Coulomb singularity: Difference between revisions

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These mostly involve modifying the Coulomb Kernel in a way that yields the same result as the unmodified kernel in the limit of large supercell sizes.
These mostly involve modifying the Coulomb Kernel in a way that yields the same result as the unmodified kernel in the limit of large supercell sizes.


=== Truncation method ===
=== Truncation methods ===
 
In the truncation method
 
 
=== Auxiliary function methods ===

Revision as of 09:15, 10 May 2022

In the unscreened HF exchange, the bare Coulomb operator

is singular in the reciprocal space at :

To alleviate this issue and to improve the convergence of the exact exchange with respect to the supercell size (or the k-point mesh density) different methods have been proposed: the auxiliary function methods[1], probe-charge Ewald [2] (HFALPHA), and Coulomb truncation methods[3] (HFRCUT). These mostly involve modifying the Coulomb Kernel in a way that yields the same result as the unmodified kernel in the limit of large supercell sizes.

Truncation methods

In the truncation method


Auxiliary function methods