Grouptheoretical Analysis




Composition Input Structure


Atomic
Number
Atomic
Symbol
Isotope Isotope
Mass
Isotope
Abundance
Number
Atoms
Mass
1H11.007899.984455.0391
6C1212.000098.9000560.0000
Total10 65.0391
Isotopomer Natural Abundance (%)94.5459


Determined Point Group: D5h








Representation ΓN


Characters of reducible representation
E 2C5 2(C5)2 5C'2 σh 2S5 2(S5)3 v
10 0.000 0.000 2 10 0.000 0.000 2

Direct sum of irreducible representation
A'1 A'2 E'1 E'2 A''1 A''2 E''1 E''2
2 0 2 2 0 0 0 0



Properties of derivatives and isotopomers by single substitution, h(D5h)=20
Atom Set*Site Symmetry**h(Site Symmetry)Identical Atoms***ElementChrialPolarIsotopomer
IsotopeMassAbundance****
1 C2v 45Cnoyes13C66.04255.2579
2 C2v 45Hnoyes2H66.04540.073757
Total Number of Atoms:10✅ Correct Number of Atoms found
*Atom Orbit
**Subgroup of point group D5h
***Calculated as h( D5h)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %


Numbers of isomers by substitution
ReplacementPatternAchiral
Isomers
Chiral
Isomer Pairs
SingleX20
DoubleX270
DoubleXY100
TripleX3160
TripleX2Y400
TripleXYZ720
QuadrupleX4260
QuadrupleX3Y880
QuadrupleX2Y21360
QuadrupleX2YZ2560
QuadrupleWXYZ5040
QuintupleX5320
QuintupleVWXYZ3.0240
SextupleX6260
SextupleUVWXYZ15.1200

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 2C5 2(C5)2 5C'2 σh 2S5 2(S5)3 v
30 0.000 -0.000 -2 10 -0.000 -0.000 2

Direct sum of irreducible representation
A'1 A'2 E'1 E'2 A''1 A''2 E''1 E''2
2 2 4 4 0 2 2 2

Molecular motions and force field analysis



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