We examine exchange coupling in the Kate quantum computer, which consists of isolated spin-1/2 <sup>31</sup>P donors in a pure Si lattice. A calculation is made using full configuration interaction, a reasonably large basis set, and a simple physical model. Basis set convergence was not obtained, and increasing the size of the matrix further appears to be computationally impractical. We therefore consider a Gaussian basis set approach. A brief description of the McMurchie-Davidson algorithm for the expansion of SGTF functions into Hermite polynomials is given. We also give the results of
a single-donor computation in this basis.