The zero-order approximation for a multielectron atom ignores the
electron–electron repulsion, so that each electron occupies a
hydrogen-like spin orbital.
The electronic wave function for a multielectron atom must be
antisymmetric. That is, the wave function must change sign if the
coordinates of two electrons are exchanged.
In an antisymmetrized orbital wave function, every electron must occupy
a different spin orbital (the Pauli exclusion principle).
In the Russell–Saunders approximation, the total orbital angular
momentum and the total spin angular momentum of a multielectron atom
can have predictable values that follow the same pattern as other angular
momenta.
