Atom-atom Lennard-Jones [18] (LJ) parameters ( 
and 
)
are used to describe
the dispersion-repulsion interactions, the contribution to the potential
energy being summed over each atom of the benzene molecule with each Ar
atom, and over all pairs of Ar atoms. The LJ potential is
for a given pair of atoms separated by distance r. We test the sensitivity of our results to details of the potential using two sets of parameters for the Ar-Ar, Ar-C and Ar-H interactions as described in §iiiA.
The charge distribution of the benzene molecule is modelled using distributed
multipoles [13, 14, 19] on each of the C and H atoms. The multipoles have been
calculated up to rank 4 (the hexadecapole) following an ab initio
geometry optimisation which employed 6-311G** 
[20] basis sets with second order
Møller-Plesset [21] perturbation theory (MP2)
correlation corrections. The first non-vanishing multipole moment is
the quadrupole -- the molecule is uncharged and according to the point group
symmetry, the dipole moment vanishes. The non-zero component of the quadrupole
moment transforms as 
and is expected to make the largest contribution to the electrostatic
energy. The first-order electrostatic energy vanishes because the unperturbed
Ar atoms have no non-vanishing multipole moments.
For the calculation of higher-order terms in the electrostatic energy (induction), dipole-dipole polarizabilities for benzene and Ar were used in conjuction with the distributed multipoles. We used tabelled polarizabilities for benzene [22] and argon. [23] Induction describes the modification of the permanent multipole moments by the electrostatic fields. Each iteration of the calculation provides an updated set of induced moments. The process is converged when the multipoles no longer change in response to the recalculated fields. Alternatively, a first-order approximation to the induction energy may be obtained from a single iteration of this calculation. The full analysis of these methods is quite lengthy and we refer the reader to Stone's recent publication [19] for a complete description.
Calculating the induction energy is
computationally expensive for larger n (especially when we iterate
to convergence) and in our more detailed study of BzAr 
we neglected
this term, as discussed below.