Comment on "Theoretical evaluation of hydrogen storage capacity in pure carbon nanostructures" [J. Chem. Phys. 119, 2376 (2003)].

In a recent paper @J. Chem. Phys. 119, 2376 ~2003!#, Li et al. concluded from a series of calculations and analysis that ‘‘when compared to other pure carbon nanostructures, we find no rational reason yet why carbon nanotubes should be superior in either binding energies or adsorption/ desorption kinetics’’ for H2 storage. 1 This is in contrast to our encouraging computational data and analysis on H2 storage in single walled carbon nanotubes ~SWNT! which Li et al. largely dismissed, while urging others to perform further calculations to resolve the issues raised. Using what is essentially a space-filling model for highly idealized ~8,8! SWNT, the analysis of Li et al. indicates that the ambient temperature H2 storage capacity cannot exceed 1.5 wt. % and that high capacity is only possible at cryogenic temperatures. In this publication, Li et al. performed three types of calculations towards modeling the interactions of H2 with ~7,7! armchair nanotubes. In the first step, they calculated the H2 adsorption energy at an endohedral site upon full relaxation of atomic coordinates using density functional theory ~DFT! as implemented in VASP, which was reported to be 2.63 kcal/mol per H2 at 0 K. Subsequently, they performed classical molecular dynamics ~MD! simulations at 300 K and 600 K on various SWNT configurations with Brenner’s bond-order potential and noticed an appreciable nanotube structural deformation @although seemingly to a lesser extent compared with our ab initio MD results for ~9,9! nanotubes#. The calculated distribution of the longitudinal angles also appears to be smoother. Finally, they selected a few random configurations from these MD simulations to perform DFT calculations to evaluate the H2 adsorption energy, which was done with a chosen rigid tube structure but relaxed H2 coordinates. The average adsorption energy per H2 is reported to be 1.8 kcal/mol. They found ‘‘no abnormal interaction between H2 and the nanotube that is outside the range of ordinary van der Waals interactions between a H2 molecule and a flat graphene sheet or graphite surface.’’ We have two principal issues with this paper, both of which stem from the choice of SWNT models on which the calculations were based: The upper bound H2 capacity ~1.5 wt. %! determined on the basis of simple H2 space filling analysis of a rigid hexagonal unit cell and the adsorption energy analysis where a different ~tetragonal! SWNT unit cell was employed. In our opinion, it is an oversimplification to predict an upper bound for H2 capacity ~1.5 wt. %! in SWNT based on simple space filling analysis on a rigid model, at least for the reason that significant SWNT dilation can occur upon H2 adsorption. The SWNT dilation can occur without a significant energy penalty and the required energy for dilation can be supplied via H2 adsorption. Figure 1 shows the potential energy change upon lattice expansion by up to 1 Å along the aW direction in a hexagonal unit cell of ~9,9! SWNT calculated by local density functional theory as implemented in VASP. It is apparent from this calculation that the energy required for the lattice expansion in this range does not exceed 5 kcal/mol. So, given an adequate adsorption energy, there is no fundamental reason that the SWNT unit cell could not expand to spatially accommodate an H2 uptake .1.5 wt. %, particularly if one is not restricted to ~8,8! nanotubes. We believe that the most serious issue is in the author’s choice of unit cell parameters which materially compromises any meaningful comparison of their calculated adsorption energies to those reported in our paper, and indeed, to the heats of adsorption of hydrogen on SWNT reported in the literature. For reasons that are not clear from their discussion, they have selected a tetragonal unit cell to represent the ~7,7! armchair nanotube lattice despite their own geometric analysis, mentioned previously, that uses a hexagonal lattice in the unit cell. The resulting square lattice structure ~Fig. 2! is clearly not close-packed and is inconsistent with any experimental description of the packing of SWNT in the literature. The unit cell parameters for the ~7,7! nanotube lattice used in their calculations are 15.66315.6634.919 Å in dimension, which gives a shortest intertube distance of 6.28 Å. This is clearly inconsistent with any experimentally reported internanotube distances ~ca. 3.15 Å! for SWNT bundles from x-ray diffraction studies. For purpose of comparison, we show the unit cells magnified by 23231 used in both their VASP calculations and ours in Fig. 2. Our opinion is that this study of SWNT in an experimentally unknown square lattice, using a lattice spacing that is nearly twice the distance determined by x-ray diffraction experiments on a range of SWNT samples, represents a de facto simulation of hydrogen interacting with essentially isolated ~7,7! nanotubes. This simply JOURNAL OF CHEMICAL PHYSICS VOLUME 120, NUMBER 19 15 MAY 2004