Category:Hybrid functionals: Difference between revisions
No edit summary |
No edit summary |
||
| Line 7: | Line 7: | ||
E_{\mathrm{xc}}^{\mathrm{hybrid}}=\alpha E_{\mathrm{x}}^{\mathrm{HF}} + (1-\alpha)E_{\mathrm{x}}^{\mathrm{GGA}} + E_{\mathrm{c}}^{\mathrm{GGA}} | E_{\mathrm{xc}}^{\mathrm{hybrid}}=\alpha E_{\mathrm{x}}^{\mathrm{HF}} + (1-\alpha)E_{\mathrm{x}}^{\mathrm{GGA}} + E_{\mathrm{c}}^{\mathrm{GGA}} | ||
</math> | </math> | ||
where <math>\alpha</math> determines the relative amount of HF and semilocal exchange. | where <math>\alpha</math> determines the relative amount of HF and semilocal exchange. The hybrid functionals can be divided into families according to the interelectronic range at which the HF exchange is applied: at full range (unscreened hybrids) or at either short or long range (called screened or range-separated hybrids). From the practical point of view the short-range hybrid functionals like HSE are preferable for periodic solids, since leading to faster convergence with respect to the number of k-points (or size of the unit cell). | ||
More detail about the formalism of the HF method and hybrids can be found [[Hybrid_functionals: formalism|here]]. | More detail about the formalism of the HF method and hybrids can be found [[Hybrid_functionals: formalism|here]]. | ||
Revision as of 12:10, 8 April 2022
Hybrid functionals, which mix the Hartree-Fock (HF) and Kohn-Sham theories[1], can be more accurate than semilocal methods like GGA, in particular for nonmetallic systems. They are suited for band gap calculations for instance. Hybrid functionals are available in VASP.
Theoretical background
In hybrid functionals the exchange part consists of a linear combination of HF and semilocal (e.g., GGA) exchange:
where determines the relative amount of HF and semilocal exchange. The hybrid functionals can be divided into families according to the interelectronic range at which the HF exchange is applied: at full range (unscreened hybrids) or at either short or long range (called screened or range-separated hybrids). From the practical point of view the short-range hybrid functionals like HSE are preferable for periodic solids, since leading to faster convergence with respect to the number of k-points (or size of the unit cell).
More detail about the formalism of the HF method and hybrids can be found here.
How to
List of available hybrid functionals and how to specify them in INCAR.
Downsampling of the Hartree-Fock operator.
Further reading
- A comprehensive study of the performance of the HSE03/HSE06 functional compared to the PBE and PBE0 functionals.[2]
- The B3LYP functional applied to solid state systems.[3]
- Applications of hybrid functionals to selected materials: Ceria,[4] lead chalcogenides,[5] CO adsorption on metals,[6][7] defects in ZnO,[8] excitonic properties,[9] SrTiO and BaTiO.[10]
References
- ↑ A. D. Becke, J. Chem. Phys. 98, 5648 (1993).
- ↑ J. Paier, M. Marsman, K. Hummer, G. Kresse, I.C. Gerber, and J.G. Ángyán, J. Chem. Phys. 124, 154709 (2006).
- ↑ J. Paier, M. Marsman, and G. Kresse, J. Chem. Phys. 127, 024103 (2007).
- ↑ J. L. F. Da Silva, M. V. Ganduglia-Pirovano, J. Sauer, V. Bayer, and G. Kresse, Phys. Rev. B 75, 045121 (2007).
- ↑ Hummer, A. Grüneis, and G. Kresse, Phys. Rev. B 75, 195211 (2007).
- ↑ A. Stroppa, K. Termentzidis, J. Paier, G. Kresse, and J. Hafner, Phys. Rev. B 76, 195440 (2007).
- ↑ A. Stroppa and G. Kresse, New Journal of Physics 10, 063020 (2008).
- ↑ F. Oba, A. Togo, I. Tanaka, J. Paier, and G. Kresse, Phys. Rev. B 77, 245202 (2008).
- ↑ J. Paier, M. Marsman, and G. Kresse, Phys. Rev. B 78, 121201(R) (2008).
- ↑ R. Wahl, D. Vogtenhuber, and G. Kresse, Phys. Rev. B 78, 104116 (2008).
Pages in category "Hybrid functionals"
The following 38 pages are in this category, out of 38 total.