  Donor spin in silicon have achieved record values of coherence times and
single-qubit gate fidelities. The next stage of development involves
demonstrating high-fidelity two-qubit logic gates, where the most natural
coupling is the exchange interaction. To aid the efficient design of scalable
donor-based quantum processors, we model the two-electron wave function using a
full configuration interaction method within a multi-valley effective mass
theory. We exploit the high computational efficiency of our code to investigate
the exchange interaction, valley population, and electron densities for two
phosphorus donors in a wide range of lattice positions, orientations, and as a
function of applied electric fields. The outcomes are visualized with
interactive images where donor positions can be swept while watching the valley
and orbital components evolve accordingly. Our results provide a physically
intuitive and quantitatively accurate understanding of the placement and tuning
criteria necessary to achieve high-fidelity two-qubit gates with donors in
silicon.
