# Fileset [adts70428-sup-0001-suppmat.pdf](https://mdr.nims.go.jp/filesets/ce3c927f-50dd-42ba-9bb8-1c2d9bfa67d5/download) ## Creator [Satoru Matsuishi](https://orcid.org/0000-0001-8905-0255), [Hidekazu Ikeno](https://orcid.org/0000-0002-3840-4049), [Yukinori Koyama](https://orcid.org/0000-0002-7090-4430), [Takashi Takeda](https://orcid.org/0000-0003-2510-4562) ## Rights [Creative Commons BY Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0/) ## Other metadata [Luminescence Spectra Simulation of Ce 3+ ‐Activated Phosphors by Accumulating Emission Lines Along First‐Principles Molecular Dynamics Trajectories](https://mdr.nims.go.jp/datasets/3e4a2cf2-e1a5-4e0f-b0c7-a2de1c77fbbd) ## Fulltext 1 Supporting Information Luminescence spectra simulation of Ce3+-activated phosphors by accumulating emission lines along first-principles molecular dynamics trajectories Satoru Matsuishi1, Hidekazu Ikeno, Yukinori Koyama, and Takashi Takeda Figure S1. Calculated absorption spectra of YAG:Ce structure model (red curve) using TDM from the lowest Ce 4f level to higher levels in Ag−1 states. Blue bars indicate the calculated transition energies and the oscillator strengths. Figure S2. Average radiative lifetime ‹τr› as a function of temperature calculated along the trajectory of FPMD for YAG:Ce structure model. 2 Figure S3. Evaluation of emission peak positions and FWHMs in experimental luminescence emission spectra of YAG:Ce at 5-600 K taken from literature.[S1] The spectral intensity ρ(λ) in the wavelength domain was converted to the spectral intensity ρ(ϵ) in the energy domain by the equation ρ(ϵ) = (λ2/hc) ρ(λ). In the reference, the YAG:Ce luminescence spectra were measured below 295 K and above 300 K using different spectrophotometers. Because the sensitivity curves of the two spectrometers are different, the spectra above 300 K were corrected using the intensity ratio of the spectra at 300 K and 295 K; ρcorr(ϵ) = ρ294(ϵ) / ρ300(ϵ) ρ(ϵ). 3 Figure S4. Configuration coordinate diagram of total energy for the CeY23Al40O96 structure model obtained by the ΔSCF approach. 4 Figure S5. Evaluation of emission peak positions and FWHMs in experimental luminescence emission spectra of 12 known Ce3+-activated phosphors measured at 300 K, taken from the literature. (a)Y3Al5O12:Ce, [S1] (b) YAlO3:Ce,[S2] (c) YAl3B4O12:Ce,[S3] (d) YBO3:Ce,[S3] (e) CaYAl3O7:Ce,[S4] (f) LiYF4:Ce,[S5] (g) CaF2:Ce,[S6] (h) CaAl2O4:Ce[S7] (i), CaSrAl2O7:Ce[S8] (j), Sr2Al2O7:Ce,[S9] (k) LiBaPO4:Ce,[S10] and (l) Sr3B2O6:Ce[S11]. 