Category:Hybrid functionals: Difference between revisions

Revision as of 14:57, 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:

{\displaystyle E_{\mathrm{xc}}^{\mathrm{hybrid}}=\alpha E_{\mathrm{x}}^{\mathrm{HF}} + (1-\alpha)E_{\mathrm{x}}^{\mathrm{GGA}} + E_{\mathrm{c}}^{\mathrm{GGA}} }

where $\alpha$ 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 either at short or at 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).

It is important to note that hybrid functionals are computationally more expensive than semilocal methods.

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.

References

Pages in category "Hybrid functionals"

The following 38 pages are in this category, out of 38 total.

[becke:jcp:93-1] A. D. Becke, J. Chem. Phys. 98, 5648 (1993).

[paier:jcp:06-2] J. Paier, M. Marsman, K. Hummer, G. Kresse, I.C. Gerber, and J.G. Ángyán, J. Chem. Phys. 124, 154709 (2006).

[paier:jcp:07-3] J. Paier, M. Marsman, and G. Kresse, J. Chem. Phys. 127, 024103 (2007).

[juarez:prb:07-4] J. L. F. Da Silva, M. V. Ganduglia-Pirovano, J. Sauer, V. Bayer, and G. Kresse, Phys. Rev. B 75, 045121 (2007).

[hummer:prb:07-5] Hummer, A. Grüneis, and G. Kresse, Phys. Rev. B 75, 195211 (2007).

[stroppa:prb:07-6] A. Stroppa, K. Termentzidis, J. Paier, G. Kresse, and J. Hafner, Phys. Rev. B 76, 195440 (2007).

[stroppa:njp:08-7] A. Stroppa and G. Kresse, New Journal of Physics 10, 063020 (2008).

[oba:prb:08-8] F. Oba, A. Togo, I. Tanaka, J. Paier, and G. Kresse, Phys. Rev. B 77, 245202 (2008).

[paier:prb:08-9] J. Paier, M. Marsman, and G. Kresse, Phys. Rev. B 78, 121201(R) (2008).

[wahl:prb:08-10] R. Wahl, D. Vogtenhuber, and G. Kresse, Phys. Rev. B 78, 104116 (2008).

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 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 either at short or at 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).
-It is important to note that hybrid functionals are computationally more expensive than semilocal methods. More detail about the formalism of the HF method and hybrids can be found [[Hybrid_functionals: formalism|here]].
+It is important to note that hybrid functionals are computationally more expensive than semilocal methods.
+More detail about the formalism of the HF method and hybrids can be found [[Hybrid_functionals: formalism|here]].
 == How to ==