The adsorption and desorption of Se on the Si(0 0 1) surface are investigated, based upon the ab initio pseudopotential calculations. Following a recent experimental work, three different adsorption models have been studied: 1/2 ML of Se on the Si-Si dimer with a bridge position within the (1 × 2) surface reconstruction, 1 ML of Se sitting above the topmost Si atoms in bridge absorption site within the (1 × 1) surface reconstruction, and 2 ML of Se half of which is embedded into the Si bulk near the surface within the (1 × 1) surface reconstruction. For 1/2 ML, we have found that the vertical displacement between the Se atom and Si-Si dimer is 1.97 Å, close to the experimentally measured value of 2.10 Å. For 1 ML, the vertical displacement between the Se atom and the Si atoms is 1.41 Å, somewhat smaller than the experimentally measured value of 1.60 Å. For 2 ML, upon relaxation, the embedded Se atoms have diffused upwards. Our results are analysed to provide support to a recent experimental study of desorption of Se from the surface. © 2002 Elsevier Science B.V. All rights reserved.