Interaction potential

The interaction potential is assumed to be a superposition of pairwise contributions between the individual carbon atoms and the guest, with the analytical form of a Buckingham formula

$$\jot9pt V_{ij}\left(r_{ij}\right)=Ae^{-{\alpha}r_{ij}}-\frac{C}{r_{ij}^{6}},$$ (1.11)

where $r_{ij}$ gives the distance between a carbon atom and the centre of mass of the guest. For the carbon/H2 system, the parameters $A$, $\alpha$ and $C$ have been obtained by ab initio calculations of a model system : Namely H2$-$benzene model (see Chapter 2), where H2 oriented perpendicular to the ring in the $C_6$ axis, has been calculated at the CCSD(T)/cc-pVTZ level. At short range, the so parametrised potential exhibits an attractive singularity. Therefore it has to be capped at a fixed value $-$ in this case at 120 kJ$\,$mol$^{-1}$ $-$ which corresponds to $r_{ij}$=1.8 Å.

The performance of the potential Eq. 1.14 has been found to agree well with Møller-Plesset perturbation (MP2 [37]) theory second order calculations of other polyaromatic hydrocarbons (PAHs) (see section 2.4). Furthermore, a comparison of the performance of two other parametrisations has been done. One parametrisation employing MP2/cc-pVTZ potential energy surface for benzene, the other parameters have been fitted to match MP2/cc-pVTZ for coronene. The parameters are given in Table 2.4 and the corresponding curves are plotted in Figs. 2.7 and 2.9. No significant difference between these parametrisations has been found when applied to graphene-based systems (see Chapter 3). However, the force field can not describe an enhancement of aromaticity, connected with stronger binding energy. More importantly, benchmarks for non-planar systems are not available, and transferability to those systems is not guaranteed. The latter point is difficult to overcome, as meaningful calculations for those systems are beyond the limit of our today’s computational capabilities. With increasing computing power, however, these approximations can be controlled, as more elaborate ab initio model calculations will be possible.

For hydrogen the pairwise additivity assumption is known to hold at relatively low guest coverages (see Chapter 2). At higher hydrogen densities, the guest-host interaction should depend on the guest density, so that the potential $v(r)$ in Eq. 1.1 can no longer be treated as given. This potential density dependence is neglected in this treatment. Alternatively, this limitation can be circumvented by applying the Hohenberg-Kohn theory for electronic systems.[38] The gas can be treated as $n$ interacting particles described by a scalar function of the particle density ${\rho}(r)$ which is influenced by external potential. However, this study is in early stage and results are not yet available.