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Point Group Tables of D2d(-42m)

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Character Table of the group D2d(-42m) *
D2d(-42m)#12-42xmdfunctions
Mult.-11222
A1Γ111111x2+y2,z2
A2Γ2111-1-1Jz
B1Γ311-11-1x2-y2
B2Γ411-1-11z,xy
EΓ52-2000(x,y),(xz,yz),(Jx,Jy)



Subgroups of the group D2d(-42m)
SubgroupOrderIndex
D2d(-42m)81
S4(-4)42
C2v(mm2)42
D2(222)42
C2(2)24
Cs(m)24
C1(1)18

[ Subduction tables ]

Multiplication Table of irreducible representations of the group D2d(-42m)
D2d(-42m)A1A2B1B2E
A1A1A2B1B2E
A2A1B2B1E
B1A1A2E
B2A1E
EA1+A2+B1+B2

[ Note: the table is symmetric ]


Symmetrized Products of Irreps
D2d(-42m)A1A2B1B2E
[A1 x A1]1····
[A2 x A2]1····
[B1 x B1]1····
[B2 x B2]1····
[E x E]1·11·


Antisymmetrized Products of Irreps
D2d(-42m)A1A2B1B2E
{A1 x A1}·····
{A2 x A2}·····
{B1 x B1}·····
{B2 x B2}·····
{E x E}·1···


Irreps Decompositions
D2d(-42m)A1A2B1B2E
V···11
[V2]2·111
[V3]11·23
[V4]41223
A·1··1
[A2]2·111
[A3]·2113
[A4]41223
[V2]xV22135
[[V2]2]61334
{V2}·1··1
{A2}·1··1
{[V2]2}12224

V ≡ the vector representation
A ≡ the axial representation


IR Selection Rules
IRA1A2B1B2E
A1xx
A2xx
B1xx
B2xx
Exxxxx

[ Note: x means allowed ]


Raman Selection Rules
RamanA1A2B1B2E
A1xxxx
A2xxxx
B1xxxx
B2xxxx
Exxxxx

[ Note: x means allowed ]


Irreps Dimensions Irreps of the point group
Subduction of the rotation group D(L) to irreps of the group D2d(-42m)
L2L+1A1A2B1B2E
011····
13···11
251·111
3711·12
4921112
51111123
61321223
71522124
81732224
91922235
102132335



* 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.


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