Grouptheoretical Analysis




Composition Input Structure


Atomic
Number
Atomic
Symbol
Isotope Isotope
Mass
Isotope
Abundance
Number
Atoms
Mass
6C1212.000098.900060720.0000
35Br7978.918350.6900241894.0401
Total84 2614.0401
Isotopomer Natural Abundance (%)0.00000426


Determined Point Group: Th








Representation ΓN


Characters of reducible representation
E 4C3 4(C3)2 3C2 i 4(S6)5 4S6 h
84 0 0 0 0 0 0 4

Direct sum of irreducible representation
Ag Eg* Tg Au Eu* Tu
4 4 10 3 3 11



Properties of derivatives and isotopomers by single substitution, h(Th)=24
Atom Set*Site Symmetry**h(Site Symmetry)Identical Atoms***ElementChrialPolarIsotopomer
IsotopeMassAbundance****
1 C1 124Cyesyes13C2615.04350.00000114
2 C1 124Cyesyes13C2615.04350.00000114
3 Cs 212Cnoyes13C2615.04350.00000057
4 C1 124Bryesyes81Br2616.03810.00009957
Total Number of Atoms:84✅ Correct Number of Atoms found
*Atom Orbit
**Subgroup of point group Th
***Calculated as h( Th)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %


Numbers of isomers by substitution
ReplacementPatternAchiral
Isomers
Chiral
Isomer Pairs
SingleX13
DoubleX215143
DoubleXY3289
TripleX3413.959
TripleX2Y4311.889
TripleXYZ623.818
QuadrupleX432780.340
QuadrupleX3Y121321.523
QuadrupleX2Y2655482.263
QuadrupleX2YZ123964.689
QuadrupleWXYZ61.929.498
QuintupleX58201.285.924
QuintupleVWXYZ0154.360.080
SextupleX64.61616.935.984
SextupleUVWXYZ012.194.446.320

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 4C3 4(C3)2 3C2 i 4(S6)5 4S6 h
252 0 0 0 0 0 0 4

Direct sum of irreducible representation
Ag Eg* Tg Au Eu* Tu
11 11 31 10 10 32

Molecular motions and force field analysis



Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement