Grouptheoretical Analysis




Composition Input Structure


Atomic
Number		 Atomic
Symbol		 Isotope Isotope
Mass		 Isotope
Abundance		 Number
Atoms		 Mass
15P3130.9738100.000010309.7376
22Ti4847.947973.7200147.9479
Total11 357.6856
Isotopomer Natural Abundance (%)73.7200


Determined Point Group: D5h







Representation ΓN


Characters of reducible representation
E 2C5 2(C5)2 5C'2 σh 2S5 2(S5)3 5σv
11 1.000 1.000 1 1 1.000 1.000 3

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



Properties of derivatives and isotopomers by single substitution, h(D5h)=20
Atom Set*Site Symmetry**h(Site Symmetry)Identical Atoms***ElementChrialPolarIsotopomer
IsotopeMassAbundance****
1 D5h 201Tinono46Ti
47Ti
49Ti
50Ti		355.6902
356.6894
358.6855
359.6824		8.2500
7.4400
5.4100
5.1800
2 Cs 210Pnoyes---
Total Number of Atoms:11✅ 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
DoubleX242
DoubleXY34
TripleX376
TripleX2Y822
TripleXYZ348
QuadrupleX41014
QuadrupleX3Y1260
QuadrupleX2Y22094
QuadrupleX2YZ12192
QuadrupleWXYZ0396
QuintupleX51220
QuintupleVWXYZ02.772
SextupleX61220
SextupleUVWXYZ016.632

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 5σv
33 1.618 -0.618 -1 1 -0.382 -2.618 3

Direct sum of irreducible representation
A'1 A'2 E'1 E'2 A''1 A''2 E''1 E''2
2 1 4 3 1 3 3 3

Molecular motions and force field analysis


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