1 Peter Deák [email protected]Challenges for ab initio defect modeling. EMRS Symposium I, 2008 Challenges for ab initio defect modeling Peter Deák, Bálint Aradi, and Thomas Frauenheim Bremen Center for Computational Materials Science, University of Bremen POB 330440, 28334 Bremen, Germany Adam Gali Dept. Atomic Physics, Budapest University of Technology & Economics H-1521 Budapest, Hungary
Challenges for ab initio defect modeling. Peter De ák , Bálint Aradi, and Thomas Frauenheim. Bremen Center for Computational Materials Science, University of Bremen POB 330440, 28334 Bremen, Germany. Adam Gali. Dept. Atomic Physics, Budapest University of Technology & Economics - PowerPoint PPT Presentation
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Challenges for ab initio defect modeling. EMRS Symposium I, 2008
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SiC:VSi
U. Gerstmann, P. Deák, et al. Physica B 340-342, 190 (2003).C.-O. Ambladh, U. von Barth, PRB 31, 3231 (1985)Using a correct asymptotic form of the exact exchange correlation potential it is shown that the eigenvalue of the uppermost occupied orbital equals the exact ionization potential of a finite system (atom, molecule, or a solid with a surface).
C.-O. Ambladh, U. von Barth, PRB 31, 3231 (1985)Using a correct asymptotic form of the exact exchange correlation potential it is shown that the eigenvalue of the uppermost occupied orbital equals the exact ionization potential of a finite system (atom, molecule, or a solid with a surface).
Popular misapprehensions1. GGA is always successful in describing the ground state of a system.2. Internal ionization energies (charge transition levels) of defects can
be calculated accurately as difference between total energies.
€
I = Egexptl + ED
+ − ED0
( ) − Eperf+ − Eperf
0( )[ ]
0
Total energies (w.o. gap error)
ASSUMPTIONSProblem of charged supercells can be handled by the Makov-Payne correction [PRB 51, 4014 (1995)].
Considering vertical transitions (no relaxation of ions) as in optical absorption experiments:
€
I = eC − eD = Eg − eD − eV( ) Kohn-Sham levels (w.gap error)
eD
eV
eC
Eg
The total energy is not affected by the “gap error”!The total energy is not affected by the “gap error”!
Challenges for ab initio defect modeling. EMRS Symposium I, 2008
Hybrid functionals as etalon1. M. Städele et al., PRB 59, 10031 (1999): “most of the gap error disappears when using exact exchange in DFT”.
eD-eV LDA G0W0 Hybrid
Si: HBC (0) +0.61 +1.05 +1.08
Si: HAB (-) -0.07 +0.10 +0.05
4H-SiC: HAB (-) +0.50 +0.62 +0.54
3C-SiC: BSi+2Ci (+) -0.12 +0.04 +0.10
3C-SiC: BSi+2Ci (-) +0.18 +0.26 +0.29
Defect levels
2. A. D. Becke, JCP 107, 8554 (1997): “mixing HF-exchange to DFT improves calculated molecular properties”3. J. Muscat et al, Chem. Phys. Lett. 342, 397 (2001): “in solids the gap improves as well”.
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LATTICE CONSTANT
BULK MODULUS
COHESIVE ENERGY
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BAND GAP
4. M. Marsman et al., J. Phys.: Condens. Matter. 20, 064201 (2008):
Challenges for ab initio defect modeling. EMRS Symposium I, 2008
An approximate correctionImplication of the previous examples: the error in energy differences between two configurations is related the error in the gap level position! Let us introduce a correction!
2. The error in EBE is not – as a rule – compensated in the expression of the total energy Etot !
3. Calculated energy differences between different charge states are not – as a rule – correct!
5. Total energy differences may be seriously wrong, for defects with different kinds of bonding configuration and levels in the gap. The ground state may not be predicted correctly!
At least checks with hybrid functionals are recommended!
6. There are catastrophe cases (e.g., TiO2:VO)!
4. If the bonding configuration does not change much, correction of the gap level in EBE is sufficient, but only then!