Group theory, nuclear spin statistics and tunneling splittings of 1,3,5-triamino-2,4,6-trinitrobenzene

The symmetry group of the non-rigid 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) is constructed for the internal rotations of the nitro groups that exhibit low rotation barriers of 5 kcal/mole. The permutation group has 48 operations characterized by the wreath product S3[S2]. The nuclear spin statistical weights for TATB with 17O, 14N and 1H species are computed and the tunneling splitting patterns of the rotational and rovibronic levels of TATB are constructed for the first time. It is shown that the ground rovibronic state of TATB is split into A1, A3, T1 and T3 levels.