  A new class of methods is introduced for solving the Kohn-Sham equations of
density functional theory, based on constructing a mapping dynamically between
the Kohn-Sham system and an auxiliary system. The resulting auxiliary density
functional equation is solved implicitly for the density response, eliminating
the instabilities that arise in conventional techniques for simulations of
large, metallic or inhomogeneous systems. The auxiliary system is not required
to be fermionic, and an example bosonic auxiliary density functional is
presented which captures the key aspects of the fermionic Kohn-Sham behaviour.
This bosonic auxiliary scheme is shown to provide good performance for a range
of bulk materials, and a substantial improvement in the scaling of the
calculation with system size for a variety of simulation systems.
