LTBOUNDLIBXC: Difference between revisions

Latest revision as of 07:10, 12 June 2024

LTBOUNDLIBXC = .TRUE. | .FALSE.
Default: LTBOUNDLIBXC = .FALSE.

Description: LTBOUNDLIBXC specifies whether or not the lower bound for the Kohn-Sham kinetic-energy density $\tau_{\sigma}$ ( $\tau_{\sigma}^{\textrm{W}}<\tau_{\sigma}$ ) is enforced before $\tau_{\sigma}$ is used in a METAGGA functional from Libxc.

The Kohn-Sham kinetic-energy density

\tau_{\sigma}=\frac{1}{2}\sum_{i}\nabla\psi_{i\sigma}^{*}\cdot\nabla\psi_{i\sigma}

should, in principle, be larger than the von Weizsäcker kinetic-energy density^[1]

\tau_{\sigma}^{\textrm{W}}=\frac{\left\vert\nabla n_{\sigma}\right\vert^{2}}{8 n_{\sigma}}.

However, for numerical reasons this may not always be the case and can potentially lead to problems depending on the meta-GGA. If LTBOUNDLIBXC=.TRUE. in INCAR, then $\tau_{\sigma}=\max(\tau_{\sigma},\tau_{\sigma}^{\mathrm{W}})$ is applied before $\tau_{\sigma}$ is used in a meta-GGA functional from Libxc.

However, according to tests, for some of the most common meta-GGA functionals like SCAN^[2], a violation of the lower bound is technically not a problem and, furthermore, applying $\tau_{\sigma}=\max(\tau_{\sigma},\tau_{\sigma}^{\mathrm{W}})$ leads to very inaccurate forces and stress tensor. Therefore, by default LTBOUNDLIBXC=.FALSE. and Libxc should be compiled with the option --disable-fhc has explained here.

References

[kurth:ijqc:1999-1] S. Kurth, J. P. Perdew, and P. Blaha, Molecular and solid-state tests of density functional approximations: LSD, GGAs, and meta-GGAs, Int. J. Quantum Chem 75, 889 (1999).

[sun:prl:15-2] J. Sun, A. Ruzsinszky, and J. P. Perdew, Phys. Rev. Lett. 115, 036402 (2015).

[1]

[2]

@@ Line 1: / Line 1: @@
 {{TAGDEF|LTBOUNDLIBXC|.TRUE. {{!}} .FALSE. |.FALSE.}}
-Description: {{TAG|LTBOUNDLIBXC}} specifies whether or not the lower bound for the Kohn-Sham kinetic-energy density <math>\tau_{\sigma}</math> (<math>\tau_{\sigma}^{\textrm{W}}<\tau_{\sigma}</math>) is enforced before <math>\tau_{\sigma}</math> is used in a meta-GGA functional from Libxc.
+Description: {{TAG|LTBOUNDLIBXC}} specifies whether or not the lower bound for the Kohn-Sham kinetic-energy density <math>\tau_{\sigma}</math> (<math>\tau_{\sigma}^{\textrm{W}}<\tau_{\sigma}</math>) is enforced before <math>\tau_{\sigma}</math> is used in a {{TAG|METAGGA}} functional from Libxc.
 ----
-The KS kinetic-energy density <math>\tau_{\sigma}</math> should in principle be larger than the von Weizsäcker kinetic-energy density <math>\tau_{\sigma}^{\textrm{W}}=\left\vert\nabla\rho_{\sigma}\right\vert^{2}/\left(8\rho_{\sigma}\right)</math>. However, for numerical reasons this may not always be the case and can potentially lead to problems depending on the meta-GGA. If {{TAG|LTBOUNDLIBXC}}=.TRUE. in {{FILE|INCAR}}, then <math>\tau_{\sigma}=\max(\tau_{\sigma},\tau_{\sigma}^{\mathrm{W}})</math> is applied before <math>\tau_{\sigma}</math> is used in a meta-GGA functional from Libxc.
+The Kohn-Sham kinetic-energy density
+:<math>\tau_{\sigma}=\frac{1}{2}\sum_{i}\nabla\psi_{i\sigma}^{*}\cdot\nabla\psi_{i\sigma}</math>
+should, in principle, be larger than the von Weizsäcker kinetic-energy density{{cite|kurth:ijqc:1999}}
+:<math>\tau_{\sigma}^{\textrm{W}}=\frac{\left\vert\nabla n_{\sigma}\right\vert^{2}}{8 n_{\sigma}}.</math>
+However, for numerical reasons this may not always be the case and can potentially lead to problems depending on the meta-GGA. If {{TAG|LTBOUNDLIBXC}}=.TRUE. in {{FILE|INCAR}}, then <math>\tau_{\sigma}=\max(\tau_{\sigma},\tau_{\sigma}^{\mathrm{W}})</math> is applied before <math>\tau_{\sigma}</math> is used in a meta-GGA functional from Libxc.
 However, according to tests, for some of the most common meta-GGA functionals like SCAN{{cite|sun:prl:15}}, a violation of the lower bound is technically not a problem and, furthermore, applying <math>\tau_{\sigma}=\max(\tau_{\sigma},\tau_{\sigma}^{\mathrm{W}})</math> leads to very inaccurate forces and stress tensor. Therefore, by default {{TAG|LTBOUNDLIBXC}}=.FALSE. and Libxc should be compiled  with the option <code>--disable-fhc</code> has explained [[Makefile.include#Libxc_.28optional.29|here]].
-== Related Tags and Sections ==
+== Related tags and articles ==
 {{TAG|LIBXC1}},
 {{TAG|LIBXC2}},
@@ Line 21: / Line 26: @@
 ----
-[[Category:INCAR]][[Category:Exchange-correlation functionals]][[Category:meta-GGA]]
+[[Category:INCAR tag]][[Category:Exchange-correlation functionals]][[Category:meta-GGA]]