mirror of https://github.com/abinit/abinit.git
52 lines
2.3 KiB
Markdown
52 lines
2.3 KiB
Markdown
---
|
|
description: How to calculate the effective Coulomb interaction
|
|
authors: BAmadon
|
|
---
|
|
<!--- This is the source file for this topics. Can be edited. -->
|
|
|
|
This page gives hints on how to calculate the effective Coulomb interaction with the ABINIT package.
|
|
|
|
## Introduction
|
|
|
|
DFT+U as well as DFT+DMFT requires as input values the effective Coulomb
|
|
interaction. Two ways to compute them are available in ABINIT.
|
|
|
|
Firstly, the constrained Random Phase Approximation [[cite:Aryasetiawan2004]]
|
|
[[ucrpa]] allows one to take into account the screening of the Coulomb
|
|
interaction between correlated electrons, by non-interacting electrons. For
|
|
non-entangled bands ([[ucrpa]]= 1), the bands excluded from the polarisability
|
|
can be specified either by a band index ([[ucrpa_bands]]) or an energy window
|
|
([[ucrpa_window]]) [[cite:Amadon2014]].
|
|
|
|
For entangled bands ([[ucrpa]]= 2}), the scheme used in ABINIT
|
|
[[cite:Shih2012]], [[cite:Sakuma2013]],[[cite:Amadon2014]] uses a band and
|
|
k-point dependent weight to define the polarisability, using Wannier orbitals
|
|
as correlated orbitals.
|
|
|
|
This method is well adapted to compute the effective interaction for the same
|
|
orbitals used in DFT+DMFT. To use the same orbitals as in DFT+U, the Wannier
|
|
functions can be ajusted such that the bare interaction is close to the bare
|
|
interaction of atomic orbitals as used in DFT+ _U_ (see tutorial).
|
|
|
|
Secondly, a linear response method [[cite:Cococcioni2005]] is implemented. The
|
|
implementation is not yet in production. The implementation in ABINIT takes
|
|
into account the truncated atomic orbitals from PAW and therefore differs from
|
|
the original work [[cite:Cococcioni2005]] treating full atomic orbitals. In
|
|
particular, considerably higher effective values for U are found.
|
|
|
|
|
|
|
|
## Related Input Variables
|
|
|
|
{{ related_variables }}
|
|
|
|
## Selected Input Files
|
|
|
|
{{ selected_input_files }}
|
|
|
|
## Tutorials
|
|
|
|
* The [[tutorial:ucalc_crpa|tutorial on the calculation of effective interactions U and J by the cRPA method]] shows how to determine the U value with the constrained Random Phase Approximation [[cite:Aryasetiawan2004]] using projected Wannier orbitals. Prerequisite: DFT+U.
|
|
* The [[tutorial:lruj|tutorial on the computation of U from linear response]] for DFT+U shows how to determine the U value with the linear response method [[cite:Cococcioni2005]], to be used in the DFT+U approach. Prerequisite: DFT+U.
|
|
|