Many experiments to study the room temperature hydrogen storage in graphitic nanofibers and carbon nanotubes could not be reproducible and this lead to a tempering of feasibility projections for hydrogen storage applications [1].

Computationally, there have been many empirical [2-3] and ab initio DFT calculations [4-5] aimed at understanding the storage mechanism. The empirical methods are usually very convenient for massive simulations, but cannot describe interactions which involve bond breaking, partial bonds and chemisorption. It is well known that current ab initio DFT methods fail to describe the interaction energy at distances where electronic overlap is very small because they are based on the local electronic density, its gradient and the local kinetic energy density. Results obtained by the Local Density Approximation (LDA) sometimes can provide a good estimate for the interaction energy [6], however, this is unphysical and largely fortuitous due to favorable error cancellations.

Two strategies have been favoured for overcoming this deficiency of DFT. The more fundamental approach is to develop a VdW density Functional [7], but unless limited to systems with nonoverlapping densities this is very computationally demanding. The other strategy is to introduce a damped correction term to account for the missing dispersive interactions [8-9].

We report the results of ab inito DFT calculations incorporating a VdW correction, performed to study the interaction of molecular hydrogen with graphitic and SWCNT surfaces. The equilibrium distance and binding energy for hydrogen on graphite, an (8,8) nanotube and its bundle were calculated and compared to the experimental and other theoretical results. Our results reveal that this VdW correction scheme is very important and effective when using DFT to study the physisorption of molecular hydrogen on graphitic and SWCNT surfaces, especially with the Gradient Generalized Approximation (GGA).

Van-der-Waals Corrected Density Functional Theory: Benchmarking for Hydrogen-Nanotube

and Nanotube-NanotubeAijun Du and Sean C. Smith

Centre for Computational Molecular Science, Chemistry Building, The University of Queensland, Qld 4072

ab initio part:

The ab initio total energy DFT calculation method has been employed as implemented in the CPMD code [10]. The core-valence interaction for C and H atoms is described by ultrasoft Vanderbilt pseudopotentials with PBE exchange correlation functional [11]. The graphite or (8,8) nanotube surface plus molecular hydrogen are modeled by a supercell geometry (See Figure.1.a, b and c). The vacuum layer is at least 12 Å, which is sufficient to avoid the interaction from its periodic images. The (8,8) nanotube bundle was modeled using a triclinic unit cell with hexagonal geometry (see Figure.1.d). All the calculations have been carried out considering the Gamma point only in the integration of the Brillouin zone (BZ) due to the large cell used. The Kohn-Sham electronic orbitals are expanded in a plane-wave basis and set up to a kinetic energy cutoff 25 Ry, which is large enough to reach convergence in the structural properties of graphite and SWCNT.

London Dispersion Term:

An energy dispersion term Edis is introduced to obtain the total energy of the interacting system. f(Rij) is the damping function which is approaches one and zero for large and small values of R, respectively. This ensures that Edis has the correct asymptotic behavior at long range, with its role diminishing at short distance. The form of the damping function used in our calculation is the same as that in ref [12], which performed well with the PBE exchange correlation functional. However, we have changed the value of R0 in that work to Rvdw because the present calculation is a pure DFT approach.As defined in ref [13], the Rvdw is the sum of atomic VdW radii of carbon and hydrogen atom [14]. The C6 coefficient for a diatomic system is obtained by the following combination rule.

We are grateful to The University of Queensland for supporting this work through the Centre for Computational Molecular Science. We also acknowledge generous grants of high-performance computer time from both the CCMS cluster computing facility and the Australian Partnership for Advanced Computing (APAC) National Facility.

Introduction

Computational Methodology

Results & Discussions (continued)

Results & Discussions

Conclusions

References

Acknowledgements

We have carried out ab initio DFT calculations with a VdW correction in order to investigate the efficacy of the approach for describing interactions involving molecular hydrogen, graphite, single-walled carbon nanotubes (SWCNTs), and SWCNT bundles. We found that a reasonable physisorption energy and equilibrium distance can be obtained for molecular hydrogen on a graphite surface by including the VdW correction term. Additionally, the calculation with a VdW correction on an (8,8) nanotube bundle is able to reproduce accurately the experimentally observed lattice constant. Calculations show the binding energy to be higher and lower than that on a graphite surface for molecular hydrogen inside or outside an (8,8) nanotube due to the curvature effect. Our results reveal that the VdW correction scheme is a very effective strategy for implementing DFT calculations with the GGA that will correctly describe interactions of hydrogen with graphite, SWCNT and SWCNT bundles as well as the nanotube-nanotube itra-bundle interactions. This provides a significant step in establishing the reliability of the approach, with a view towards diverse applications in many important areas of SWCNT research where an accurate simulation of physisorption interaction energies as well as chemical bonding is required. Given that we have adopted a plausible formulation of the short-range damping function for the VdW correction terms without any further modification or fitting, and the C6 coefficient used therein is derived directly from the experimental atomic polarizabilities, extending the present VdW correction scheme to other gas-SWCNT systems such as NO2-SWCNT and peptide-SWCNT systems for sensor applications is anticipated to be relatively straightforward

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The binding energy and equilibrium distance obtained after including VDW correction term is in general agreement with the experimental value(BE=4.2X10-2 eV and d0=2.87 Angstrom).

(a) Without VDW correction (b) With VDW correction

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The BE for H2 on SWCNT is lower than BE on graphitic surface (Curvature effect)

(a) H2 inside nanotube(b) H2 outside nanotube

Nanotube surface at 0

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Please see J.Chem.Phys., 109(1998)4981. Science, 273(1996)483.

(a) without VDW (b) with VDW

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The lowest binding energy (about 7.6X10-2 eV) is located in center of interstitial area (high symmetry site).

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J.Am.Chem.Soc.,

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Figure 1 Model used in our calculation

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Figure 2 Variation of the interaction energy as a function of the distance of molecular hydrogen from the graphitic surface without and with VdW correction, respectively. Interaction energy is defined as Etot(Graphite+H2)-Etot(H2)-Etot(Graphite) (a) Calculation without VdW correction. (b) Calculation with VdW correction.

Figure 3 Variation of the interaction energy as a function of distance for the interaction of hydrogen with a (8,8) nanotube (a) H2 inside tube (b) H2 outside tube. Interaction energy is defined as Etot(SWNT+H2)-Etot(H2)-Etot(SWNT) and the nanotube surface is defined at the origin

Figure 4 Results for molecular hydrogen interacting with an (8,8) nanotube bundle without VDW and with VDW (see Fig.1.d). Variation of the nanotube interaction energy as a function of lattice constant. The minimum corresponds to the equilibrium lattice constant.

Figure 5 Variation of binding energy of molecular as a function of interstitial position along the diagonal direction of the hexagonal lattice.