Grouptheoretical Analysis




Composition Input Structure


Atomic
Number
Atomic
Symbol
Isotope Isotope
Mass
Isotope
Abundance
Number
Atoms
Mass
1H11.007899.984466.0470
6C1212.000098.9000672.0000
8O1615.994999.7620347.9847
Total15 126.0317
Isotopomer Natural Abundance (%)92.8254


Determined Point Group: C3h








Representation ΓN


Characters of reducible representation
E C3 (C3)2 σh S3 (S3)5
15 0 0 15 0 0

Direct sum of irreducible representation
A' E'* A'' E''*
5 5 0 0



Properties of derivatives and isotopomers by single substitution, h(C3h)=6
Atom Set*Site Symmetry**h(Site Symmetry)Identical Atoms***ElementChrialPolarIsotopomer
IsotopeMassAbundance****
1 Cs 23Cnoyes13C127.03503.0973
2 Cs 23Cnoyes13C127.03503.0973
3 Cs 23Onoyes18O
17O
128.0359
127.0359
0.5583
0.1061
4 Cs 23Hnoyes2H127.03800.043449
5 Cs 23Hnoyes2H127.03800.043449
Total Number of Atoms:15✅ Correct Number of Atoms found
*Atom Orbit
**Subgroup of point group C3h
***Calculated as h( C3h)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %


Numbers of isomers by substitution
ReplacementPatternAchiral
Isomers
Chiral
Isomer Pairs
SingleX50
DoubleX2350
DoubleXY700
TripleX31550
TripleX2Y4550
TripleXYZ9100
QuadrupleX44550
QuadrupleX3Y1.8200
QuadrupleX2Y22.7300
QuadrupleX2YZ5.4600
QuadrupleWXYZ10.9200
QuintupleX51.0010
QuintupleVWXYZ120.1200
SextupleX61.6750
SextupleUVWXYZ1.201.2000

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 C3 (C3)2 σh S3 (S3)5
45 0 0 15 0 0

Direct sum of irreducible representation
A' E'* A'' E''*
10 10 5 5

Molecular motions and force field analysis



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