Grouptheoretical Analysis




Composition Input Structure


Atomic
Number		 Atomic
Symbol		 Isotope Isotope
Mass		 Isotope
Abundance		 Number
Atoms		 Mass
82Pb208207.976752.4000122495.7198
Total12 2495.7198
Isotopomer Natural Abundance (%)0.042852


Determined Point Group: Ih







Representation ΓN


Characters of reducible representation
E 12C5 12(C5)2 20C3 15C2 i 12S10 12(S10)3 20S6 15σd
12 2.000 2.000 0 0 0 0.000 0.000 0 4

Direct sum of irreducible representation
Ag T1g T2g Gg Hg Au T1u T2u Gu Hu
1 0 0 0 1 0 1 1 0 0



Properties of derivatives and isotopomers by single substitution, h(Ih)=120
Atom Set*Site Symmetry**h(Site Symmetry)Identical Atoms***ElementChrialPolarIsotopomer
IsotopeMassAbundance****
1 C5v 1012Pbnoyes206Pb
207Pb
204Pb		2493.7176
2494.7191
2491.7162		0.2365
0.2169
0.013739
Total Number of Atoms:12✅ Correct Number of Atoms found
*Atom Orbit
**Subgroup of point group Ih
***Calculated as h( Ih)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %


Numbers of isomers by substitution
ReplacementPatternAchiral
Isomers		Chiral
Isomer Pairs
SingleX10
DoubleX230
DoubleXY30
TripleX350
TripleX2Y72
TripleXYZ68
QuadrupleX482
QuadrupleX3Y1310
QuadrupleX2Y21720
QuadrupleX2YZ1542
QuadrupleWXYZ696
QuintupleX5102
QuintupleVWXYZ0792
SextupleX6126
SextupleUVWXYZ05.763

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 12C5 12(C5)2 20C3 15C2 i 12S10 12(S10)3 20S6 15σd
36 3.236 -1.236 0 0 0 0.000 -0.000 0 4

Direct sum of irreducible representation
Ag T1g T2g Gg Hg Au T1u T2u Gu Hu
1 1 0 1 2 0 2 1 1 1

Molecular motions and force field analysis


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