# Libxc

MPL2 Libxc Developers Download Page Manual https://www.tddft.org/programs/libxc

Libxc is a library of exchange-correlation functionals for density-functional theory. The aim is to provide a portable, well tested and reliable set of exchange and correlation functionals that can be used by all the DFT codes.

## Description

In Libxc you can find different types of functionals: LDA, GGA, hybrids, and mGGA. These functionals depend on local information, in the sense that the value of the potential at a given point depends only on the values of the density – and the gradient of the density and the kinetic energy density, for the GGA and mGGA cases – at a given point:

$$E^{\rm LDA}_{\rm xc} = E^{\rm LDA}_{\rm xc}[n(\vec{r})]\,,$$

$$E^{\rm GGA}_{\rm xc} = E^{\rm GGA}_{\rm xc}[n(\vec{r}), \vec{\nabla}n(\vec{r})],,$$

$$E^{\rm Hyb}_{\rm xc} = a_x E^{\rm EXX} + E^{\rm GGA}_{\rm xc}[n(\vec{r}), \vec{\nabla}n(\vec{r})]\,,$$

$$E^{\rm mGGA}_{\rm xc} = E^{\rm mGGA}_{\rm xc}[n(\vec{r}), \vec{\nabla}n(\vec{r}), \nabla^2 n(\vec{r}), \tau(\vec{r})]\,.$$

It can calculate the functional itself and its derivative. Higher-order derivatives up to third-order are available for most functionals.

## Publications

The library is described in detail in the following papers:

• Susi Lehtola, Conrad Steigemann, Micael J.T. Oliveira, and Miguel A.L. Marques, Recent developments in Libxc - A comprehensive library of functionals for density functional theory, Software X 7, 1 (2018). DOI: 10.1016/j.softx.2017.11.002

• Miguel A. L. Marques, Micael J. T. Oliveira, and Tobias Burnus, Libxc: a library of exchange and correlation functionals for density functional theory, Comput. Phys. Commun. 183, 2272 (2012). DOI: 10.1016/j.cpc.2012.05.007