Accurate finite element method for atomic calculations based on density functional theory and HartreeFock method
An accurate finite element method is developed for atomic calculations based on density functional theory (DFT) within local density approximation (LDA) and HartreeFock (HF) method. The radial wave functions are expanded by cubic Hermite spline functions on a uniform mesh for x = r , and all the associated integrals are analytically evaluated in conjunction with fitting procedures of the Hartree and the exchangecorrelation potentials to the same cubic Hermite spline functions using a set of recurrence formulas. The total energy of atoms systematically converges from above, and the error algebraically decays as the mesh spacing decreases. When the mesh spacing d  is taken to be 0.025 / Z bohr 1 / 2 , the total energy for an atom of atomic number Z  can be calculated within error of 10?7 10 ? 7 hartree for both the LDA and HF methods. The equal applicability of the method to DFT and the HF method with a similar degree of high accuracy enables the method to be a reliable platform for development of new functionals in DFT such as hybrid functionals.
finite element method atomic calculations density functional theory hartreefock method