Grouptheoretical Analysis




Composition Input Structure


Atomic
Number
Atomic
Symbol
Isotope Isotope
Mass
Isotope
Abundance
Number
Atoms
Mass
1H11.007899.98444242.3287
6C1212.000098.900042504.0000
7N1414.003199.634028392.0861
8O1615.994999.762014223.9288
Total126 1162.3435
Isotopomer Natural Abundance (%)54.4907


Determined Point Group: D7h








Representation ΓN


Characters of reducible representation
E 2C7 2(C7)2 2(C7)3 7C'2 σh 2S7 2(S7)5 2(S7)3 v
126 0.000 0.000 0.000 0 28 0.000 0.000 0.000 10

Direct sum of irreducible representation
A'1 A'2 E'1 E'2 E'3 A''1 A''2 E''1 E''2 E''3
8 3 11 11 11 1 6 7 7 7



Properties of derivatives and isotopomers by single substitution, h(D7h)=28
Atom Set*Site Symmetry**h(Site Symmetry)Identical Atoms***ElementChrialPolarIsotopomer
IsotopeMassAbundance****
1 Cs 214Cnoyes13C1163.34698.4849
2 Cs 214Hnoyes2H1163.34980.1190
3 C1 128Nyesyes15N1163.34065.6047
4 Cs 214Cnoyes13C1163.34698.4849
5 Cs 214Onoyes18O
17O
1164.3478
1163.3477
1.5294
0.2906
6 Cs 214Cnoyes13C1163.34698.4849
7 Cs 214Hnoyes2H1163.34980.1190
8 Cs 214Hnoyes2H1163.34980.1190
Total Number of Atoms:126✅ Correct Number of Atoms found
*Atom Orbit
**Subgroup of point group D7h
***Calculated as h( D7h)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %


Numbers of isomers by substitution
ReplacementPatternAchiral
Isomers
Chiral
Isomer Pairs
SingleX71
DoubleX282256
DoubleXY99513
TripleX368211.284
TripleX2Y1.27034.240
TripleXYZ1.76468.868
QuadrupleX45.106355.404
QuadrupleX3Y11.5261.424.112
QuadrupleX2Y216.4822.137.548
QuadrupleX2YZ24.0664.277.592
QuadrupleWXYZ37.6208.560.440
QuintupleX532.7098.705.883
QuintupleVWXYZ857.5201.046.239.740
SextupleX6190.456175.813.156
SextupleUVWXYZ19.450.800126.637.163.100

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 2C7 2(C7)2 2(C7)3 7C'2 σh 2S7 2(S7)5 2(S7)3 v
378 0.000 0.000 -0.000 0 28 0.000 -0.000 -0.000 10

Direct sum of irreducible representation
A'1 A'2 E'1 E'2 E'3 A''1 A''2 E''1 E''2 E''3
17 12 29 29 29 10 15 25 25 25

Molecular motions and force field analysis



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