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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 and 8Å. 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  inGAMESS using  the FIXPVA scheme at 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: levels (number of triangles per sphere) of either  60 and 240 to give a normally tesselated surface and finely tesselated surface, respectively. 240.  The PCM Connolly  surface is always generated similarly with  a single layer. scaling factor of 1.4 instead.  The difference in tesselation is that the  Connolly surface is generated by having 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}  Figure~\ref{fig:sysred} shows the reduction in size of the system of linear equations when solving for the unknown charges, $\mathbf{q}$, from eq~\ref{eqn:linear} as the scale of the van der Waal radius is increased. We observe for both the PCM and MK surfaces, that the system size is reduced for increasing van der Waal radii. This is expected since the increasing radius will make the final surface appear more and more uniform and thus all atoms will contribute equally in the construction of $\mathbf{A}$ (see also eq~\ref{eqn:amatrix}). For a very low scaling of the vdw-radius, the PCM-240 surface and the MK-4 surface sees little to no reduction in the size of the system of linear equations (77 and 75, respectively). As the scaling is increased, the system size of the PCM surface drops off notably faster than the MK surface. This, we can explain by the fact that even though the PCM surface has more points which is very good for reproducing a sphere and yields an appropriate surface at low scaling factors, but at larger scaling factors, the whole surface will more quickly approach a uniform sphere when standing in any atom with resulting linear dependencies as a consequence. Contrary, the MK surface is quite orientation dependent and is much less uniform.