Lithium phosphorus oxynitride materials have been investigated for many years, especially in relation to the thin film electrolyte LiPON, developed at Oak Ridge National Laboratory. We have carried out first principles simulations of related crystalline materials in as a first step toward understanding the sources of stability and mechanisms of Li ion conductivity in these materials. In addition to a comprehensive survey of known crystalline materials related to LiPON, we have also predicted some materials. For example, starting with crystalline LiPO3 which has twisted phosphate chains, we considered the possibility of modifying the structure by substituting N and Li for O. The optimized structures were computed to have regularized phosphate chains which form planar -P-N-P-N- backbones. To the best of our knowledge, the predicted crystals, which we call s1-Li2PO2N with a 24 atom unit cell and s2-Li2PO2N with a 12 atom unit cell, have not yet been observed experimentally. We suggest several possible exothermic reaction pathways to synthesize these crystals.