LTHOMAS: Difference between revisions

Latest revision as of 11:51, 9 February 2026

LTHOMAS = .TRUE. | .FALSE.
Default: LTHOMAS = .FALSE.

Description: LTHOMAS selects a decomposition of the exchange functional based on Thomas-Fermi exponential screening.

If LTHOMAS=.TRUE. the decomposition of the exchange operator (in a range-separated hybrid functional) into a short range (SR) and a long range (LR) part will be based on Thomas-Fermi exponential screening:

[math]\displaystyle{ E_{\mathrm{xc}}^{\mathrm{hybrid}}=a_{\mathrm{SR}} E_{\mathrm{x,SR}}^{\mathrm{HF}}(\mu) + (1-a_{\mathrm{SR}})E_{\mathrm{x,SR}}^{\mathrm{SL}}(\mu) + E_{\mathrm{x,LR}}^{\mathrm{SL}}(\mu) + E_{\mathrm{c}}^{\mathrm{SL}} }[/math]

The mixing [math]\displaystyle{ a_{\mathrm{SR}} }[/math] and screening [math]\displaystyle{ \mu=k_{\rm TF} }[/math] are controlled by the AEXX and HFSCREEN tags, respectively.

For typical semiconductors, a Thomas-Fermi screening length [math]\displaystyle{ k_{\rm TF} }[/math] of about 1.8 Å^-1 yields reasonable band gaps. In principle, however, the Thomas-Fermi screening length depends on the valence-electron density. VASP determines [math]\displaystyle{ k_{\rm TF} }[/math] from the number of valence electrons (read from the POTCAR file) and the volume (leading to an average density [math]\displaystyle{ \bar{n} }[/math]) and writes the corresponding value of [math]\displaystyle{ k_{\rm TF}=\sqrt{4\bar{k}_{\rm F}/\pi} }[/math], where [math]\displaystyle{ \bar{k}_{\rm F}=(3\pi^2\bar{n})^{1/3} }[/math] to the OUTCAR file (note that this value is only printed for information and is not used during the calculation):

 Thomas-Fermi vector in A             =   2.00000

The setting of the sX-LDA functional is shown on the page listing the hybrid functionals.

Mind:

If LTHOMAS=.TRUE., then LHFCALC=.TRUE. is automatically set.
If LTHOMAS=.TRUE., then AEXX=1 is automatically set, but AEXX can be set to another value.

Important: When AEXX=1 (the default for LTHOMAS=.TRUE.), the correlation [math]\displaystyle{ E_{\mathrm{c}}^{\mathrm{SL}} }[/math] is not included. However, it can be included by setting ALDAC=1.0 and AGGAC=1.0.

Since VASP counts the semi-core states and d-states as valence electrons, although these states do not contribute to the screening, the values reported by VASP are often not recommended.

Another important detail concerns the implementation of the local LDA part in VASP. Literature [see Eqs. (3.10), (3.14), and (3.15) in Ref. ^[1]] suggests to use in the enhancement factor [math]\displaystyle{ F(z) }[/math] a position-independent variable [math]\displaystyle{ z=k_{\rm TF}/\bar{k}_{\rm F} }[/math] where [math]\displaystyle{ \bar{k}_{\rm F} }[/math] is as defined above but using the average density [math]\displaystyle{ \bar{n} }[/math] in the unit cell. However, implemented in VASP is a position-dependent variable [math]\displaystyle{ z({\bf r})=k_{\rm TF}/k_{\rm F}({\bf r}) }[/math], where [math]\displaystyle{ k_{\rm F}({\bf r})=(3\pi^2 n({\bf r}))^{1/3} }[/math] is the Fermi wave vector calculated with the local density [math]\displaystyle{ n({\bf r}) }[/math], while the constant [math]\displaystyle{ k_{\rm TF} }[/math] is set by HFSCREEN.

@@ Line 3: / Line 3: @@
 Description: {{TAG|LTHOMAS}} selects a decomposition of the exchange functional based on Thomas-Fermi exponential screening.
 ----
-If {{TAG|LTHOMAS}}=.TRUE. the decomposition of the exchange operator (in a [[Hybrid functionals: formalism|range-separated hybrid functional]]) into a short range and a long range part will be based on Thomas-Fermi exponential screening.
+If {{TAG|LTHOMAS}}=.TRUE. the decomposition of the exchange operator (in a [[Hybrid functionals: formalism|range-separated hybrid functional]]) into a short range (SR) and a long range (LR) part will be based on Thomas-Fermi exponential screening:
-The Thomas-Fermi screening length ''k''<sub>TF</sub> is specified by means of the {{TAG|HFSCREEN}} tag.
+:<math>E_{\mathrm{xc}}^{\mathrm{hybrid}}=a_{\mathrm{SR}} E_{\mathrm{x,SR}}^{\mathrm{HF}}(\mu) + (1-a_{\mathrm{SR}})E_{\mathrm{x,SR}}^{\mathrm{SL}}(\mu) + E_{\mathrm{x,LR}}^{\mathrm{SL}}(\mu) + E_{\mathrm{c}}^{\mathrm{SL}}</math>
+The mixing <math>a_{\mathrm{SR}}</math> and screening <math>\mu=k_{\rm TF}</math> are controlled by the {{TAG|AEXX}} and {{TAG|HFSCREEN}} tags, respectively.
 For typical semiconductors, a Thomas-Fermi screening length <math>k_{\rm TF}</math> of about 1.8 &Aring;<sup>-1</sup> yields reasonable band gaps. In principle, however, the Thomas-Fermi screening length depends on the valence-electron density. VASP determines <math>k_{\rm TF}</math> from the number of valence electrons (read from the {{FILE|POTCAR}} file) and the volume (leading to an average density <math>\bar{n}</math>) and writes the corresponding value of <math>k_{\rm TF}=\sqrt{4\bar{k}_{\rm F}/\pi}</math>, where <math>\bar{k}_{\rm F}=(3\pi^2\bar{n})^{1/3}</math> to the {{FILE|OUTCAR}} file ('''note that this value is only printed for information and is not used during the calculation'''):
@@ Line 17: / Line 20: @@
 Another important detail concerns the implementation of the local LDA part in VASP. Literature [see Eqs. (3.10), (3.14), and (3.15) in Ref. {{cite|seidl:prb:96}}] suggests to use in the enhancement factor <math>F(z)</math> a position-independent variable <math>z=k_{\rm TF}/\bar{k}_{\rm F}</math> where <math>\bar{k}_{\rm F}</math> is as defined above but using the average density <math>\bar{n}</math> in the unit cell.
-However, implemented in VASP is a position-dependent variable <math>z({\bf r})=k_{\rm TF}/k_{\rm F}({\bf r})</math>, where <math>k_{\rm F}({\bf r})=(3\pi^2 n({\bf r}))^{1/3}</math> is the Fermi wave vector calculated with the local density <math>n({\bf r})</math>.
+However, implemented in VASP is a position-dependent variable <math>z({\bf r})=k_{\rm TF}/k_{\rm F}({\bf r})</math>, where <math>k_{\rm F}({\bf r})=(3\pi^2 n({\bf r}))^{1/3}</math> is the Fermi wave vector calculated with the local density <math>n({\bf r})</math>, while the constant <math>k_{\rm TF}</math> is set by {{TAG|HFSCREEN}}.
 == Related tags and articles ==