# Configuration Interaction for the Helium Isoelectronic Series

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Configuration interaction (CI) provides a systematic method for improving on single-configuration Hartree–Fock (HF) computations [1, 2]. This Demonstration considers the two-electron atoms in the helium isoelectronic series. The HF wavefunction is the optimal product of one-electron orbitals approximating the ground-state configuration. An improved representation of the ground state can be obtained by a superposition containing excited electronic configurations, including , , , …, with relative contributions determined by the variational principle.

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Contributed by: S. M. Blinder (February 2018)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Snapshot 1: the single-configuration Hartree–Fock result

Snapshot 2: approximation to the -limit; a more accurate computation gives hartrees

Snapshot 3: result using optimized parameters; reaching is considered a milestone

References

[1] S. M. Blinder, "The Hartree–Fock Approximation," *Mathematical Physics in Theoretical Chemistry* (S. M. Blinder and J. E. House, eds.), Amsterdam: Elsevier, forthcoming.

[2] Wikipedia. "Configuration Interaction." (Feb 14, 2018) en.wikipedia.org/wiki/Configuration_interaction.

[3] H. Shull and P.-O. Löwdin, "Superposition of Configurations and Natural Spin Orbitals: Applications to the He Problem," *Journal of Chemical Physics*, 30(3), 1959 pp. 617–626. doi:10.1063/1.1730019.

## Permanent Citation