We have performed ab initio linear combination of atomic orbitals-density functional theory calculations on biperiodic supercells to model the electronic and geometrical involvements of Ti intercalated atom in either octahedral or tetrahedral sites of the (001) Ti S2 surfaces. For each type of defect, both the relaxed atomic structure and the electronic properties of the defect states were carefully analyzed. For the titanium atom in the van der Waals gap, the partial filling of the conduction band is in agreement with the metallic behavior reported by experimental studies and the last filled states in the bottom of the conduction band-mainly developed on titanium 3d orbitals-permit us to explain the dark defects observed on the scanning tunneling microscopy image of the (001) Ti S2 surfaces. On the other hand, the intercalated titanium atom in the tetrahedral site which is just below the top sulfur atom plane governs the electronic density detected by the tip. It permits us to explain the triangular defect with a clear maximum of intensity in its center and dark sides.