Slater orbitals

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.

They possess exponential decay at long range and Kato's cusp condition at short range (when combined as hydrogen-like atom functions, i.e. the analytical solutions of the stationary Schrödinger for one electron atoms). Unlike the hydrogen-like ("hydrogenic") Schrödinger orbitals, STOs have no radial nodes (neither do Gaussian-type orbitals).

STOs have the following radial part:

where

The normalization constant is computed from the integral

Hence

It is common to use the spherical harmonics ${\displaystyle Y_{l}^{m}(\mathbf {r} )}$ depending on the polar coordinates of the position vector ${\displaystyle \mathbf {r} }$ as the angular part of the Slater orbital.

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