Density-functional calculation of CeO2 surfaces and prediction of effects of oxygen partial pressure and temperature on stabilities

Abstract

We have used density-functional theory to investigate (111), (110), (210), (211), (100), and (310) surfaces of ceria (CeO2). Compared with previous interatomic-potential-based studies, our calculations reported a slightly different relative stability ordering and significantly lower surface energies for the stoichiometric surfaces. Using a defect model, the surface stabilities were evaluated as functions of oxygen partial pressure and temperature. Our investigations were restricted to ideal surface terminations, without considering defect formation on those surfaces. We found that at 300 K, the stoichiometric (111) has the lowest free energy for a wide range of oxygen partial pressures up to 1 atm, and only at ultrahigh vacuum does the Ce-terminated (111) becomes the most stable one. The transition point for the Ce-terminated (111) surfaces moves to higher oxygen partial pressures when temperature increases. To improve the prediction of electron density of states, we used the local-density approximation plus U(J) correction method to correct the on-site Coulomb correlation and exchange interaction due to the strongly localized Ce-4f electrons. The optimal parameter combination of U = 7 eV and J = 0.7 eV was found to improve the O 2p-Ce 4f gap without much degradation of ground-state bulk properties or the O 2p-Ce 5d gap. The bulk and surface electronic structures were then analyzed based on the improved density of states.

First-principlesLDA+UandGGA+Ustudy of cerium oxides: Dependence on the effective U parameter

“…Other earlier theoretical work on bulk cerium dioxide which is not presented in the table is also available. 9,11,12,[41][42][43] In any case, most of these results, although obtained using different computational approaches, accurately predict the experimental lattice parameter and the experimental bulk 6 instead, the value was reproduced by us when using LDA. The structural data of CeO 2 in Table I seem to be only modestly influenced by the value of U eff chosen in the LDA+ U or GGA+ U calculations.…”

“…Table I displays the lattice parameter and bulk modulus B of CeO 2 taken from recent state-of-the-art DFT calculations. 3,4,6,7,13,20 The present a 0 and B values have been obtained from the corresponding energy minimization at constant volumes and by fitting a Birch-Murnaghan equation of state to the resulting energy-volume data, 39,40 respectively. Other earlier theoretical work on bulk cerium dioxide which is not presented in the table is also available.…”

“…4 Therefore, a more practically oriented approach consists in taking U eff as a sort of empirical parameter and fitting its value to reproduce certain experimental observables much in the same way as it has been done in molecular quantum chemistry for the so-called hybrid functionals 27 but avoiding the introduction of nonlocal exchange and its concomitant computational complications. Although some work in this direction has been published rather recently, i.e., the determination of U eff in an empirical way for CeO 2 with the PBE functional, 6 a more systematic study is needed. In particular, Ce 2 O 3 should also be included in the set of benchmarks when probing U eff , specially if one is interested in more problematic cases involving Ce͑III͒, such as defective ceria, ceria nanoparticles, and surface redox reactions.…”

“…The challenge arises when one aims at a unified treatment of both oxidation states as has been addressed recently by a number of theoretical studies of bulk ceria [3][4][5][6][7][8] and ͑defective͒ ceria surfaces. 6,[9][10][11][12][13][14] In principle, the computational description of the insulating CeO 2 within conventional density functional theory ͑DFT͒ is more or less straightforward due to the unoccupied Ce ͑4f͒ state. The band gap is still underestimated but this is a well-known deficiency of standard DFT, in particular in the description of transition metal oxides such as NiO.…”

Surface structure of coherently strained ceria ultrathin films

“…Theoretical [14][15][16][17][18] and experimental studies [19][20][21][22] show that there are differences in the activities of various low-index planes of ceria, which could impact their catalytic behaviors.…”