The K/graphite adsorption system is studied in a cluster model using ab initio density-functional methods. From the investigation of the potential energy surface a lower bound for the potassium atom binding energy 1.5 eV is obtained, and a surface diffusion barrier of 0.2 eV. To simulate experimentally reported thermal desorption spectra, a two-phase kinetic model is investigated and a desorption energy of 1 eV is found. The thermally activated surface diffusion of K atoms leads to intercalation at defects or steps, which is followed by desorption when further heating the sample. A normal mode analysis yields a K-graphite in-phase and out-of-phase vibrational mode with an energy split of 8 meV, which indicates a relatively strong dynamical coupling between the adsorbed K atom and the graphite substrate. The calculated electron density distribution is verified by an accurate reproduction of the measured dipole moment. From a projected density of state analysis we find a K 4s and an antibonding K 4p resonance located slightly above and 2.6 eV above the Fermi level, respectively. The location of the K 4s resonance, with a lower occupied tail, is consistent with an incomplete charge transfer, and the location of the K 4p resonance is consistent with a proposed hot-electron model to explain recent photodesorption data. The new assignment of the K-induced states near the Fermi level resolves previous apparent discrepancies of the charge state of the dispersed K atom. (C) 2000 American Institute of Physics. [S0021-9606(00)70310-2].