Determining the optimal modeling parameters for maximum precise calculations of energy in BCC-iron

The ab initial modeling of the equilibrium structure and properties of BCC-iron is performed in the new version (11.1) of WIEN2k software package. A full-potential method of linear joined plane waves LAPW is used for the calculations, taking into account the generalized gradient approximation PBE-GGA, in supercell consisted of $54$ iron atoms with periodic boundary conditions. This is the most accurate method used in the framework of density functional theory. Integration into the reciprocal space and calculation of electron density is held in accordance with the Monkhorst–Pack scheme with a grid of $N_k$ points in the Brillouin zone. The criterion for the convergence in all the calculations is to achieve the accuracy of the calculation of the total energy of the system, charge and force of interaction between two atoms of not less than $10^{-4}$Ry, $10^{-3}e$ and $1$ mRy/a.u. respectively.
The optimal values of the basic simulation parameters of carbon impurities in the BCC-iron are determined. They allow calculating the energy performance of the system with an accuracy of not less than $0,01$ eV. These parameters compile $N_k = 64$ points, $K_{\mathrm{max}} = 5$ a.u.$^{-1}$. It is shown that the use of the simulation parameters obtained in previous versions of WIEN2k leads to the error in determining the carbon dissolving power in BCC-iron at $0,07$ eV.
The calculation of energy of dissolution of carbon atoms in the ferromagnetic phase of BCC-iron is conducted using the obtained simulation parameters. It amounts to $0,85\pm0,01$ eV, which is a good fit to the experimental results and other first-principle calculations.