Bilbao Crystallographic Server bcs Point Group Tables Help

Point Group Tables of C4h(4/m)

Click here to get more detailed information on the symmetry operations

Character Table of the group C4h(4/m) *
C4h(4/m)#124+4--1m-4+-4-functions
AgΓ1+11111111x2+y2,z2,Jz
BgΓ2+11-1-111-1-1xy,x2-y2
1Eg
2Eg
Γ4+
Γ3+
1
1
-1
-1
-1j
1j
1j
-1j
1
1
-1
-1
-1j
1j
1j
-1j
(xz,yz),(Jx,Jy)
AuΓ1-1111-1-1-1-1z
BuΓ2-11-1-1-1-111
1Eu
2Eu
Γ4-
Γ3-
1
1
-1
-1
-1j
1j
1j
-1j
-1
-1
1
1
1j
-1j
-1j
1j
(x,y)



Subgroups of the group C4h(4/m)
SubgroupOrderIndex
C4h(4/m)81
C4(4)42
S4(-4)42
C2h(2/m)42
C2(2)24
Cs(m)24
Ci(-1)24
C1(1)18

[ Subduction tables ]

Multiplication Table of irreducible representations of the group C4h(4/m)
C4h(4/m)AgAuBgBu1Eg1Eu2Eg2Eu
AgAgAuBgBu1Eg1Eu2Eg2Eu
AuAgBuBg1Eu1Eg2Eu2Eg
BgAgAu2Eg2Eu1Eg1Eu
BuAg2Eu2Eg1Eu1Eg
1EgBgBuAgAu
1EuBgAuAg
2EgBgBu
2EuBg

[ Note: the table is symmetric ]


Symmetrized Products of Irreps
C4h(4/m)AgAuBgBu1Eg1Eu2Eg2Eu
[Ag x Ag]1·······
[Au x Au]1·······
[Bg x Bg]1·······
[Bu x Bu]1·······
[1Eg x 1Eg]··1·····
[1Eu x 1Eu]··1·····
[2Eg x 2Eg]··1·····
[2Eu x 2Eu]··1·····


Antisymmetrized Products of Irreps
C4h(4/m)AgAuBgBu1Eg1Eu2Eg2Eu
{Ag x Ag}········
{Au x Au}········
{Bg x Bg}········
{Bu x Bu}········
{1Eg x 1Eg}········
{1Eu x 1Eu}········
{2Eg x 2Eg}········
{2Eu x 2Eu}········


Irreps Decompositions
C4h(4/m)AgAuBgBu1Eg1Eu2Eg2Eu
V·1···1·1
[V2]2·2·1·1·
[V3]·2·2·3·3
[V4]5·4·3·3·
A1···1·1·
[A2]2·2·1·1·
[A3]2·2·3·3·
[A4]5·4·3·3·
[V2]xV·4·4·5·5
[[V2]2]7·6·4·4·
{V2}1···1·1·
{A2}1···1·1·
{[V2]2}3·4·4·4·

V ≡ the vector representation
A ≡ the axial representation


IR Selection Rules
IRAgAuBgBu1Eg1Eu2Eg2Eu
Agxxx
Auxxx
Bgxxx
Buxxx
1Egxxx
1Euxxx
2Egxxx
2Euxxx

[ Note: x means allowed ]


Raman Selection Rules
RamanAgAuBgBu1Eg1Eu2Eg2Eu
Agxxxx
Auxxxx
Bgxxxx
Buxxxx
1Egxxxx
1Euxxxx
2Egxxxx
2Euxxxx

[ Note: x means allowed ]


Irreps Dimensions Irreps of the point group
Subduction of the rotation group D(L) to irreps of the group C4h(4/m)
L2L+1AgAuBgBu1Eg1Eu2Eg2Eu
011·······
13·1···1·1
251·2·1·1·
37·1·2·2·2
493·2·2·2·
511·3·2·3·3
6133·4·3·3·
715·3·4·4·4
8175·4·4·4·
919·5·4·5·5
10215·6·5·5·



* George F. Koster, John O. Dimmock, Robert G. Wheeler, Hermann Statz (1963). Properties of the thirty-two point groups. Published by the M.I.T. press, Cambridge, Massachusetts.
* Simon L. Altmann and Peter Herzig (1994). Point-Group Theory Tables. Oxford Science Publications.


Bilbao Crystallographic Server
http://www.cryst.ehu.es
For comments, please mail to
cryst@wm.lc.ehu.es