Grouptheoretical Analysis




Composition Input Structure


Atomic
Number
Atomic
Symbol
Isotope Isotope
Mass
Isotope
Abundance
Number
Atoms
Mass
1H11.007899.98441212.0939
6C1212.000098.900012144.0000
24Cr5251.940583.7890151.9405
Total25 208.0344
Isotopomer Natural Abundance (%)73.2368


Determined Point Group: D6d








Representation ΓN


Characters of reducible representation
E 2S12 2C6 2S4 2C3 2(S12)5 C2 6C'2 d
25 1.000 1 1 1 1.000 1 1 5

Direct sum of irreducible representation
A1 A2 B1 B2 E1 E2 E3 E4 E5
3 0 0 2 2 2 2 2 2



Properties of derivatives and isotopomers by single substitution, h(D6d)=24
Atom Set*Site Symmetry**h(Site Symmetry)Identical Atoms***ElementChrialPolarIsotopomer
IsotopeMassAbundance****
1 D6d 241Crnono53Cr
50Cr
54Cr
209.0345
206.0399
210.0328
8.3045
3.7978
2.0672
2 Cs 212Cnoyes13C209.03789.7748
3 Cs 212Hnoyes2H209.04070.1371
Total Number of Atoms:25✅ 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
SingleX30
DoubleX21011
DoubleXY1020
TripleX33085
TripleX2Y40271
TripleXYZ30560
QuadrupleX476509
QuadrupleX3Y1102.054
QuadrupleX2Y21603.121
QuadrupleX2YZ1306.260
QuadrupleWXYZ6012.620
QuintupleX51642.151
QuintupleVWXYZ60265.620
SextupleX63107.291
SextupleUVWXYZ05.313.000

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
75 0.732 2 -1 0 -2.732 -1 -1 5

Direct sum of irreducible representation
A1 A2 B1 B2 E1 E2 E3 E4 E5
4 2 2 5 7 6 6 6 6

Molecular motions and force field analysis



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