The electronic structure of positronium hydride has been studied using explicitly correlated Gaussian functions. The resulting energy constitutes new upper bound to the exact nonrelativistic energy of PsH within the Born-Oppenheimer approximation. The two photon annihilation rate was computed using the optimized wave function. Preliminary results for the positron bonded with the lithium atom indicate the stability of this system against the dissociation into Li+ cation and Ps atom.