Quadrupolar level crossing resonance (QLCR) occurs in the muSR of solids with diamagnetic muon states in close proximity to quadrupolar nuclei. This effect provides uniquely valuable sensitivity to charge states in muSR. Recent progress in the computation of muon states in materials using density functional theory (DFT+mu) can also be applied to predicting and interpreting QLCR spectra. Solid nitrogen provides an excellent example system to test these calculations against experiment. In our latest muon studies of solid nitrogen two key discoveries are firstly the presence of negative diamagnetic muon states, along with the usual positive states, and secondly an anomalously fast relaxation rate for some of the resonances. The QLCR spectra are strongly temperature dependent and further studies are needed to establish the full dependence and relate it to properties of the molecular solid