Table 4. Vertical and Adiabatic Ionization Potentials (I_vertical and I_adiabatic), Vertical and Adiabatic Electron Affinities (A_vertical and A_adiabatic), Self-Trapping Energies (E_hole^ST and E_electron) of a Hole or an Electron, the Average First-Neighbor Bond Length around the Hole or Electron (r_{Ce⁴⁺–O^1–} and r_{Ce³⁺–O^2–}), and the Band Gap (E_g) of CeO₂ Calculated by the M-L Approach and QM/MM Calculations^a.

	M-L (with modified shell charges)b	M-L (with modified shell charges and potentials)b	QM/MMB97-2b	QM/MM PBE0b	QM/MM BB1Kb	Periodic HSE06c	Periodic PBE+Uc
Ivertical (eV)	9.64	5.10	4.92	5.10	5.38
Iadiabatic (eV)	7.11	3.78	4.35	4.41	3.80
EholeST (eV)	–2.53	–1.32	–0.57	–0.69	–1.58
rCe4+–O1– (Å)	2.533	2.451	2.447	2.451	2.452
Avertical (eV)	0.18	0.28	0.70	0.51	0.11
Aadiabatic (eV)	1.44	1.20	1.31	1.20	1.50
EelectronST (eV)	–1.26	–0.92	–0.61	–0.69	–1.39	–0.30	–0.54
rCe3+–O2– (Å)	2.474	2.444	2.448	2.442	2.435	2.42
Eg (eV)	8.08	4.82	4.22	4.59	5.27

^aIn M-L calculations, the first column shows the results using modified shell charges for Ce³⁺ and O^1– but the same potential for Ce⁴⁺-O^2– interactions, while the second column shows the calculated results using IP10b presented in Table 3.

^bPresent work.

^cReference (30).