has been synthesized successfully (Fig.~1a). Similarly, dodecahedrane and various isomers of C60Hn (up to n=32) have been also synthesized. These novel polyhedral molecules which represent the zero dimensional case, exhibit many interesting properties. However, due to the one dimensional nature and the curvature of carbon nanotubes, the hydrogen-carbon interactions in these systems may be quite different than those in polyhedral molecules. Therefore, it is important to know if it is also possible to hydrogenate carbon nanotubes in a similar way and if so what their structural and electronic properties would be. This paper addresses this important issue by performing extensive first-principles calculations and shows that the chemisorption of hydrogen is dependent on the radius and chirality of the nanotubes. Theoretical predictions from first-principles studies played an important role in guiding experimental studies in the past and we expect that many findings reported here may have important implications in this interesting system as well.


In order to obtain a reasonably complete understanding, we studied a very large number of systems including zigzag (n,0) (n=7,8,9, 10 and 12) and armchair (m,m) (m=4,5,6,8, and 10) nanotubes as well as cubane, dodecahedrane, C60H60 and finally hydrogenated graphene sheet (i.e. infinite limit of tube radius). The first principles total energy and electronic structure calculations were carried out using the pseudopotential plane wave method. The results have been obtained within the generalized gradient approximation (GGA). This method has already been applied to many carbon systems, including fullerenes and cubane with remarkable success. Interactions between molecules or nanotubes in periodic cells are avoided by using large supercells. The supercell parameters are chosen such that the closest H-H distance is 6 A. All carbon and hydrogen positions were relaxed without assuming any symmetry. For nanotube calculations, the c-axis of the supercell (corresponding to the tube axis) is also optimized.

Various parameters of the fully optimized structures of exohydrogenated armchair and zigzag carbon nanotubes and other polyhedral molecules TABLE 1. Various parameters of the fully optimized structures of exohydrogenated armchair and zigzag carbon nanotubes and other polyhedral molecules. For graphene (i.e. RCH --> inf.) dCH and dCC are 1.066 A and 1.622 A, respectively.

Table 1 summarizes the parameters obtained for fully optimized structures. Upon hybridization of carbons with hydrogens, the C-C bond length (dCC) increases from ~1.4 A to ~1.55 A. The latter is typical for sp3 CC-bonds. The increase in dCC results in an increase in the tube radius (RHC) by about 13 - 16 \% for armchair nanotubes and by about 15 - 17\% for zigzag nanotubes. Interestingly, these values are almost twice of those found for the polyhedral molecules. Using projection techniques we estimated the total charge transfer from hydrogen to carbon to be around 0.26 electrons for nanotubes and 0.3 electrons for polyhedral molecules.

The stability and energetics of CH-bond formation are derived from the average binding energy per atom for exo-hydrogenated nanotubes defined as

EB = ( ECnHn - EC - n EH)/n .
Here ECnHn , EC, and EH are the total energies of the fully optimized exo-hydrogenated nanotube, nanotube alone, and hydrogen atom, respectively. According to this definition, a stable system will have a negative binding energy. Figure 2a shows the radius dependence of EB for nanotubes and polyhedral molecules (see inset). Two interesting observations are apparent. First, as shown by solid and dotted lines, the binding energies can be very well described by a one parameter fit;
EB = E0 -C(n,m)/RCH,
where E0 is the limit RCH --> inf. (i.e. graphene) and calculated to be -1.727 eV. The fit results for C(n,m) are given in Fig.~2a for zigzag and armchair nanotubes. The inset to Fig.~2a shows that while EB for cubane falls on the same curve as nanotubes, dodecahedrane and C60H60 have lower energies than nanotubes due to the their more spherical shape.

Figure 2 FIGURE 2. (a) Binding energies EB of (n,n) (square) and (n,0) (circle) nanotubes as a function of RCH. The solid and dashed lines are one parameter fits to EB = E0 -C(n,m)/RCH as discussed in the text. Inset shows the binding energies of cubane, dodecahedrane, and C60H60. (b) Full circles indicate the energy to break a single CH-bond to form a CnHn-1 zigzag nanotubes as depicted in the top inset. Full squares indicate energy gain DEG by attaching a single H atom to a nanotube to form a CnH as depicted in the bottom inset. The solid and dashed lines are two parameter fits as discussed in the text, indicating 1/RHC behavior.

