Abstract The plane-wave pseudopotential density functional theory method has been used to study the Si(0 0 1)2 × 1–K adsorption system for 0.5 and 1.0 monolayer coverage. The minimum energy atomic configuration for 0.5 monolayer coverage was found to correspond to the potassium atom in each 2 × 1 surface unit cell occupying the valley bridge site. A double-layer model was determined to be the optimised geometry of the Si(0 0 1)2 × 1–K chemisorption system for 1.0 monolayer coverage. The geometry of this double-layer model was found to be in good agreement with the current experimental data. A detailed analysis of the electronic structure of this double-layer model has also been performed. The overall dispersion of the occupied and unoccupied surface state bands has been shown to be in excellent agreement with the angle-resolved and inverse photoemission data. The nature and dispersion of the surface states of the double-layer model in the vicinity of the energy gap provide evidence of strong interactions, both between the two inequivalent potassium atoms in each 2 × 1 surface unit cell, and between these adatoms and the underlying substrate.