Grouptheoretical Analysis




Composition Input Structure


Atomic
Number
Atomic
Symbol
Isotope Isotope
Mass
Isotope
Abundance
Number
Atoms
Mass
6C1212.000098.900016192.0000
16S3231.972194.99008255.7766
Total24 447.7766
Isotopomer Natural Abundance (%)55.5346


Determined Point Group: D8h








Representation ΓN


Characters of reducible representation
E 2C8 2C4 2(C8)3 C2 4C'2 4C''2 i 2(S8)3 2S4 2S8 σh v d
24 0.000 0 0.000 0 4 2 0 0.000 0 0.000 24 4 2

Direct sum of irreducible representation
A1g A2g B1g B2g E1g E2g E3g A1u A2u B1u B2u E1u E2u E3u
3 0 2 1 0 3 0 0 0 0 0 3 0 3



Properties of derivatives and isotopomers by single substitution, h(D8h)=32
Atom Set*Site Symmetry**h(Site Symmetry)Identical Atoms***ElementChrialPolarIsotopomer
IsotopeMassAbundance****
1 C2v 48Cnoyes13C448.77994.9414
2 C2v 48Cnoyes13C448.77994.9414
3 C2v 48Snoyes34S
33S
36S
449.7724
448.7760
451.7716
19.8776
3.5078
0.046771
Total Number of Atoms:24✅ Correct Number of Atoms found
*Atom Orbit
**Subgroup of point group D8h
***Calculated as h( D8h)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %


Numbers of isomers by substitution
ReplacementPatternAchiral
Isomers
Chiral
Isomer Pairs
SingleX30
DoubleX2250
DoubleXY380
TripleX31430
TripleX2Y3980
TripleXYZ7650
QuadrupleX47120
QuadrupleX3Y2.6930
QuadrupleX2Y24.0800
QuadrupleX2YZ8.0080
QuadrupleWXYZ15.9450
QuintupleX52.7390
QuintupleVWXYZ318.7800
SextupleX68.5810
SextupleUVWXYZ6.056.8200

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 2C8 2C4 2(C8)3 C2 4C'2 4C''2 i 2(S8)3 2S4 2S8 σh v d
72 0.000 0 -0.000 0 -4 -2 0 -0.000 0 0.000 24 4 2

Direct sum of irreducible representation
A1g A2g B1g B2g E1g E2g E3g A1u A2u B1u B2u E1u E2u E3u
3 3 3 3 3 6 3 0 3 1 2 6 3 6

Molecular motions and force field analysis



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