We have used atomistic simulations to identify and characterize interstitial defect cluster configurations candidate for W and X photoluminescence centers in crystalline Si. The configurational landscape of small self-interstitial defect clusters has been explored through nanosecond annealing and implantation recoil simulations using classical molecular dynamics. Among the large collection of defect configurations obtained, we have selected those defects with the trigonal symmetry of the W center, and the tetrahedral and tetragonal symmetry of the X center. These defect configurations have been characterized using ab initio simulations in terms of their donor levels, their local vibrational modes, the defect induced modifications of the electronic band structure, and the transition amplitudes at band edges. We have found that the so-called I3-V is the most likely candidate for the W PL center. It has a donor level and local vibrational modes in better agreement with experiments, a lower formation energy, and stronger transition amplitudes than the so-called I3-I, which was previously proposed as the W center. With respect to defect candidates for the X PL center, our calculations have shown that none of the analyzed defect candidates match all of the experimental characteristics of the X center. Although the Arai tetra-interstitial configuration previously proposed as the X center cannot be excluded, the other defect candidates for the X center found, I3-C and I3-X, cannot be discarded either.