A method of conducting assays for analytes, usually from biological samples, utilizing bioaffinity reagents linked to luminescent lanthanide chelates, which are synthesized so that the non-radiative quenching of the ion luminescence through C--H bond vibrational energy manifolds is avoided using a stable chelate where the CH and CH.sub.2 groups in the vicinity of the emittive ion are substituted with CD and CD.sub.2 groups hence producing improved luminescence quantum yield and higher assay sensitivities.