Construction of the potential

Just like the charge density the effective potential is also represented in a region-dependent way as

$$\begin{equation} \renewcommand{\vec}[1]{\mathbf{#1}} V_\text{eff}(\vec{r})=\left\lbrace \begin{array}{l l l} \sum\limits_{\vec{G}} V_{\vec{G}}^\text{eff} e^{i\vec{G}\vec{r}} & \text{for } \vec{r} \in \text{IR} \\ \sum\limits_{L} V_L^{\text{eff},\alpha}(r_\alpha) Y_L(\vec{\hat{r}_\alpha}) & \text{for } \vec{r} \in \text{MT}^\alpha\\ \sum\limits_{\vec{G}_\parallel} V_{\vec{G}_\parallel}^{\text{eff},\text{vac}}(z) e^{i\vec{G}_\parallel \vec{r}_\parallel} & \text{for } \vec{r} \in \text{VR}^\text{vac} \\ \end{array} \right.. \end{equation}$$

As a sum of the Hartree potential, the external potential, and the exchange-correlation potential it is given by

$$\begin{equation} \renewcommand{\vec}[1]{\mathbf{#1}} V_\text{eff}(\vec{r}) = V_\text{H}(\vec{r}) + V_\text{ext}(\vec{r}) + V_\text{xc}(\vec{r}) \end{equation}$$

The construction of the Hartree potential together with the external potential involves neither approximations nor special input parameters. It is therefore neglected in this discussion. For details on this part of the calculation see M. Weinert, Solution of Poisson's equation: Beyond Ewaldtype methods, JMP 22, 2433 (1981).

The exchange-correlation potential

There are some user-specified parameters that control the construction of the XC part of the potential.

First the construction of the XC potential in the interstitial region has its own reduced reciprocal cutoff parameter calculationSetup/cutoffs/@GmaxXC. It has to comply with the constraint

$$\begin{equation} G_\text{max} \ge G_\text{max}^\text{XC} \ge 2\cdot K_\text{max}. \end{equation}$$

Next the type of XC functional is specified in xcFunctional/@name. See the reference on the Fleur input file for a list of available options.

Finally the user can choose to enable relativistic corrections according to A.H. MacDonnald and S.H. Vosko, A relativistic density functional formalism, JPhysC: Solid State Physics 12, 2977 (1979) with the logical switch xcFunctional/@relativisticCorrections.