Direct sum of irreducible representation

A'1	A'2	E'	A''1	A''2	E''
5	0	4	0	3	2

Properties of derivatives and isotopomers by single substitution, h(D_3h)=12

Atom Set*	Site Symmetry**	h(Site Symmetry)	Identical Atoms***	Element	Chrial	Polar	Isotopomer
							Isotope	Mass	Abundance****
1	C2v	4	3	C	no	yes	13C	364.8275	2.4890
2	C3v	6	2	Fe	no	yes	54Fe 57Fe 58Fe	361.8288 364.8246 365.8224	9.5037 3.4454 0.4585
3	C2v	4	3	O	no	yes	18O 17O	365.8283 364.8283	0.4486 0.085240
4	Cs	2	6	C	no	yes	13C	364.8275	4.9780
5	Cs	2	6	O	no	yes	18O 17O	365.8283 364.8283	0.8973 0.1705
Total Number of Atoms:			20	✅ Correct Number of Atoms found

*Atom Orbit
**Subgroup of point group D_3h
***Calculated as h( D_3h)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %

Numbers of isomers by substitution

Replacement	Pattern	Achiral Isomers	Chiral Isomer Pairs
Single	X	5	0
Double	X2	21	8
Double	XY	33	16
Triple	X3	63	69
Triple	X2Y	125	227
Triple	XYZ	188	476
Quadruple	X4	150	342
Quadruple	X3Y	353	1.445
Quadruple	X2Y2	450	2.220
Quadruple	X2YZ	653	4.523
Quadruple	WXYZ	900	9.240
Quintuple	X5	302	1.160
Quintuple	VWXYZ	3.480	153.300
Sextuple	X6	521	3.002
Sextuple	UVWXYZ	10.200	2.320.500

Further Reading

• P.W. Fowler, J. Chem. Soc. Faraday Trans. 91(15) 2241 (1995)
  Isomer Counting using Point Group Symmetry
  
  

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Representation Γ_3N