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# Results  Figure \ref{fig:sysred} shows the reduction in size of the system of linear equations when solving for the unknown charges, \(\mathbf{x}\), 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 quite expected since the increasing radius will make the final surface appear more and more spherical and thus all atoms will contribute equally in the construction of \(\mathbf{A}\).