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# Slater-type orbital

Slater-type orbitals (STOs) are functions used as atomic orbitals in the linear combination of atomic orbitals molecular orbital method. They are named after the physicist John C. Slater, who introduced them in 1930[1].

### Additional recommended knowledge

STOs have the following radial part:

$R(r) = N r^{n-1} e^{-\zeta r}\,$

where

n is a natural number that plays the role of principal quantum number, n = 1,2,...,
N is a normalization constant,
r is the distance of the electron from the atomic nucleus, and
ζ is a constant related to the effective charge of the nucleus, the nuclear charge being partly shielded by electrons.

The normalization constant is computed from the integral

$\int_0^\infty x^n e^{-\alpha x} dx = \frac{n!}{\alpha^{n+1}}.$

Hence

$N^2 \int_0^\infty \left(r^{n-1}e^{-\zeta r}\right)^2 r^2 dr =1 \Longrightarrow N= (2\zeta)^n \sqrt{\frac{2\zeta}{(2n)!}}.$

It is common to use the real form of spherical harmonics depending on the polar coordinates θ and φ as the angular part of the Slater orbital.

## References

1. ^ J.C. Slater, Atomic Shielding Constants, Phys. Rev. vol. 36, p. 57 (1930)

## See also

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Slater-type_orbital". A list of authors is available in Wikipedia.
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