Quadrupolar level crossing resonance (QLCR) in muSR of solid state systems with diamagnetic muon states in proximity to quadrupolar nuclei was discovered many years ago, however its application has been held back by the lack of a computational framework for predicting, analyzing and interpreting such resonance spectra. QLCR is unique among muSR methods in being sensitive to charge as well as spin and thus has great potential for new application areas of muon spectroscopy. Recent progress in the computation of muon states in materials using density functional theory (DFT+mu) can also be applied to QLCR. Solid nitrogen provides an excellent benchmark system to test calculations against experiment. A comprehensive QLCR data set will be collected for solid nitrogen in its fully ordered alpha-phase and DFT-based spectral calculation methods for QLCR will be refined against the data obtained