Table 3. Optimized Potential IP10b (Defined in Equation 5) for CeO2 Combined with Parameters for Modeling Hole (O1–) and Electron (Ce3+) Polaronsa.
| (a) Short-Range Potential | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Interaction | A (eV) | ρ (Å) | C6(eV Å6) | E(eV Å12) | D (eV) | a (Å–1) | r0 (Å) | c0 (eV) | rmin (Å) | rmax (Å) |
| O2––Ce4+ | 1138.963021 | 0.417578 | 25.082349 | 1.0 | –1.15172262 | 0.4 | 4.53327 | –1.077767 | 0 | 5.278 |
| O2––Ce3+ | 1025.066719 | 0.417578 | 25.082349 | 1.0 | –1.036550358 | 0.4 | 4.53327 | –0.9249903 | 0 | 5.532 |
| O1––Ce4+ | 706.157073 | 0.417578 | 25.082349 | 1.0 | –0.714068 | 0.4 | 4.53327 | –0.7462155 | 0 | 5.278 |
| O2––O2– | 22764.3 | 0.149 | 20.983768 | 1.0 | 0 | 15.0 | ||||
| O1––O2– | 22764.3 | 0.149 | 20.983768 | 1.0 | 0 | 15.0 | ||||
| O1––O1– | 22764.3 | 0.149 | 20.983768 | 1.0 | 0 | 15.0 | ||||
| Ce4+–Ce4+ | 1.0 | 0.1 | 30.481293 | 1.0 | 0 | 15.0 | ||||
| Ce3+–Ce4+ | 1.0 | 0.1 | 30.481293 | 1.0 | 0 | 15.0 | ||||
| Ce3+–Ce3+ | 1.0 | 0.1 | 30.481293 | 1.0 | 0 | 15.0 | ||||
| (b) Shell Model | ||
|---|---|---|
| Species | Y (e) | k2(eV Å–2) |
| Ce4+ shell | 13.85 | 1071.1845 |
| Ce3+ shell | 12.85 | 1071.1845 |
| O2– shell | –2.936345 | 53.022513 |
| O1– shell | –1.936345 | 53.022513 |
a
Short-range potentials were designed only for shell–shell interactions. A GULP-readable format is also provided in Section S3 of the Supporting Information.