Mulliken Symbols

Symbols used to identify irreducible representations of Groups:

$A=$ singly degenerate state which is symmetric with respect to Rotation about the principal $C_n$ axis,

$B=$ singly Degenerate state which is antisymmetric with respect to Rotation about the principal $C_n$ axis,

$E=$ doubly Degenerate,

$T=$ triply Degenerate,

$X_g=$ (gerade, symmetric) the sign of the wavefunction does not change on Inversion through the center of the atom,

$X_u=$ (ungerade, antisymmetric) the sign of the wavefunction changes on Inversion through the center of the atom,

$X_1=$ (on $a$ or $b$) the sign of the wavefunction does not change upon Rotation about the center of the atom,

$X_2=$ (on $a$ or $b$) the sign of the wavefunction changes upon Rotation about the center of the atom,

' = symmetric with respect to a horizontal symmetry plane $\sigma_h$,

'' = antisymmetric with respect to a horizontal symmetry plane $\sigma_h$.

See also Group Theory