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 input variables:
... 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 input variables:
... dmatpawu [initial Density MATrix for PAW+U]
... usedmatpu [USE of an initial Density MATrix in Paw+U]
Relevant internal variables:
... %natpawu [Number of AToms on which PAW+U is applied]
Input variables for experts:
... 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]
... pawujrad [PAW+macro_UJ, sphere RADius]
... pawujv [PAW+macro_UJ, potential shift (V)]
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tests/v5/Input: t08.in t14.in t15.in t16.in t19.in t20.in t33.in t37.in t38.in t39.in t40.in
tests/v7/Input: t21.in
t22.in
t44.in
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