Solution of the Hartree - Fock Equations tor Atoms and Diatomic Moleeules with the Finite Element Method

(2) 8;<1>j(r); i = 1, ... ,N mentioned above. A review of the basis sets used in the quantum chemical calculations is given by Wilson [13]. The new developments are the two dimensional fully numerical finite difference method (FDM) [14] and the finite element method (FEM) [15]. It has been shown in both methods that the accuracy to calculate e.g., the total energy is many orders of magnitude better than in the old quantum mechanical method because both methods are basis set independent. With regard to the comparison ofthese two purely numerical methods the FEM seems to be even more stable and accurate than the FDM at least for the total energy. An overview of the finite difference method and a comparison with further numerical methods like the seminumerical partial wave method by McCullough [17] is given in Ref. [14]. Preliminary results for the solution ofthe HF equations with the FEM are given by Sundholm et al. in Ref. [15]. The papers published so far on the FEM from our group for the oneand twodimensional solution of the Hartree-Fock-Slater (HFS) and spin polarized HFS calculations are given in Ref. [16] and [18-21]. In Chapter 2 we are going to discuss in brief the HartreeFock problem for atoms and molecules as weIl as the FEM and computational approach. In Section 3 we discuss the results of the solution of the HF problem in a two dimensional way for the atoms Be, Ne and Ar as weIl as LiH, BH, N 2 and CO as examples for diatomic molecules.