Fig. 1. (a) Theoretical spectrum of Ti⁴⁺ under different electron interactions: 1) no interaction, 2) including 2p spin-orbit coupling, 3) including crystal field interaction, and 4) including the multiplet effect; (b) The theoretical spectrum of Co³⁺ with O_h symmetry at different 10 Dq; (c) Cu L₃ edge experimental spectra of NaCuO₂(Cu³⁺) and CuO(Cu²⁺), and Ni L₃ edge experimental spectra of NiO(Ni²⁺)^[19]

Fig. 2. Energy-level diagram for the d shell in trigonal (D_3d), octahedral (O_h), and tetragonal symmetry (D_4h)

Fig. 3. (a) Co L_2,3 edge spectra of different valence states, from top to bottom: BaCoO₃(Co⁴⁺), EuCoO₃(Co³⁺), CoO(Co²⁺)^[20]; (b) Mn L_2,3 edge spectra of different valence states, from top to bottom: SrMnO₃(Mn⁴⁺), LaMnO₃(Mn³⁺), MnO(Mn²⁺)^[31]; (c) Experimental V-L_2,3 XAS spectra of Ba₁₅V₁₂S₃₄O₃ together with calculated V^III, V^IV, V^V and their sum ^[32]; (d) The Cr-L_2,3 XAS spectra of Sr₂Cr_0.5Ni_0.5OsO₆ together with Cr₂O₃, PbCrO₃, and Ag₂Cr₂O₇ as references^[33] (color inline)

Fig. 4. (a) 1) Co-L_2,3 XAS spectra of a the LaMn_0.5Co_0.5O₃ samples with T_C = 225 K and T_C = 150 K, their difference, and 2) LaCoO₃ as Co³⁺ reference^[31]; (b) 1) Mn-L_2,3 XAS spectra of a the two LaMn_0.5Co_0.5O₃ samples with T_C = 225 K, T_C = 150 K, their difference, and 2) LaMnO₃ (Mn³⁺) for comparison^[31]

Fig. 5. (a) Experimental spectra of Co L_2,3 edge with different symmetries: YBaCo₃AlO₇(Co²⁺-T_d)^[36], CoO(Co²⁺-O_h), and Ca₃CoRhO₆(Co²⁺-D_3d)^[37]; (b) Energy-level diagram for the d shell in trigonal (D_3d), octahedral (O_h), and tetrahedral symmetry (T_d)

Fig. 6. (a) 1) The Co L_2,3-edge spectra of EuCoO₃(LS-Co³⁺) and Sr₂CoO₃Cl(HS-Co³⁺), 2) Comparison between the Sr₂CoO₃Cl spectrum and a theoretical simulation for high-spin (HS), 3) Comparison between the EuCoO₃ spectrum and a theoretical simulation for low-spin (LS)^[30]; (b) The Co L_2,3-edge spectra of BaCoO₃ and calculated Co L_2,3 XAS spectra for a CoO₆ cluster with 3d⁵ low-spin (LS), intermediate-spin (IS), and high-spin (HS) state configurations^[49]

Fig. 7. (a) 1) Experimental and 2) theoretical polarization-dependent Mn L_2,3-edge X-ray absorption spectra of o-YMnO₃ on a YAlO₃(001) substrate, experimental and theoretical LD spectra of 3) (E//c)-(E//a), 4) (E//b)-(E//c), and 5) (E//b)-(E//a). The inset shows the polarization-dependent Mn L₃-edge absorption spectra of the o-DyMnO₃ crystal^[56]; (b) Experimental geometry with polarization of the light. θ is the angle between the electric field vector E⃗ and the c-axis surface normal, and α is the tilt between the Poynting vector and the surface normal^[57]; (c) Polarization-dependent Co L_2,3 XAS spectra of Na_0.5CoO₂ and Na_0.75CoO₂, where 1) and 5) are the experimental spectra; 3) and 7) are the theoretical spectra of Co³⁺, 4) and 8) are the theoretical spectra of Co⁴⁺, and 2) and 6) are the corresponding fitted theoretical spectra^[57]

