This page gives hints on how to calculate the effective Coulomb interaction with the ABINIT package.
LDA+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 [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) [Amadon2014].
For entangled bands (ucrpa= 2}), the scheme used in ABINIT [Shih2012], [Sakuma2013],[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 [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 [Cococcioni2005] treating full atomic orbitals. In particular, considerably higher effective values for U are found.
Related Input Variables¶
- ucrpa calculation of the screened interaction U with the Constrained RPA method
- ucrpa_bands For the calculation of U with the Constrained RPA method, gives correlated BANDS
- ucrpa_window For the calculation of U with the Constrained RPA method, gives energy WINDOW
Selected Input Files¶
- The lesson 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 [Aryasetiawan2004] using projected Wannier orbitals. Prerequisite: DFT+U.
- The lesson on the determination of U for DFT+U shows how to determine the U value with the linear response method [Cococcioni2005], to be used in the DFT+U approach. Prerequisite: DFT+U.