Table 3 Comparison between different schemes for the determination of U.

From: Hubbard U through polaronic defect states

Defect

Uk

ULR

\({E}_{{{{\rm{f}}}}}^{{U}_{{{{\rm{k}}}}}}\)

\({E}_{{{{\rm{f}}}}}^{{U}_{{{{\rm{LR}}}}}}\)

\({E}_{{{{\rm{f}}}}}^{{\alpha }_{{{{\rm{k}}}}}}\)

BiVO4 (self-trapped)

3.5

5.4

−0.49

−1.34

−0.63

MgO (self-trapped)

7.7

10.9

−0.64

−1.67

−0.53

MgO (Li-trapped)

7.5

10.9

−2.01

−3.09

−1.82

α-SiO2 (Al-trapped)

8.3

10.1

−3.27

−4.00

−3.11

  1. Hubbard parameter Uk obtained with the scheme introduced in this work compared with the parameter ULR resulting from the linear-response method10, together with the corresponding defect formation energies. For reference, we also give the formation energies \({E}_{{{{\rm{f}}}}}^{{\alpha }_{{{{\rm{k}}}}}}\) obtained with the piecewise linear PBE0(αk) hybrid functional.
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