# Simplified Hartree-Fock Computations on Second-Row Atoms

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Modern computational quantum chemistry has developed largely from applications of the Hartree–Fock method to atoms and molecules [1–3]. A simple representation of a many-electron atom is given by a Slater determinant constructed from occupied spin-orbitals:

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Contributed by: S. M. Blinder (October 2017)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Following are the optimized values of the energies and orbital parameters, found using the built-in Mathematica function FindMinimum:

Z = 2, {-2.84766, {α 1.6875}} Z = 3, {-7.42617, {α 2.69716, β 0.721027}} Z = 4, {-14.5413, {α 3.71867, β 1.10264}} Z = 5, {-24.4442, {α 4.72562, β 1.50386, γ 1.2137}} Z = 6, {-37.4687, {α 5.72987, β 1.90153, γ 1.53991}} Z = 7, {-53.9194, {α 6.73255, β 2.29803, γ 1.86317}} Z = 8, {-74.1007, {α 7.73422, β 2.69406, γ 2.18487}} Z = 9, {-98.3167, {α 8.73521, β 3.08988, γ 2.50566}} Z = 10, {-126.872, {α 9.73572, β 3.48558, γ 2.82585}}

These can be slightly improved by hand.

References

[1] S. M. Blinder, *Introduction to Quantum Mechanics*, Amsterdam: Elsevier, 2004 section 9.7.

[2] A. Szabo and N. S. Ostlund, *Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory,* Mineola, NY: Dover, 1996.

[3] S. M. Blinder, "Introduction to the Hartree–Fock Method," in *Mathematical Physics in Theoretical Chemistry* (S. M. Blinder and J. E. House, eds.), Elsevier, 2018, in press.

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