We introduce a new method for calculating the broadening of atomic levels as a function of the atom's position outside the surface. The surface is studied using a cluster model, and the adsorbate-cluster eigenproblem is solved using quantum chemistry codes. The resulting density of states is projected on the adsorbate orbitals, revealing the broadening of adsorbate energy levels into resonances. We extract the width of these resonances from the projected density of states to calculate the broadening. Arbitrary lateral adsorbate positions and surface geometries can be explored by specifying different atom-cluster configurations.