# Exchange and correlation functionals

### This page gives hints on how to set parameters related to the exchange and correlation functionals with the ABINIT package.

##### Copyright (C) 2016-2017 ABINIT group (FJ)

Mentioned in help_features#2.2.

### Table of content:

- 1. Introduction.
- 2. Related lesson(s) of the tutorial.
- 3. Related input variables.
- 4. Selected input files.
- 5. References.

### 1. Introduction.

Total energy computation in ABINIT is done according to Density Functional Theory (DFT). Although formally exact, an approximate exchange-correlation (XC) functional must be chosen. This is governed by the input variable ixc.
However, the pseudopotentials (or PAW data sets) are constructed for one specific XC functional. If ixc is not specified, ABINIT will simply take the ixc of the given pseudopoential(s) - hoping they are coherent with each others. One introduces an error by using a pseudopotential generated with an XC functional that is not the same as the one explicitly specified by ixc. However, ABINIT will nevertheless do the calculation.

Many exchange-correlation functionals are available (see the list in the description of ixc), through two different implementations : one is the native ABINIT implementation, the other is the ETSF library of XC functionals (LibXC is a plug-in to ABINIT). In the native ABINIT set, most of the important local approximations (LDA) are available, including the Perdew-Zunger one. Two different local spin density (LSD) are available, including the Perdew Wang 92, and one due to M. Teter. The Perdew-Burke-Ernzerhof, the revPBE, the RPBE and the HCTH GGAs (spin unpolarized as well as polarized) are also available.
In the LibXC 2.0 library, as interfaced with ABINIT, there are 24 functional forms of the 3D LDA type, and over 80 functional forms of the GGA type. They can be used with norm-conserving pseudopotentials as well as PAW atomic data. Also, some metaGGA can be used with ABINIT (norm-conserving case only). For response-function type calculations, the native ABINIT LDA and GGA kernels can be used as well as the LibXC ones.

#### Hybrid functionals:

The exchange can also be computed on the basis of the Fock expression (exact exchange), and the correlation can be computed on the basis of the RPA approximation (see the GW section). Hybrid functionals calculations (HSE06, PBE0, B3LYP) can be performed. The implementation of the exact exchange, correlation and hybrid does not deliver the forces and stresses at present, at the exception of forces with norm-conserving pseudopotentials.

#### Local exact exchange:

When useexexch=1, the hybrid functional PBE0 is used in PAW, inside PAW spheres only, and only for correlated orbitals given by lexexch. To change the ratio of exact exchange, see also exchmix. The implementation of local exact exchange in ABINIT is provided in [Jollet2009]. See useful input variables exchmix, lexexch and useexexch.

#### Van der Waals functionals:

Several Van der Waals functionals are available : Grimme (D2, D3, D3(Becke-Johnson)), Silvestrelli.
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### 2. Related lesson(s) of the tutorial.

- The lesson_base2 deals with the H2 molecule: convergence studies, LDA versus GGA
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### 3. Related input variables.

Basic input variables:

... ixc [Index of eXchange-Correlation functional]

Useful input variables:

... exchmix [EXCHange MIXing]
... lexexch [value of angular momentum L for EXact EXCHange]
... useexexch [USE of EXact EXCHange]

Relevant internal variables:

... %xclevel [eXchange Correlation functional LEVEL]

Input variables for experts:

... densty [initial DENSity for each TYpe of atom]
... intxc [INTerpolation for eXchange-Correlation]
... optnlxccc [OPTion for the calculation of Non-Linear eXchange-Correlation Core Correction]
... usekden [USE Kinetic energy DENsity]
... xc_denpos [eXchange-Correlation - DENsity POSitivity value]
... xc_tb09_c [Value of the c parameter in the eXchange-Correlation TB09 functional]
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### 4. Selected input files.

WARNING : as of ABINITv8.6.x, the list of input files provided in the specific section of the topics Web pages is still to be reviewed/tuned. In some cases, it will be adequate, and in other cases, it might be incomplete, or perhaps even useless.
The user can find some related example input files in the ABINIT package in the directory /tests, or on the Web:

tests/v1/Input: t10.in t11.in t12.in t13.in t14.in t15.in t16.in t17.in t18.in t19.in t20.in t21.in t22.in t23.in t24.in t25.in t28.in t29.in t30.in

tests/v5/Input: t18.in
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### 5. References.

[Jollet2009] F. Jollet, G. Jomard, B. Amadon, J.P. Crocombette and D. Torumba, "Hybrid functional for correlated electrons in the projector augmented-wave formalism: Study of multiple minima for actinide oxides", Phys. Rev. B 80, 235109 (2009).

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