Appendix 3 Character Tables
The letters in the final column indicate the irreducible representations of vi-
brations (x,y, and zlabels) and rotations (Rx,Ry, and Rzlabels) for molecules
having that symmetry. Degeneracies are indicated by more than one label in
parentheses. More than one label but without parentheses indicates that de-
generacy will not necessarily exist (see, for example, the C2hpoint group).
C 1 E
A 1all
Cs(C1h) E (^) h
A 11 x,y,Rz,x^2 ,y^2 ,z^2 ,xy
A 1 1 z,Rx,Ry,yz,xz
Ci(S 2 ) Ei
Ag 11 Rx,Ry,Rz, all second-order functions
Au 1 1 x,y,z
C 2 EC 2
A 11 z,Rz,x^2 ,y^2 ,z^2 ,xy
B 1 1 x,y,Rx,Ry,yz,xz
C 3 EC 3 C^23 e^2 i/3
A 1 1 1 z,Rz,x^2 y^2 ,z^2
E (^11) (x,y)(Rx,Ry)(x^2 y^2 ,xy)(xz,yz)
C 4 EC 4 C 2 C^34
A 1 1 1 1 z,Rz,x^2 y^2 ,z^2
B 1 1 1 1 x^2 y^2 ,xy
E 11 ii 1 ^1 ii (x,y)(Rx,Ry)(xz,yz)
D 2 EC 2 C 2 C 2
A 1 1 1 1 x^2 ,y^2 ,z^2
B 1 1 1 1 1 z,Rz,xy
B 2 1 1 1 1 y,Ry,xz
B 3 1 1 11 x,Rx,yz
D 3 E 2 C 3 3 C 2
A 1 11 1 x^2 y^2 ,z^2
A 2 11 1 z,Rz
E 2 10 (x,y)(Rx,Ry)(x^2 y^2 ,xy), (xz,yz)
D 4 E 2 C 4 C 2 2 C 2 2 C 2
A 1 11 1 1 1 x^2 y^2 ,z^2
A 2 11 1 1 1 z,Rz
B 1 1 11 1 1 x^2 y^2
B 2 1 11 11 xy
E 20 20 0 (x,y)(Rx,Ry)(xz,yz)
Appendix 3 Character Tables 797