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| description | authors |
|---|---|
| How to calculate the effective Coulomb interaction | BAmadon |
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
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Selected Input Files
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Tutorials
- The tutorial:ucalc_crpa 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 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.