KERNEL TRUNCATION/LCOARSEN: Difference between revisions

Revision as of 10:22, 17 March 2026

KERNEL_TRUNCATION/LCOARSEN = .True. | .False.
Default: KERNEL_TRUNCATION/LCOARSEN = .True.

Description: Coarsen the charge density before padding to speed up the computation of the local potential in the Coulomb-kernel-truncation method.

The Coulomb-kernel-truncation method (KERNEL_TRUNCATION/LTRUNCATE) modifies the electrostatic potential to remove spurious interactions between periodic images in systems with reduced dimensionality (e.g. molecules or surfaces). KERNEL_TRUNCATION/LCOARSEN = T avoids significantly increasing FFT-grid sizes by using a coarsen-before-padding approach:

The full electrostatic potential is first computed under standard 3D periodic boundary conditions.
A coarse representation of the charge density with [math]\displaystyle{ 1/3 }[/math] of the FFT-grid size is constructed by retaining only the long-wavelength (low-|G|) components responsible for long-range interactions.
The truncated Coulomb kernel is applied only to this coarse density using a padded grid.
The final potential is obtained by subtracting the long-range periodic contribution and replacing it with the correctly truncated one.

This procedure exploits the fact that long-range electrostatics depends only on low-frequency components of the charge density, allowing the expensive padded FFTs to be performed on a much smaller grid with minimal loss of accuracy.

Mind: If KERNEL_TRUNCATION/LTRUNCATE = F, all other KERNEL_TRUNCATION tags including KERNEL_TRUNCATION/LCOARSEN are ignored.

@@ Line 1: / Line 1: @@
 {{TAGDEF|KERNEL_TRUNCATION/LCOARSEN| .True. {{!}} .False.|.True.}}
-Description: {{TAG|KERNEL_TRUNCATION/LCOARSEN}} speeds up computation of the local potential in the kernel truncation method by coarsening the charge density before padding it
+Description: Coarsen the charge density before padding to speed up the computation of the local potential in the Coulomb-kernel-truncation method.
 ----
+The Coulomb-kernel-truncation method ({{TAG|KERNEL_TRUNCATION/LTRUNCATE}}) modifies the electrostatic potential to remove spurious interactions between periodic images in systems with reduced dimensionality (e.g. molecules or surfaces).
+{{TAG|KERNEL_TRUNCATION/LCOARSEN|T}} avoids significantly increasing [[Energy cutoff and FFT meshes|FFT-grid sizes]] by using a ''coarsen-before-padding'' approach:
-Kernel truncation methods pad the computational cell with vacuum.
+* The full electrostatic potential is first computed under standard 3D periodic boundary conditions.
-This padded cell is expensive to compute due to FFTs being performed on a larger grid.
+* A coarse representation of the charge density with <math>1/3</math> of the [[Energy cutoff and FFT meshes|FFT-grid size]] is constructed by retaining only the long-wavelength (low-|G|) components responsible for long-range interactions.
-The {{TAG|KERNEL_TRUNCATION/LCOARSEN}} method selectively replaces the long range potential with the truncated potential instead of computing the entire potential on a padded grid.
+* The truncated Coulomb kernel is applied only to this coarse density using a padded grid.
-This selective replacement of the potential bypasses the need for padding, speeding up the computation of the kernel truncation methods.
+* The final potential is obtained by subtracting the long-range periodic contribution and replacing it with the correctly truncated one.
-{{NB|mind|IF {{TAG|KERNEL_TRUNCATION/LTRUNCATE}} is switched off, all other KERNEL_TRUNCATION tags, i.e. {{TAG|KERNEL_TRUNCATION/IDIMENSIONALITY}}, {{TAG|KERNEL_TRUNCATION/LCOARSEN}}, and {{TAG|KERNEL_TRUNCATION/ISURFACE}} will be ignored.}}
+This procedure exploits the fact that [[electrostatics |long-range electrostatics]] depends only on low-frequency components of the charge density, allowing the expensive padded FFTs to be performed on a much smaller grid with minimal loss of accuracy.
+{{NB|mind|If {{TAG|KERNEL_TRUNCATION/LTRUNCATE|F}}, all other KERNEL_TRUNCATION tags including {{TAG|KERNEL_TRUNCATION/LCOARSEN}} are ignored.}}
 == Related tags and articles ==
@@ Line 17: / Line 21: @@
 {{TAG|KERNEL_TRUNCATION/FACTOR}}
-[[Category:INCAR tag]][[Category:Electrostatics]]
+[[Category:INCAR tag]][[Category:Electrostatics]][[Category:2D materials]]