Grouptheoretical Analysis




Composition Input Structure


Atomic
Number
Atomic
Symbol
Isotope Isotope
Mass
Isotope
Abundance
Number
Atoms
Mass
6C1212.000098.900072864.0000
Total72 864.0000
Isotopomer Natural Abundance (%)45.0955


Determined Point Group: D6d








Representation ΓN


Characters of reducible representation
E 2S12 2C6 2S4 2C3 2(S12)5 C2 6C'2 d
72 0.000 0 0 0 0.000 0 0 4

Direct sum of irreducible representation
A1 A2 B1 B2 E1 E2 E3 E4 E5
4 2 2 4 6 6 6 6 6



Properties of derivatives and isotopomers by single substitution, h(D6d)=24
Atom Set*Site Symmetry**h(Site Symmetry)Identical Atoms***ElementChrialPolarIsotopomer
IsotopeMassAbundance****
1 Cs 212Cnoyes13C865.00346.0188
2 Cs 212Cnoyes13C865.00346.0188
3 C1 124Cyesyes13C865.003412.0376
4 C1 124Cyesyes13C865.003412.0376
Total Number of Atoms:72✅ Correct Number of Atoms found
*Atom Orbit
**Subgroup of point group D6d
***Calculated as h( D6d)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %


Numbers of isomers by substitution
ReplacementPatternAchiral
Isomers
Chiral
Isomer Pairs
SingleX22
DoubleX220107
DoubleXY6210
TripleX3702.452
TripleX2Y747.418
TripleXYZ1214.904
QuadrupleX438642.857
QuadrupleX3Y206171.362
QuadrupleX2Y2768257.181
QuadrupleX2YZ210514.290
QuadrupleWXYZ121.028.784
QuintupleX51.190582.386
QuintupleVWXYZ069.957.720
SextupleX64.6926.509.715
SextupleUVWXYZ04.687.167.240

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 2S12 2C6 2S4 2C3 2(S12)5 C2 6C'2 d
216 0.000 0 0 0 -0.000 0 0 4

Direct sum of irreducible representation
A1 A2 B1 B2 E1 E2 E3 E4 E5
10 8 8 10 18 18 18 18 18

Molecular motions and force field analysis



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