Grouptheoretical Analysis




Composition Input Structure


Atomic
Number
Atomic
Symbol
Isotope Isotope
Mass
Isotope
Abundance
Number
Atoms
Mass
6C1212.000098.9000672.0000
8O1615.994999.7620695.9695
74W184183.950930.67001183.9509
Total13 351.9204
Isotopomer Natural Abundance (%)28.2932


Determined Point Group: Oh








Representation ΓN


Characters of reducible representation
E 8C3 6C2 6C4 3C2 i 6S4 8S6 h d
13 1 1 5 5 1 1 1 9 5

Direct sum of irreducible representation
A1g A2g Eg T1g T2g A1u A2u Eu T1u T2u
3 0 2 0 0 0 0 0 2 0



Properties of derivatives and isotopomers by single substitution, h(Oh)=48
Atom Set*Site Symmetry**h(Site Symmetry)Identical Atoms***ElementChrialPolarIsotopomer
IsotopeMassAbundance****
1 Oh 481Wnono186W
182W
183W
180W
353.9239
349.9177
350.9197
347.9162
26.3836
24.2619
13.1918
0.1199
2 C4v 86Cnoyes13C352.92381.8881
3 C4v 86Onoyes18O
17O
353.9247
352.9246
0.3403
0.064662
Total Number of Atoms:13✅ Correct Number of Atoms found
*Atom Orbit
**Subgroup of point group Oh
***Calculated as h( Oh)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %


Numbers of isomers by substitution
ReplacementPatternAchiral
Isomers
Chiral
Isomer Pairs
SingleX30
DoubleX290
DoubleXY140
TripleX3210
TripleX2Y472
TripleXYZ788
QuadrupleX4392
QuadrupleX3Y10616
QuadrupleX2Y214532
QuadrupleX2YZ24274
QuadrupleWXYZ408176
QuintupleX5576
QuintupleVWXYZ1.9202.280
SextupleX67012
SextupleUVWXYZ7.56021.960

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 8C3 6C2 6C4 3C2 i 6S4 8S6 h d
39 0 -1 5 -5 -3 -1 0 9 5

Direct sum of irreducible representation
A1g A2g Eg T1g T2g A1u A2u Eu T1u T2u
2 0 2 2 2 0 0 0 5 2

Molecular motions and force field analysis



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