Grouptheoretical Analysis




Composition Input Structure


Atomic
Number		 Atomic
Symbol		 Isotope Isotope
Mass		 Isotope
Abundance		 Number
Atoms		 Mass
1H11.007899.98441212.0939
8O1615.994999.7620695.9695
12Mg2423.985078.9900123.9850
Total19 132.0484
Isotopomer Natural Abundance (%)77.7231


Determined Point Group: Th







Representation ΓN


Characters of reducible representation
E 4C3 4(C3)2 3C2 i 4(S6)5 4S6 3σh
19 1 1 3 1 1 1 9

Direct sum of irreducible representation
Ag Eg* Tg Au Eu* Tu
3 2 1 0 0 3



Properties of derivatives and isotopomers by single substitution, h(Th)=24
Atom Set*Site Symmetry**h(Site Symmetry)Identical Atoms***ElementChrialPolarIsotopomer
IsotopeMassAbundance****
1 Th 241Mgnono26Mg
25Mg		134.0460
133.0492		10.8334
9.8396
2 C2v 46Onoyes18O
17O		134.0527
133.0526		0.9349
0.1776
3 Cs 212Hnoyes2H133.05470.1455
Total Number of Atoms:19✅ 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
SingleX30
DoubleX2113
DoubleXY186
TripleX33329
TripleX2Y7587
TripleXYZ126180
QuadrupleX482129
QuadrupleX3Y216546
QuadrupleX2Y2290837
QuadrupleX2YZ4681.710
QuadrupleWXYZ7563.498
QuintupleX5162415
QuintupleVWXYZ3.78056.250
SextupleX62801.013
SextupleUVWXYZ15.120806.400

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 3σh
57 0 0 -3 -3 0 0 9

Direct sum of irreducible representation
Ag Eg* Tg Au Eu* Tu
3 3 6 1 1 9

Molecular motions and force field analysis


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