“…n core = 0), all TM d levels are shifted down by U dc to screen the core hole. By fitting to published experimental data from XPS of SrTiO 3 , ellipsometry, and angle-resolved photoemission spectroscopy (ARPES) [15,32,[41][42][43], we take ǫ d (e g ) = 2.0 eV, ǫ d (t 2g ) = 0 eV, ǫ p (Γ) = −3.0 eV, V (e g ) = 2.5eV, V (t 2g ) = −1.3 eV, U = 6.0 eV, and U dc = 8.0 eV [44]. This problem can be solved exactly by the technique introduced by Gunnarsson and Schönhammer [12,45], and the details are provided in Appendix B.…”