Hartree-Fock calculation for two-electron atoms

(Project 1 of PHYS382)

Cheung Ngo Yin

03702570

Date of submission: Oct 20, 2005

Introduction

        The well analysis-tic of the atom was Hydrogen, but there are not simple as hydrogen if there are multi-electrons involved and others corrections are introduced to the system. At least hydrogen-like model is a way of  approximations for numerically approach to the real situations. 

        One of the method to simplify the multi-electron model and used to found the upper bound of the ground state energy is Hartree-Fock approximation.

        In the program, the self-consistent field approximation ( Hartree-Fock ) was used for solving the two-electron system.  In general, the multi-electron system Hamiltonian involved the correction due to electronic repulsion term, J-S, J-J coupling corrections, relativistic correction etc, but the written program was considering the interaction between electrons and up to two-electron system only.  The two-electron system in the program is 1s electron, which has spherical symmetry property.

        In the program, the following two atom system, helium He and hydrogen H were studied and used Hartree-Fock approximation to estimate the corresponding upper bound of the ground state energy for different situation in different electronic configurations , 1s¹ and 1s².

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