The elements of the electric field gradient tensor at Li position in the intercalation compound LixTiS2 (with x=0.25, 0.33, 0.67, and 1.0) were calculated with first-principles methods and periodic supercell models. The theoretical results obtained with density functional and Hartree-Fock hybrid methods were compared with experimental field gradients extracted from 7Li NMR spectra from the literature and from our measurements presented here. The dependence of calculated field gradients on the basis set and the explicit form of the exchange-correlation density functional was investigated. In agreement with earlier studies a pronounced effect of polarization functions at the Li site was observed. After optimization of internal degrees of freedom in LiTiS2 all methods under consideration give quadrupole coupling constants in close agreement with experiment. For x < 1 the calculated quadrupole coupling constants were found to depend more sensitively on the method which was attributed to differences in the description of spin localization. The calculations allow one to distinguish between Li atoms placed at octahedral and tetrahedral interstitial sites of the host lattice TiS2. © 2004 American Physical Society