5 Figure S6. Relation between the FWHM 𝑾𝑾𝐞𝐞𝐞𝐞𝐜𝐜𝐜𝐜𝐜𝐜 of whole emission band and the FWHMs 𝒘𝒘𝐞𝐞𝐞𝐞𝐜𝐜𝐜𝐜𝐜𝐜 of 5d1→2F5/2 and 5d1→2F7/2 bands in the spectra at 300 K in the Ce3+-activated phosphor series. Figure S7. KSO energies as functions of UCe obtained by PBEsol+U calculation for CeY23Al40O96 model, compared with KSO energies calculated by HSE06 hybrid functional. 6 Figure S8. (a) KSO energies at Γ, (b) 𝜖𝜖15 − 𝜖𝜖1 and 𝜖𝜖15 − 𝜖𝜖7 transition energies and spin-orbit splitting ΔSO for Ae−1 state in YAG:Ce model as a function of UCe. Table S1. List of Ce3+-activated phosphor systems with 𝑈𝑈Ceopt used for structure optimization and total energy calculation and ΔSCF parameters, absorption energy at 0 K (𝜖𝜖absΔSCF(0), eV), emission energy at 0 K (𝜖𝜖emΔSCF(0), eV), Stoks shift at 0 K (ΔS(0), eV) Franck–Condon shifts for GS (EFS,g) and ES (EFS,e) electronic states, and total normal coordinate change (ΔQ, amu1/2Å). Compounds 𝑈𝑈Ceopt 𝜖𝜖absΔSCF(0) 𝜖𝜖emΔSCF(0) ΔS(0) EFS,g EFS,e ΔQ Y3Al5O12:Ce 4.68 2.751 2.194 0.557 0.347 0.210 1.423 YAlO3:Ce 3.83 4.114 3.672 0.442 0.285 0.157 1.231 YAl3B4O12:Ce 3.51 4.045 3.126 0.919 0.701 0.218 2.026 YBO3:Ce 3.77 3.646 3.211 0.435 0.263 0.172 1.132 CaYAl3O7:Ce 3.84 3.466 2.352 1.114 0.768 0.347 1.473 LiYF4:Ce 3.71 4.642 4.485 0.157 0.087 0.070 0.226 CaF2:Ce, F 3.40 4.180 3.993 0.187 0.106 0.081 0.895 CaAl4O7:Ce, Na 3.61 4.089 3.067 1.022 0.693 0.329 2.188 CaSrAl2SiO7:Ce, Na 3.61 3.799 2.703 1.096 0.821 0.275 1.626 Sr2Al2SiO7:Ce, Na 3.73 3.702 2.810 0.892 0.632 0.261 2.179 LiBaPO4:Ce,Na 3.50 4.264 3.581 0.683 0.390 0.294 2.349 Sr3B2O6:Ce,Na 3.53 3.558 2.943 0.615 0.358 0.256 2.514 7 Table S2. Parameters obtained by harmonic oscillator model analysis of ΔSCF data: Associated effective vibrational energies for GS (ℏΩg, meV) and ES (ℏΩe, meV) electronic states, Huang-Rhys parameters for GS (Sg) and ES (Se) states, emission energy at 300 K (𝜖𝜖emΔSCF(300), eV) and FWHM of emission peak at 300 K (𝜖𝜖emΔSCF(300), eV). System ℏΩg ℏΩe Sg Se 𝜖𝜖emΔSCF(300) 𝑤𝑤emΔSCF(300) Y3Al5O12:Ce 37.8 29.4 9.17 7.13 2.265 0.426 YAlO3:Ce 39.6 29.4 7.19 5.34 3.722 0.405 YAl3B4O12:Ce 37.8 21.1 18.55 10.35 3.332 0.826 YBO3:Ce 41.4 33.5 6.35 5.14 3.251 0.362 CaYAl3O7:Ce 54.4 36.6 14.12 9.49 2.533 0.752 LiYF4:Ce 119.3 107.0 0.73 0.65 4.496 0.257 CaF2:Ce,F 33.3 29.1 3.19 2.79 4.008 0.209 CaAl4O7:Ce,Na 34.8 24.0 19.92 13.73 3.194 0.669 CaSrAl2SiO7:Ce,Na 50.9 29.5 16.12 9.33 2.942 0.882 Sr2Al2SiO7:Ce,Na 33.4 21.4 18.95 12.18 2.959 0.681 LiBaPO4:Ce,Na 24.3 21.1 16.05 13.93 3.619 0.396 Sr3B2O6:Ce,Na 21.8 18.4 16.45 13.91 2.989 0.387 8 Table S3. Peak energies (𝜖𝜖5/2cal and 𝜖𝜖7/2cal , eV), SO splitting (∆SOcal, eV), FWHMs (𝑤𝑤5/2cal and 𝑤𝑤7/2cal , eV) and areal intensity ratio (𝑠𝑠7/2cal /𝑠𝑠5/2cal ) of 5d1→2F5/2 and 5d1→2F7/2 emission bands from peak fitting for emission