Symbols used to identify irreducible representations of groups:

singly degenerate state which is symmetric
with respect to rotation about the principal axis,

singly degenerate
state which is antisymmetric with respect to rotation
about the principal
axis,

doubly degenerate,

triply degenerate,

(gerade, symmetric) the sign of the
wavefunction does not change on inversion
through the center of the atom,

(ungerade, antisymmetric) the sign
of the wavefunction changes on inversion through
the center of the atom,

(on or ) the sign of the wavefunction does not change upon rotation
about the center of the atom,

(on or ) the sign of the wavefunction changes upon rotation
about the center of the atom,

' = symmetric with respect to a horizontal symmetry plane ,

" = antisymmetric with respect to a horizontal symmetry plane .

## See also

Character Table,

Group
Theory,

Irreducible Representation
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## References

Cotton, F. A. *Chemical Applications of Group Theory, 3rd ed.* New York: Wiley, pp. 90-91, 1990.## Referenced
on Wolfram|Alpha

Mulliken Symbols
## Cite this as:

Weisstein, Eric W. "Mulliken Symbols."
From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/MullikenSymbols.html

## Subject classifications