Grouptheoretical Analysis




Composition Input Structure


Atomic
Number
Atomic
Symbol
Isotope Isotope
Mass
Isotope
Abundance
Number
Atoms
Mass
9F1918.9984100.0000475.9936
54Xe132131.904226.90001131.9042
Total5 207.8978
Isotopomer Natural Abundance (%)26.9000


Determined Point Group: D4h








Representation ΓN


Characters of reducible representation
E 2C4 C2 2C'2 2C''2 i 2S4 σh v d
5 1 1 3 1 1 1 5 3 1

Direct sum of irreducible representation
A1g A2g B1g B2g Eg A1u A2u B1u B2u Eu
2 0 1 0 0 0 0 0 0 1



Properties of derivatives and isotopomers by single substitution, h(D4h)=16
Atom Set*Site Symmetry**h(Site Symmetry)Identical Atoms***ElementChrialPolarIsotopomer
IsotopeMassAbundance****
1 D4h 161Xenono129Xe
131Xe
134Xe
136Xe
130Xe
128Xe
124Xe
126Xe
204.8984
206.8987
209.8990
211.9008
205.8971
203.8971
199.8995
201.8979
26.4000
21.2000
10.4000
8.9000
4.1000
1.9100
0.100000
0.090000
2 C2v 44Fnoyes---
Total Number of Atoms:5✅ Correct Number of Atoms found
*Atom Orbit
**Subgroup of point group D4h
***Calculated as h( D4h)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %


Numbers of isomers by substitution
ReplacementPatternAchiral
Isomers
Chiral
Isomer Pairs
SingleX20
DoubleX230
DoubleXY40
TripleX330
TripleX2Y60
TripleXYZ90
QuadrupleX420
QuadrupleX3Y40
QuadrupleX2Y260
QuadrupleX2YZ90
QuadrupleWXYZ150
QuintupleX510
QuintupleVWXYZ150
SextupleX600
SextupleUVWXYZ00

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 2C'2 2C''2 i 2S4 σh v d
15 1 -1 -3 -1 -3 -1 5 3 1

Direct sum of irreducible representation
A1g A2g B1g B2g Eg A1u A2u B1u B2u Eu
1 1 1 1 1 0 2 0 1 3

Molecular motions and force field analysis



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