Finite element method (FEM) calculation

A highly accurate finite element method (FEM) [20] is available for all electron calculations within LDA by Vosko, Wilk, and Nusair [2] and the Hartree-Fock scheme. In the calculations, spherical charge distribution and sherical potential are assumed for the Schrödinger equation. The FEM calculation is not supported for the Dirac equation. The following keywords are especially relevant for the FEM calculation:

calc.type
ALLFEM (FEMLDA) and FEMHF are available for the all electron LDA and HF calculations using the finite element method (FEM) [11], respectively. Note that due to a technical reason during development, two specifications, ALLFEM and FEMLDA are equivalent to each other.

grid.xmax
In the FEM calculation, the grid is generated at regular intervals on a coordinate $x$, where the relation between the radial coordinate $r$ and $x$ is given by $r=x^2$. The keyword, grid.xmax, specifies the upper bound of $x$ in this case. Note that the definition of $x$ is different from the conventional calculations in ADPACK. The lower bound of $x$ is always set to zero.

The roles of the other keywords are same as in the conventional calculations. Also, the database for all electron calculation performed by the FEM scheme can be found at http://www.openmx-square.org/miscellaneous.html. The database provides calculation results and input files used for the calculations. In the database, it is estimated based on the virial theorem [21] that the absolute error in the total energy is less than nano-Hartree and micro-Hartree for the LDA and HF calculations of all elements in the periodic table, respectively.