  The Barker-Henderson perturbation theory is a bedrock of liquid-state
physics, providing quantitative predictions for the bulk thermodynamic
properties of realistic model systems. However, this successful method has not
been exploited for the study of inhomogeneous systems. We develop and implement
a first-principles 'Barker-Henderson density functional', thus providing a
robust and quantitatively accurate theory for classical fluids in external
fields. Numerical results are presented for the hard-core Yukawa model in three
dimensions. Our predictions for the density around a fixed test particle and
between planar walls are in very good agreement with simulation data. The
density profiles for the free liquid vapour interface show the expected
oscillatory decay into the bulk liquid as the temperature is reduced towards
the triple point, but with an amplitude much smaller than that predicted by the
standard mean-field density functional.
