Starting from Newton's equations of motion, we derive a dynamical density
functional theory (DDFT) applicable to atomic liquids. The theory has the
feature that it requires as input the Helmholtz free energy functional from
equilibrium density functional theory. This means that, given a reliable
equilibrium free energy functional, the correct equilibrium fluid density
profile is guaranteed. We show that when the isothermal compressibility is
small, the DDFT generates the correct value for the speed of sound in a dense
liquid. We also interpret the theory as a dynamical equation for a coarse
grained fluid density and show that the theory can be used (making further
approximations) to derive the standard mode coupling theory that is used to
describe the glass transition. The present theory should provide a useful
starting point for describing the dynamics of inhomogeneous atomic fluids.Comment: 14 pages, accepted for publication in J. Phys.: Condens. Matte