On the experimental determination of 4$f$–4$f$ intensity parameters from the emission spectra of europium (III) compounds

Eu$^{3+}$ complexes and specially $\beta$-diketonate compounds are well known and studied in several areas due to their luminescence properties, such as sensors and lightning devices. A unique feature of the Eu$^{3+}$ ion is the experimental determination of the 4$f$–4$f$ intensity parameters $\Omega_\lambda$ directly from the emission spectrum. The equations for determining $\Omega_\lambda$ from the emission spectra are different for the detection of emitted power compared to modern equipment that detects photons per second. It is shown that the differences between $\Omega_\lambda$ determined by misusing the equations are sizable for $\Omega_4$ (ca. 15.5%) for several Eu$^{3+}$ $\beta$-diketonate complexes and leads to differences of ca. 5% in the intrinsic quantum yields $Q_{\mathrm{Ln}}^{\mathrm{Ln}}$. Due to the unique features of trivalent lanthanide ions, such as the shielding of 4$f$-electrons, which lead to small covalency and crystal field effects, a linear correlation was observed between $\Omega_\lambda$ obtained using the emitted power and photon counting equations. We stress that care should be exercised with the type of detection should be taken and provide the correction factors for the intensity parameters. In addition, we suggest that the integrated intensity (proportional to the areas of the emission band) and the centroid (or barycenter) of the transition for obtaining $\Omega_\lambda$ should be determined in the properly Jacobian-transformed spectrum in wavenumbers (or energy). Due to the small widths of the emission bands of typical 4$f$–4$f$ transitions, the areas and centroids of the bands do not depend on the transformation within the experimental uncertainties. These assessments are relevant because they validate previously determined $\Omega_\lambda$ without the proper spectral transformation.