Grouptheoretical Analysis




Composition Input Structure


Atomic
Number
Atomic
Symbol
Isotope Isotope
Mass
Isotope
Abundance
Number
Atoms
Mass
1H11.007899.98441616.1252
6C1212.000098.900016192.0000
92U238238.050899.27451238.0508
Total33 446.1760
Isotopomer Natural Abundance (%)82.9649


Determined Point Group: D8h








Representation ΓN


Characters of reducible representation
E 2C8 2C4 2(C8)3 C2 4C'2 4C''2 i 2(S8)3 2S4 2S8 σh v d
33 1.000 1 1.000 1 1 1 1 1.000 1 1.000 1 9 1

Direct sum of irreducible representation
A1g A2g B1g B2g E1g E2g E3g A1u A2u B1u B2u E1u E2u E3u
3 0 2 0 2 2 2 0 2 0 2 2 2 2



Properties of derivatives and isotopomers by single substitution, h(D8h)=32
Atom Set*Site Symmetry**h(Site Symmetry)Identical Atoms***ElementChrialPolarIsotopomer
IsotopeMassAbundance****
1 D8h 321Unono235U
234U
443.1691
442.1662
0.6017
0.004596
2 Cs 216Cnoyes13C447.179314.7642
3 Cs 216Hnoyes2H447.18230.2071
Total Number of Atoms:33✅ Correct Number of Atoms found
*Atom Orbit
**Subgroup of point group D8h
***Calculated as h( D8h)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %


Numbers of isomers by substitution
ReplacementPatternAchiral
Isomers
Chiral
Isomer Pairs
SingleX30
DoubleX21812
DoubleXY1824
TripleX354148
TripleX2Y96468
TripleXYZ126960
QuadrupleX42021.212
QuadrupleX3Y3424.944
QuadrupleX2Y25287.476
QuadrupleX2YZ59415.048
QuadrupleWXYZ75630.312
QuintupleX54787.212
QuintupleVWXYZ3.780888.120
SextupleX61.25834.140
SextupleUVWXYZ15.12024.912.720

Further Reading

  • P.W. Fowler, J. Chem. Soc. Faraday Trans. 91(15) 2241 (1995)
    Isomer Counting using Point Group Symmetry




Representation Γ3N


Characters of reducible representation
E 2C8 2C4 2(C8)3 C2 4C'2 4C''2 i 2(S8)3 2S4 2S8 σh v d
99 2.414 1 -0.414 -1 -1 -1 -3 -2.414 -1 0.414 1 9 1

Direct sum of irreducible representation
A1g A2g B1g B2g E1g E2g E3g A1u A2u B1u B2u E1u E2u E3u
4 2 4 2 6 6 6 2 5 2 4 7 6 6

Molecular motions and force field analysis



Last update April, 29th 2022 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement