  Endohedral fullerenes, or endofullerenes, are chemical systems of fullerene
cages encapsulating single atoms or small molecules. These species provide an
interesting challenge of Potential Energy Surface (PES) determination as
examples of non-covalently bonded, bound systems. While the majority of studies
focus on C$_{60}$ as the encapsulating cage, introducing some anisotropy by
using a different fullerene, e.g., C$_{70}$ can unveil a double well potential
along the unique axis. By approximating the potential as a pairwise
Lennard-Jones (LJ) summation over the fixed C cage atoms, the parameter space
of the Hamiltonian includes three tunable variables: $(M,\varepsilon,\sigma)$
representing the mass of the trapped species, the LJ energy, and length scales
respectively. Fixing the mass and allowing the others to vary can imitate the
potentials of endohedral species trapped in more elongated fullerenes. We
choose to explore the LJ parameter space of an endohedral atom in C$_{70}$ with
$\varepsilon\in$ [20cm$^{-1}$, 150cm$^{-1}$], and $\sigma\in$ [2.85\r{A} ,
3.05\r{A}].
  As the barrier height and positions of these wells vary between [1cm$^{-1}$,
264cm$^{-1}$] and [0.35\r{A}, 0.85\r{A}] respectively, using a 3D direct
product basis of 1D harmonic oscillator (HO) wavefunctions centred at the
origin where there is a local maximum is unphysical. Instead we propose the use
of a non-orthogonal basis set, using 1D HO wavefunctions centred in each
minimum and compare this to other choices. The ground state energy of the
X@C$_{70}$ is tracked across the LJ parameter space, along with its
corresponding nuclear translational wavefunctions. A classification of the
wavefunction characteristics, namely the prolateness and ``peanut-likeness''
based on its statistical moments is also proposed.