The second interesting observation in Fig.~2a is that the binding energies of zigzag nanotubes are always lower than those in armchair nanotubes with similar radius by about 30 meV/atom. This is a natural result of the fact that the CCH-bond angles in zigzag nanotubes are closer to the optimum tetrahedral sp3 bonding than those in armchair nanotubes. We expect this observation is also valid for hybridization of nanotubes oith other elements, such as Cl and F and this may have important implications for separating similar radius nanotubes from each other by selective chemical functionalization.

Even though CnHn nanotubes are found to be stable with respect to a pure carbon nanotube (Cn) and n H atoms for all values of the radius, it is of interest to see if they are also stable against breaking a single CH-bond. We, therefore, calculated energies of fully optimized hydrogenated nanotubes after breaking one of the CH-bonds and putting the H atom at the center of supercell as shown in the top inset to Fig.~2b. We note that for radius around RHC ~ 6.25 A, the binding energy becomes negative, suggesting instability. Hence, (12,0) and (8,8) nanotubes are at the limit for stable, fully exo-hydrogenated nanotubes. We are currently studying this problem for half-coverage case as well.

The energy, DEG, gained by attaching a single H atom to a carbon nanotube is calculated by performing structure optimization of a CnH-nanotube as depicted in the bottom inset to Fig~2b. Unlike DEG, there is no change in the sign of DEG, suggesting that for any radius of carbon nanotube hybridization of a single carbon atom is always stable. However the energy gain from two such processes is around 5--6 eV which is slightly less than the dissosiation energy of H2, 6.65 eV. Hence Cn nanotube plus H2 system is stable against forming a CnH2 hydrogenated nanotube. Therefore, in order to realize the CH-bonding discussed here, one first has to break H2 molecules into hydrogen atoms, probably by using a metal catalyst or electrochemical techniques.

Figure 3 FIGURE 3. Band gap as a function of tube radius RHC. Inset shows the full scale plot to include the band gaps of the polyhedral molecules.

Hydrogenation of nanotubes is also important in the modification of the electronic structure for device applications. Figure 3 shows the density of states (DOS) for a (9,0) exo-hydrogenated nanotube, which is typical to other nanotubes that we studied. Using projected DOS, we find that the bottom of the conduction bands are mainly derived from hydrogen while the top of the valence bands are mainly carbon-origin. In contrast to pure nanotubes which are metal or semiconductors depending on their structure, the CnHn nanotubes are found to be direct band insulators with a gap of 1.5--2 eV at the Gamma-point. This value is about one-third of those for the molecular polyhedrals, indicating less stability of hydrogenated nanotubes than molecules. The band gaps decrease with increasing tube radius but unlike binding energies there is no apparent 1/RHC type behavior. Interestingly, the band gaps of armchair nanotubes are higher in energy by about 0.2 eV than those in zigzag nanotubes. This is surprising because the band gap is usually higher for more stable saturated hydrocarbons.

Figure 4 FIGURE 4. The observed band gap opening via hydrogenation of nanotubes can be used for band gap engineering for device applications such as metal-insulator heterojunctions as shown in this figure.

For example, various quantum structures (see Fig.4) can easily be realized on an individual carbon nanotube, and the properties of these structures can be controlled by partial hydrogenation of carbon nanotubes. If the different regions of a SWNT are covered with hydrogen atoms, the band gap and hence the electronic structure will vary along the axis of the tube. This way various quantum structures of the desired size and electronic character can be formed. In this respect, present scheme is quite similar to our previous constructions of nanotube heterostructures or quantum dots, where periodic applied transverse compressive stress is used for band gap opening.


In summary, we have presented first-principles calculations of the structural and electronic properties of various nanotubes which are fully protonated by sp3 hybridization of carbons. We find that CnHn nanotubes are stable for tube radius RHC smaller than 6.25 A, roughly corresponding to a (8,8) nanotube. Hybridization of a single carbon atom is found to be always exothermic regardless of tube radius. Weak but stable CH-bonding in nanotubes may be an important consideration for possible hydrogen storage applications. We also found that hybridization of zigzag nanotubes is more likely than armchair nanotubes with the same radius, suggesting a possible selective chemical functionalization of nanotubes. The fact that other carbon clusters such as cubane, dodecahedrane, and C60H32 have been synthesized successfully, suggest that it may possible in the near future to hydrogenate carbon nanotubes, yielding new structures with novel properties.