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\section{Results}  We have calculated the electronic coupling, $J$, between the the excited states of an ergosterol dimer. The ergosterol molecules are separated by distances of 6Å, 7Å 6 \AA, 7 \AA  and 8Å. 8 \AA.  To obtain reference values for the coupling, supermolecule calculations were carried out in Gaussian at the CAM-B3LYP/6-31G level of theory. These numbers are presented in Table~\ref{tab:qmjvalues}. We have tested the numerical requirements of the more approximate method using transition density fitted charges. \subsection{Traditional approach}  First, a traditional approach is taken where the charges on chromophore A are fitted to reproduce the molecular electrostatic potential on a surface defining the cavity of it self. We have tested both a PCM surface and a Conolloy surface. Methods such as Tr-ESP and XX use this approach and has been used extensively for small to medium sized molecules. The PCM surface is generated by tesselated spheres around each atom in the molecule. The radius of each sphere is the van der Waal radius of the atom multiplied by some constant. For PCM the value of this constant is typically 1.2. We have tested two different tesselation levels (number of triangles per sphere) of either 60 and 240. The Connolly surface is generated similarly with a scaling factor of 1.4 instead. The difference in tesselation is that the Connolly surface has a constant number of points per surface area around each atom. Thus, scaling the distance to the surface by a larger constant will increase the total number of points whereas for PCM the number is constant. In this work we have used a density of 0.28 Bohr$^{-2}$. Traditionally, the Connolly surface is used with 4 layers typically separated by 0.2 \AA. We have also tested using only one layer for the Connolly surface.  \subsubsection{Effects of linear dependency}