Accurate finite element method for atomic calculations based on density functional theory and Hartree-Fock method
An accurate finite element method is developed for atomic calculations based on density functional theory (DFT) within local density approximation (LDA) and Hartree-Fock (HF) method. The radial wave functions are expanded by cubic Hermite spline functions on a uniform mesh for x = root r, and all the associated integrals are analytically evaluated in conjunction with fitting procedures of the Hartree and the exchange-correlation 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/root Z bohr(1/2). the total energy for an atom of atomic number Z can be calculated within error of 10(-7) hartree for both the LDA and HF methods. The equal applicability of the method to OFT 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. (C) 2011 Elsevier B.V. All rights reserved.
finite element method atomic calculations density functional theory hartree-fock method