  We present a first-principles investigation of the spin-ice state in
Dy$_2$Ti$_2$O$_7$ using a magnetic source-free exchange and correlation
functional, implemented in the Castep electronic-structure code. By comparing
results from the conventional local spin-density approximation, we show that a
spin-ice state in Dy$_2$Ti$_2$O$_7$ can be reliably obtained by removing the
magnetic sources from the exchange and correlation contributions to the
potential, and we contrast this against the computed ground states of other
frustrated pyrochlore magnets.