spectra obtained by FPMD spectra accumulation method 𝐼𝐼5/2(𝜖𝜖) and 𝐼𝐼7/2(𝜖𝜖) at 300 K. System 𝜖𝜖5/2cal 𝜖𝜖7/2cal ∆SOcal 𝑤𝑤5/2cal 𝑤𝑤7/2cal 𝑠𝑠7/2cal /𝑠𝑠5/2cal Y3Al5O12:Ce 2.226 1.856 0.370 0.455 0.458 0.524 YAlO3:Ce 3.512 3.132 0.380 0.388 0.393 0.627 YAl3B4O12:Ce 3.196 2.816 0.380 0.750 0.731 0.599 YBO3:Ce 3.269 2.898 0.371 0.314 0.316 0.636 CaYAl3O7:Ce 2.578 2.198 0.380 0.491 0.482 0.630 LiYF4:Ce 4.648 4.278 0.370 0.279 0.280 0.642 CaF2:Ce,F 4.375 4.005 0.370 0.243 0.243 0.602 CaAl4O7:Ce,Na 2.918 2.528 0.390 0.360 0.337 0.707 CaSrAl2SiO7:Ce,Na 2.813 2.443 0.370 0.885 0.875 0.659 Sr2Al2SiO7:Ce,Na 3.187 2.817 0.370 0.670 0.712 0.667 LiBaPO4:Ce,Na 3.374 2.924 0.450 0.384 0.399 0.526 Sr3B2O6:Ce,Na 2.910 2.530 0.380 0.334 0.333 0.576 9 Table S4. Peak energy (𝐸𝐸emcal , eV) and FWHM (𝑊𝑊emcal , eV) of calculated whole emission spectrum I(ϵ) at 300 K compared with their experimental values (𝐸𝐸emexpand 𝑊𝑊emexp, eV) taken from literature. System 𝐸𝐸emcal 𝑊𝑊emcal 𝐸𝐸emexp 𝑊𝑊emexp Y3Al5O12:Ce 2.186 0.660 2.339 0.427 YAlO3:Ce 3.492 0.676 3.455 0.488 YAl3B4O12:Ce 2.946 0.938 3.590 0.513 YBO3:Ce 3.269 0.609 3.189 0.464 CaYAl3O7:Ce 2.508 0.759 2.876 0.435 LiYF4:Ce 4.648 0.586 4.024 0.347 CaF2:Ce,F 4.375 0.537 3.863 0.368 CaAl4O7:Ce,Na 2.908 0.692 3.203 0.431 CaSrAl2SiO7:Ce,Na 2.673 1.014 2.748 0.542 Sr2Al2SiO7:Ce,Na 2.837 0.909 2.989 0.515 LiBaPO4:Ce,Na 3.374 0.673 2.709 0.514 Sr3B2O6:Ce,Na 2.900 0.616 2.866 0.432 10 Table S5. Statistical analyses of ΔSCF emission energy 𝜖𝜖em∆SCF against calculated emission peak energy 𝜖𝜖5/2cal and ΔSCF emission band FWHM against calculated emission FWHM 𝑤𝑤5/2cal at 300 K. ME (eV), MAE (eV), MRE (%) and MARE (%) stand for the mean error, mean absolute error, mean relative error, and mean absolute relative error, respectively. The slope, intercept and coefficient of determination (R2) correspond to the linear fitting. The number in parentheses indicates the standard deviation. 𝜖𝜖5/2cal vs 𝜖𝜖em∆SCF 𝑤𝑤5/2cal vs 𝑤𝑤em∆SCF ME (eV) −0.03(20) −0.06(11) MAE (eV) 0.16(11) 0.07(10) MRE (%) 0(6) −8(18) MARE (%) 5(3) 13(14) Slope 1.07(10) 0.77(14) Intercept (eV) −0.25(33) 0.06(8) R2 0.91 0.76 Table S6. Statistical analysis of peak energy Eem and FWHM Wem of whole emission spectra of Ce3+-activated phosphors calculated by FPMD spectra accumulation method. ME (eV), MAE (eV), MRE (%) and MARE (%) stand for the mean error, mean absolute error, mean relative error, and mean absolute relative error, respectively. The slope, intercept (eV) and coefficient of determination (R2) correspond to the linear fitting. The number in parentheses indicates the standard deviation. 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