# DFT+U

This page gives hints on how to perform a DFT+U calculation with the ABINIT package.

## Introduction¶

This feature is available only in PAW. The DFT+U framework is described in [Anisimov1991] and [Liechtenstein1995]. In ABINIT, the DFT+U approximation is implemented inside the PAW atomic spheres only. Two choices of double counting are provided: the Full Localized limit and the Around Mean Field approximation. Our implementation is described in [Amadon2008a]. It follows the main lines of [Bengone2000]. See also [Czyzyk1994]. Forces and stress are implemented. For details on keywords (lpawu, upawu, jpawu, usedmatpu, dmatpuopt, dmatudiag) see keyword usepawu in input variables.

In both the output and log files, we can find:

• The DFT+U contribution of energy which is contained inside the PAW Spherical terms in the output file.

• The Decomposition of the LDA+U energy is given (Interaction energy, Double counting term, and sum of the two) in the log file.

• The orbital density matrix ($n_{m,m'}^{\sigma}$), also called occupation matrix (corresponding to Eq.(9) of [Bengone2000] and Eq.(1) of [Liechtenstein1995], see also [Amadon2008a] and variable dmatpuopt) is also given for each atom in the basis of real spherical harmonics. It is given at each SCF step in the log file: one can thus check the convergency of the calculation.

Consistency between total energy and forces in DFT+U have been checked.

The implementation of DFT+U in ABINIT allows also to impose a starting density matrix in order to compare the energy of various electronic configuration (see keywords usedmatpu and dmatpawu).

compulsory:

• jpawu value of J for PAW+U
• lpawu value of angular momentum L for PAW+U
• upawu value of U for PAW+U
• usepawu USE PAW+U (spherical part)

useful:

• dmatpawu initial Density MATrix for PAW+U
• usedmatpu USE of an initial Density MATrix in Paw+U

expert:

• atvshift ATomic potential (V) energy SHIFTs
• dmatpuopt Density MATrix for PAW+U OPTion
• dmatudiag Density MATrix for paw+U, DIAGonalization
• f4of2_sla F4 Over F2 ratio of Slater integrals
• f6of2_sla F6 Over F2 ratio of Slater integrals
• macro_uj MACRO variable that activates the determination of the U and J parameter (for the PAW+U calculations)
• natvshift Number of ATomic potential (V) energy SHIFTs (per atom)
• normpawu NORMalize atomic PAW+U projector
• pawujat PAW+macro_UJ, ATom number
• pawujv PAW+macro_UJ, potential shift (V)

internal:

• %natpawu Number of AToms on which PAW+U is applied

v5:

v7:

## Tutorials¶

• The lesson on DFT+U shows how to perform a DFT+U calculation using ABINIT, and will lead to compute the projected DOS of NiO. Prerequisite: PAW1.