We report theoretical studies on orientationally disordered crystals K:Br:CN and Ar:N2. Tunneling Two-Level Systems (TLSs) responsible for the low-temperature thermal behavior of the K:Br:CN were recently identified as pairs of states related to each other by inversion symmetry,[1] and specifically in K:Br:CN as CN inversions.[2] Ar:N2 is a system of the same class which displays analogous properties but where there are no easily identifiable centrosymmetric TLSs. Here we present the numerical study and first results on ArN2, using Lennard-Jones potentials of medium-sized 2D and 3D fragments. We suggest a family of TLS candidates in 2D based on collective inversions involving two or more N2 molecules. We present possible strategies to extend these results to 3D.