Table 5. Comparison of Zone-Center Fundamental IR and Raman Phonon Frequencies ω (cm–1), as Well as IR Intensities I (km/mol) of Rutile-TiO2, Obtained Using PBEsol and PBE Functionals, in Conjunction with the PAW Potentials Ti_std, Ti_pv, and Ti_sv Centered on Tiabcdef.
| symmetryf | exptg | expth,i | PBEsol |
PBE |
||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Ti_std | Ti_pv | Ti_sv | Ti_std | Ti_pv | Ti_sv | |||||||||
| ω | I | Ω | I | ω | I | ω | I | ω | I | ω | I | |||
| B2g(R) | 825.5 | 826 (826.6) | 810.2 | 0.0 | 795.3 | 0.0 | 793.1 | 0.0 | 783.6 | 0.0 | 770.3 | 0.0 | 769.3 | 0.0 |
| A1g(R) | 609.8 | 612 (610.4) | 605.8 | 0.0 | 591.0 | 0.0 | 589.8 | 0.0 | 580.9 | 0.0 | 568.4 | 0.0 | 568.0 | 0.0 |
| Eu(IR) | 500 (494.0) | 495.3 | 20.7 | 476.9 | 13.4 | 478.4 | 13.2 | 481.8 | 15.3 | 467.8 | 10.5 | 468.9 | 10.3 | |
| Eu(IR) | 500 (494.0) | 495.3 | 20.7 | 476.9 | 13.4 | 478.3 | 13.2 | 481.8 | 15.3 | 467.8 | 10.5 | 468.9 | 10.3 | |
| Eg(R) | 445.8 | 447 (444.9) | 459.6 | 0.0 | 448.0 | 0.0 | 447.1 | 0.0 | 440.6 | 0.0 | 430.0 | 0.0 | 429.6 | 0.0 |
| Eg(R) | 445.8 | 447 (444.9) | 459.6 | 0.0 | 448.0 | 0.0 | 447.1 | 0.0 | 440.6 | 0.0 | 430.0 | 0.0 | 429.6 | 0.0 |
| A2g (S) | 405.5 | 0.0 | 413.6 | 0.0 | 415.1 | 0.0 | 407.7 | 0.0 | 414.8 | 0.0 | 416.4 | 0.0 | ||
| B1u(S) | (406.3) | 395.8 | 0.0 | 372.5 | 0.0 | 373.9 | 0.0 | 369.7 | 0.0 | 354.3 | 0.0 | 357.1 | 0.0 | |
| Eu(IR) | 388 (374.4) | 375.0 | 9.7 | 366.4 | 4.0 | 366.9 | 3.7 | 356.9 | 3.2 | 353.9 | 1.0 | 355.1 | 0.9 | |
| Eu(IR) | 388 (374.7) | 375.0 | 9.7 | 366.4 | 4.0 | 366.9 | 3.7 | 356.9 | 3.2 | 353.9 | 1.0 | 355.0 | 0.9 | |
| A2u(IR) | 167 (188.8) | 180.5 | 179.2 | 61.2 | 168.0 | 71.2 | 165.3 | 99.6 | 184.2 | 106.1i | 171.5 | 98.8i | 168.3 | |
| Eu(IR) | 235.5 | 183 (172.7) | 158.7 | 105.2 | 93.0 | 110.1 | 98.4 | 108.5 | 95.4 | 115.5 | 62.8 i | 114.1 | 54.3i | 111.5 |
| Eu(IR) | 235.5 | 183 (172.7) | 158.7 | 105.2 | 93.0 | 110.1 | 98.2 | 108.4 | 95.4 | 115.5 | 62.8 i | 114.1 | 54.5i | 111.7 |
| B1g(R) | 140.2 | 143 (141.6) | 134.2 | 0.0 | 139.7 | 0.0 | 140.5 | 0.0 | 143.9 | 0.0 | 148.5 | 0.0 | 149.0 | 0.0 |
| B1u(S) | (113.0) | 118.3 | 0.0 | 74.9 | 0.0 | 78.3 | 0.0 | 84.8 | 0.0 | 30.1i | 0.0 | 16.7i | 0.0 | |
| A2u(IR) | 0.0 | 13.7 | 0.1 | 8.5 | 0.4 | 8.2 | 0.0 | 8.9 | 0.1 | 8.3 | 0.6 | 9.0 | ||
| Eu(IR) | 0.0 | 9.1 | 0.1 | 8.5 | 0.3 | 8.3 | 0.0 | 8.9 | 0.1 | 8.3 | 0.4 | 11.6 | ||
| Eu(IR) | 0.0 | 9.1 | 0.1 | 13.0 | 0.2 | 12.6 | 0.1 | 14.2 | 0.1 | 13.2 | 0.4 | 10.1 | ||
Experimental frequencies are included wherever available, and an energy cutoff of 700 eV was used.
Negative value in columns 12 and 14 represent imaginary frequency.
Schöche et al.25 reported the four room-temperature IR-active phonon modes (three degenerate Eu and one non-degenerate A2u) to be 188.6 ± 1.2, 379.3 ± 0.2, 500.5 ± 0.3, and 172.3 ± 1.9 cm–1, respectively.
Gervais and Piriou85 reported the four IR-active phonon modes (three degenerate Eu and one non-degenerate A2u) at 189, 381.5, 508, and 172 cm–1, respectively.
Eagles reported the four IR-active phonon modes (three degenerate Eu and one non-degenerate A2u) at 183, 388, 500, and 167 cm–1, respectively.86
R, IR, and S correspond to Raman- and IR-active and silent modes, respectively.
Ref (83).
Ref (82).
Values in parentheses represent coherent inelastic neutron determination of phonon frequencies at high-symmetry points of Brillouin zone.81