The Racah parameters in conjunction with the Tanabe-Sugano energy-level diagram are widely used as a means of describing the effects of electron-electron repulsion within the metal complexes in coordination chemistry. A determination of the excitation energy levels in the 3d(3)-configuration ions (Mn4+, Cr3+, etc.) is possible from a set of Racah parameters (B and C) and crystal-field splitting parameter (Dq), and vice versa. The Tanabe-Sugano diagram promises that the zero-phonon line E-2(g) energies, E(E-2(g))(ZPL), over B of the Mn4+ and Cr3+ ions should be nearly crystal field independent, since they are practically parallel to the horizontal axis in the whole range of Dq/B variation. However, the experimental E(E-2(g))(ZPL) plots showed a gradual increase with increasing Dq/B, in disagreement with the Tanabe-Sugano diagram. Therefore, a new analysis model assuming the Racah parameter ratio of C/B similar to 4.7 has been recently proposed [ECS J. Solid State Sci. Technol., 8, R164 (2019); 8, R183 (2019)]. However, the new model has been used without rigorous validation. The present study focused on this problem and analyzed the luminescence properties of LiBaF3:Cr3+ and LaGaO3:Mn4+ phosphors. More generalized expressions were proposed for analyzing the various kinds of phosphors at an optional ratio of C/B = r. (C) 2020 The Electrochemical Society ("ECS"). Published on behalf of ECS by IOP Publishing Limited.