Grouptheoretical Analysis




Composition Input Structure


Atomic
Number		 Atomic
Symbol		 Isotope Isotope
Mass		 Isotope
Abundance		 Number
Atoms		 Mass
1H11.007899.98441010.0783
6C1212.000098.900010120.0000
26Fe5655.934991.7540155.9349
Total21 186.0132
Isotopomer Natural Abundance (%)82.0182


Determined Point Group: D5d







Representation ΓN


Characters of reducible representation
E 2C5 2(C5)2 5C'2 i 2(S10)3 2S10 5σd
21 1.000 1.000 1 1 1.000 1.000 5

Direct sum of irreducible representation
A1g A2g E1g E2g A1u A2u E1u E2u
3 0 2 2 0 2 2 2



Properties of derivatives and isotopomers by single substitution, h(D5d)=20
Atom Set*Site Symmetry**h(Site Symmetry)Identical Atoms***ElementChrialPolarIsotopomer
IsotopeMassAbundance****
1 D5d 201Fenono54Fe
57Fe
58Fe		184.0179
187.0136
188.0115		5.2248
1.8942
0.2521
2 Cs 210Cnoyes13C187.01659.1224
3 Cs 210Hnoyes2H187.01950.1280
Total Number of Atoms:21✅ Correct Number of Atoms found
*Atom Orbit
**Subgroup of point group D5d
***Calculated as h( D5d)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %


Numbers of isomers by substitution
ReplacementPatternAchiral
Isomers		Chiral
Isomer Pairs
SingleX30
DoubleX2108
DoubleXY1016
TripleX32656
TripleX2Y36184
TripleXYZ30384
QuadrupleX461280
QuadrupleX3Y901.152
QuadrupleX2Y21321.752
QuadrupleX2YZ1103.536
QuadrupleWXYZ607.152
QuintupleX5115972
QuintupleVWXYZ60122.064
SextupleX62002.644
SextupleUVWXYZ01.953.504

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 i 2(S10)3 2S10 5σd
63 1.618 -0.618 -1 -3 -1.618 0.618 5

Direct sum of irreducible representation
A1g A2g E1g E2g A1u A2u E1u E2u
4 2 6 6 2 5 7 6

Molecular motions and force field analysis


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