Ab initio plane-wave pseudopotential density functional theory $(\mathrm{DFT})$ calculations have been carried out to determine the atomic and electronic structure of the $\mathrm{Si}(001)2\ifmmode\times\else\texttimes\fi{}2\text{\ensuremath{-}}\mathrm{Li}$ adsorption system at 0.5 monolayer $(\mathrm{ML})$ coverage. The minimum energy configuration is found to be characterized by alternating symmetric and asymmetric $\mathrm{Si}\text{\ensuremath{-}}\mathrm{Si}$ dimers along each dimer row independently of the details of the $\mathrm{Li}$ adatom topology. This is due to virtually all of the $\mathrm{Li}$ charge being transferred to just one of the dimers in each $2\ifmmode\times\else\texttimes\fi{}2$ surface unit cell, leaving the second dimer essentially unchanged. The nature and dispersion of the theoretically predicted occupied electronic surface state bands are found to be in good agreement with the angle-resolved photoemission data and little dependent on the actual $\mathrm{Li}$ adatom geometry. The composition of the second and third lowest unoccupied surface state bands, however, clearly depends on the $\mathrm{Li}$ adatom topology. The nature of the lowest energy unoccupied surface state band suggests that the $\mathrm{Si}(001)\text{\ensuremath{-}}\mathrm{Li}$ chemisorption system at $0.5\phantom{\rule{0.3em}{0ex}}\mathrm{ML}$ coverage will exhibit a reactivity similar to that of the clean $\mathrm{Si}(001)$ surface.