Response to ‘‘Comment on ‘Theoretical evaluation of hydrogen storage

In our recent paper, we tried to rationally understand previous results of modeling hydrogen adsorption in pure single-walled carbon nanotubes ~SWNTs!, including the results of Cheng et al., by doing simpler calculations that a large percentage of the community can perform and check. For this purpose all the raw data of our calculations were put on the web. Cheng et al.’s comments do not seem to object to the technical correctness of our numbers, but rather the interpretation and significance of these numbers. Our calculation setup in Sec. III of Ref. 1 indeed differs from that of Ref. 2—a point that was quite clear in Ref. 1 and further clarified in Cheng et al.’s comments—even though the same plane-wave density functional theory ~DFT! program under the local density approximation ~LDA! and, probably, even the same pseudopotentials were used. Our goal was to understand the nature of isolated nanotube–H2 molecule interactions when the nanotube is distorted to a degree that is commensurate with thermal fluctuations at T5300 K. We avoided SWNT–SWNT coupling and free-energy sampling, which are still challenging to treat to good statistical accuracy in DFT calculations. Due to the differences in setups, our calculation results are not yet in direct conflict with those of Ref. 2. So our reply below may still be somewhat speculative. But we believe it will lead to a good discussion and probably more clarifying evidence later on. Cheng et al. raised two major concerns: ~A! The relevance of the room-temperature and -pressure H2 physisorption capacity upper bound estimated in our Sec. II based on a rigid SWNT bundle geometry and assuming the binding energy of H2 to an isolated SWNT is the same as that of H2 to a graphene sheet, and that the binding energies to multiple tubes are pair additive. The concern here is that the SWNT bundles are not fixed, and the tube–tube separation w can deviate from 3.4 Å significantly to accommodate more hydrogen. ~B! The relevance of our H2-isolated SWNT ‘‘instantaneous’’ adsorption energy results in Sec. III. We used an isolated, distorted but fixed SWNT @obtained from finite-T molecular dynamics ~MD! simulation using the Brenner empirical potential# in the DFT calculation while relaxing the adsorbed H2 molecule. The concern is that real SWNTs exist in bundles, so they are not isolated. Also, they are not rigid and the C–C–C angles have thermal fluctuations, and there are also concerns whether the Brenner potential is capable of reproducing the transient thermal fluctuations to a good measure. Before replying to the comments, we would like to introduce some terminology. ~a! Although the experimentally determined binding energy of a H2 molecule to a flat graphene layer, EH2-graphene experiment , is 30–50 meV/H2 ~Ref. 3!, for a self-consistent discussion of the DFT-LDA calculations results, we cite the results of Arellano et al., who obtained EH2-graphene DFT-LDA 586 meV/H2 . This gives a large margin of safety for our discussions below. An ‘‘abnormal interaction’’ is said to occur between a H2 molecule and an isolated SWNT if their binding energy EH2-SWNT is much greater than EH2-graphene , with both energies obtained by the same method: that is, if EH2-SWNT DFT-LDA @EH2-graphene DFT-LDA or EH2-SWNT experiment