. 2022 Dec 21;35(1):207–227. doi: 10.1021/acs.chemmater.2c03019

Table 1. Calculated Lattice Constant a₀, Band Gap E_g, High-Frequency Dielectric Constant ε_∞, Born Effective Charges Z_Ce^* and Z_O, and Surface Energies of CeO₂ Using VASP Compared with Previous Experimental and Theoretical Results.

	a₀ (Å)	E_g (eV)	ε_∞	Z_Ce^*	Z_O^*	E₍₁₀₀₎^surf(J m^–2)	E₍₁₁₀₎^surf(J m^–2)	E₍₁₁₁₎^surf(J m^–2)
PBE+U (U_Ce 4f = 5 eV)^a	5.490	2.29	6.59	5.53	–2.77	1.45	1.06	0.69
PBEsol+U (U_Ce 4f = 5 eV)^a	5.435	2.41	6.57	5.51	–2.75	1.77	1.27	0.90
PBE0^a	5.397	4.38	5.67	5.67	–2.84	1.61	1.21	0.85
PBEsol0^a	5.361	4.46	5.68	5.68	–2.84	1.83	1.33	0.96
HSE06^a	5.396	3.63	5.71	5.67	–2.84	1.59	1.20	0.84
PBE+U (U_Ce 4f = 5 eV)^b	5.489					1.44	1.06	0.71
PBEsol+U (U_Ce 4f = 5 eV)^c	5.431		6.55	5.53	–2.76
PBE0^d	5.403	4.35
PBE0^e	5.401					1.64	1.27	0.86
PBEsol0^d	5.368	4.40
HSE06^f	5.40	3.50
GW₀^g		3.88
Experiment	5.411^h	2.9–3.3^k	5.31^q			1.20 ± 0.2 (averaged)^r
	5.401ⁱ	4.0^l
	5.395^j	3.6–4.11^m
		4.0ⁿ
		4.4^o
		4.3–4.4^p

Present work.

Reference (121).

Reference (122).

Reference (37).

Reference (38).

Reference (35).

Reference (123).

Room-temperature measurements.^108−110

ⁱ

Low-temperature measurement at 100 K.¹¹³

Extrapolated to 0 K from thermal expansion measurements.^81,111−113

Spectroscopic ellipsometry measurement on nanocrystalline or single-crystal CeO_2–x films.^106,116

Steady-state and ultrafast transient absorption spectra measurement on stoichiometric CeO₂ thin film. A revised optical band gap of 4 eV was proposed for bulk ceria, and the absorption tail below 4 eV was identified as the Urbach tail.¹¹⁷

Optical measurement on polycrystalline CeO₂ films with 140–180 nm thicknesses.¹²⁴

ⁿ

The electron energy loss spectroscopy (EELS) spectrum captured the O_2p → Ce_4f transition starting at 4 eV on single-crystal thin films, and the intensity between 0 and 3 eV indicates the Ce³⁺ state.¹²⁰

High-resolution EELS study on stoichiometric thin films observed a 4.4 eV energy loss from O_2p to the empty Ce_4f state transition.¹¹⁹

Measurement from the optical absorption spectrum on the CeO₂ nanoparticles.¹¹⁸

Transmissivity and reflectivity measurement on CeO₂ quasi-single crystal sample.⁸³

Measurement on nanoparticle samples by calorimetry methods.^125,126

Table 1. Calculated Lattice Constant a0, Band Gap Eg, High-Frequency Dielectric Constant ε∞, Born Effective Charges ZCe* and ZO, and Surface Energies of CeO2 Using VASP Compared with Previous Experimental and Theoretical Results.

Table 1. Calculated Lattice Constant a₀, Band Gap E_g, High-Frequency Dielectric Constant ε_∞, Born Effective Charges Z_Ce^* and Z_O, and Surface Energies of CeO₂ Using VASP Compared with Previous Experimental and Theoretical Results.