Computational Helium

By Alejandro Strachan1

1. Purdue University

This notebook solves the ground state for the helium atom computationally within the mean field approximation using four Gaussian functions as the basis set.

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Version 1.0 - published on 07 Jul 2017

doi:10.4231/D32R3NZ97 cite this

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Abstract

Summary. This notebook solves the ground state for the helium atom computationally within the mean field approximation using four Gaussian functions as the basis set. Assuming the two-electron wavefunction to be the product of two like orbitals, the two-particle Schrodinger equation reduces to single particle one but the effective Hamiltonian depends on the orbital one is trying to find (to describe electron-electron repulsion within mean field). This equation can be solved iteratively using self-consistent field (SCF) approach.
The initial part of the notebook go over the initial step in the SCF calculation starting from a guess wave function. All steps are described in detail. The second part performs the iterative SCF calculation until convergence is achieved.

Cite this work

Researchers should cite this work as follows:

  • Alejandro Strachan (2017), "Computational Helium," https://nanohub.org/resources/comphe. (DOI: 10.4231/D32R3NZ97).

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Submitter

Martin Hunt

Purdue University