Grouptheoretical Analysis




Composition Input Structure


Atomic
Number
Atomic
Symbol
Isotope Isotope
Mass
Isotope
Abundance
Number
Atoms
Mass
1H11.007899.984499.0704
5B1111.009380.1000555.0465
Total14 64.1170
Isotopomer Natural Abundance (%)32.9270


Determined Point Group: C4v








Representation ΓN


Characters of reducible representation
E 2C4 C2 v d
14 2 2 6 4

Direct sum of irreducible representation
A1 A2 B1 B2 E
5 0 2 1 3



Properties of derivatives and isotopomers by single substitution, h(C4v)=8
Atom Set*Site Symmetry**h(Site Symmetry)Identical Atoms***ElementChrialPolarIsotopomer
IsotopeMassAbundance****
1 C4v 81Bnoyes10B63.12068.1804
2 C4v 81Hnoyes2H65.12320.005137
3 Cs 24Bnoyes10B63.120632.7215
4 Cs 24Hnoyes2H65.12320.020550
5 Cs 24Hnoyes2H65.12320.020550
Total Number of Atoms:14✅ Correct Number of Atoms found
*Atom Orbit
**Subgroup of point group C4v
***Calculated as h( C4v)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %


Numbers of isomers by substitution
ReplacementPatternAchiral
Isomers
Chiral
Isomer Pairs
SingleX50
DoubleX2155
DoubleXY2113
TripleX33430
TripleX2Y58109
TripleXYZ72237
QuadrupleX46198
QuadrupleX3Y122441
QuadrupleX2Y2154679
QuadrupleX2YZ1861.410
QuadrupleWXYZ1922.907
QuintupleX591210
QuintupleVWXYZ36029.850
SextupleX6115323
SextupleUVWXYZ360270.090

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 2C4 C2 v d
42 2 -2 6 4

Direct sum of irreducible representation
A1 A2 B1 B2 E
8 3 5 4 11

Molecular motions and force field analysis



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