关键词: Hartree Product, Hartree方程, 平均场近似, 3-21G基组, 自洽法

Abstract: Determining the wave function of multi-electron systems constitutes a fundamental aspect of quantum chemistry education. This study employs the Hartree method to calculate the ground-state electron orbitals and corresponding wave function of a helium atom as a representative example. Initially, we introduce the Hartree Product approximation for the multi-electron wave function based on the Schrödinger equation, subsequently deriving the Hartree equations for electron orbitals. The 3-21G basis set is then implemented, with basis set coefficients optimized through the linear variation method combined with self-consistent field calculations to obtain the electron orbitals. Corresponding computational programs are developed based on these derivations to enable students to compare theoretical formulations with practical implementations. This work aims to enhance students' comprehension of multi-electron wave function derivation, mean-field approximation within the Hartree framework, and self-consistent solution methodologies.

Key words: Hartree product, Hartree equation, Mean-field approximation, 3-21G basis set, Self-consistent method