We have obtained energy-minimized atomic and the resultant electronic structures for Na adsorbed on Si(001)-(2×1) at two different coverages. The passage through a 2×3 structure before reaching the 2×1 structure at a monolayer coverage is explained based on these results. At a monolayer coverage the calculated structure is puckered in accord with recent experiments. The observed reentrant behavior to an insulating state at the monolayer coverage of alkali metals also follows naturally from these calculations. We also find that up to this coverage, the reversal to ideal surface structure is energetically unfavorable and this is to be contrasted with Si(111)-(2×1). An explanation is offered for differing values of charge transfer quoted in the literature. © 1989 The American Physical Society.