Fig. 8. The comparison of theoretical spectra (solid curve)^[59] and experimental spectra (dash-dotted curve)^[60] about Cu L_2,3-edge in NaCuO₂

Fig. 9. (a) Ni L_3,2 edge XAS spectra of LiNi_0.5Mn_1.5O₄ in different states and the calculated spectra of Ni²⁺, Ni³⁺, and Ni^4+[67]; (b) Experimental Mn L_2,3 XAS spectra of LiMn₂O₄, LiNi_0.2Mn_1.8O₄, and LiNi_0.5Mn_1.5O₄, as well as the relevant spectra of MnO(Mn²⁺), LaMnO₃(Mn³⁺), and SrMnO₃(Mn⁴⁺, green). The simulated Mn L_2,3 XAS spectra of LiMn₂O₄ and LiNi_0.5Mn_1.5O₄ are also shown below the corresponding experimental spectra^[75]; (c) MLCT and LMCT models^[81]; (d) CTs from Ni 3d(t_2g) orbital to antibonding-type for NiFe-PBA^[81]; (e) Ni L_2,3 edge XAS spectra of Li_xNiFe-PBA; the theoretical spectrum of the [Ni_II(NC)₆]^4- cluster for NiFe-PBA and that of the ionic Ni²⁺ state are also shown. The theoretical spectra were convoluted from the line spectra, using Lorentzian and Gaussian functions (with each width 0.25 eV)^[81]; (f) Fe L_2,3 edge XAS spectra of Li_xNiFe-PBA, and the theoretical spectra of the [Fe_III(CN)₆]^3- and [Fe_II(CN)₆]^4- clusters for NiFe-PBA^[81] (color online)

Fig. 10. (a, b) The schematic depiction of the experimental setup of the in situ cell for simultaneous cycling and X-ray spectroscopic measurement. An array of holes 50 mm in diameter is drilled into the current collector with a high-precision laser. The incident soft X-ray beam and excited fluorescence photon pass through the array of holes on the current collector^[87]; (c) Ni L-edge sXAS TFY spectra of NMC cathode Spectra are taken at different state-of-charge levels, denoted as A-L^[87]; (d) In situ Fe L_2,3-edge sXAS of LFP^[87]

Fig. 11. (a) Ni L_2,3 XAS of LiNiO₂, along with a simulated spectrum of nominal 3d⁸L configurations^[94]; (b) Ni L_2,3 XAS of LiNiO₂ after OER, along with the sum (black curve) of calculated spectra of 75% 3d⁸L² and 25% 3d⁸L configurations^[94]; (c) Simulation of Co L_2,3-edge of CF-PBA-400. The simulation spectrum is the sum of HS Co²⁺ and LS Co³⁺, and the experimental spectrum is shown in black^[95]; (d) Simulation of Fe L_2,3-edge of CF-PBA-400. The simulation spectrum is the sum of LS Fe²⁺, HS Fe²⁺, and HS Fe³⁺. The experimental spectrum is shown in black^[95] (color online)

Fig. 12. Experimental and theoretical spectra of Co-L_2,3 sXAS spectra of Li₂Co₂O₄. (a) Experimental Co-L_2,3 sXAS spectrum of Li₂Co₂O₄ taken in operando after 20 min under an applied voltage of 1.6 V^[96]; (b) Experimental data taken in vacuo after the OER. Theoretical spectra constructed from a weighted sum of the theoretical simulation for an LS-Co³⁺ spectra and an LS-Co⁴⁺ spectra^[96]; (c) Schematic illustration of in operando soft-XAS setup under ultrahigh-vacuum condition; (d) Cu L₃ edge sXAS spectra in operando at different voltages^[98], Co L₃ sXAS spectra of D-Co₃O₄ under OCP; (e, f) 1.7 V vs. RHE with spectral weights of Co²⁺(O_h) (CoO), Co²⁺(T_d) (YBaCo₃AlO₇), Co³⁺(O_h) (Li₂Co₂O₄), and Co⁴⁺(BaCoO₃)^[100] (color online)