An expression is derived for the total energy of a system of interacting atoms based on an ansatz for the total electron density of the system as a superposition of atom densities taken from calcula- tions for the atoms embedded in a homogeneous electron gas. This leads to an expression for the in- teraction energy in terms of the embedding energy of the atoms in a homogeneous electron gas, and corrections accounting, for instance, for the d-d hybridization in the transition metals. The density of the homogeneous electron gas is chosen as the average of the density from the surrounding atoms. Due to the variational property of the total-energy functional, the errors in the interaction energy are second order in the deviation of the ansatz density from the true ground-state value. The appli- cability of the approach is illustrated by calculations of the cohesive properties of some simple met- als and all the 3d transition metals. The interaction energy can be expressed in a form simple enough to allow calculations for low-symmetry systems and is very well suited for simulations of time-dependent and finite-temperature problems. Preliminary results for the phonon-dispersion re- lations and the surface energies and relaxations for Al are used to illustrate the versatility of the ap- proach. The division of the total energy into a density-dependent part, an electrostatic "pairpotential" part, and a hybridization part provides a very simple way of understanding a number of these phenomena.