Direct sum of irreducible representation

A'1	A'2	E'	A''1	A''2	E''
5	0	2	0	2	0

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	D3h	12	1	Fe	no	no	54Fe 57Fe 58Fe	193.9142 196.9100 197.9078	5.4650 1.9812 0.2637
2	C2v	4	3	C	no	yes	13C	196.9129	2.8625
3	C3v	6	2	C	no	yes	13C	196.9129	1.9084
4	C2v	4	3	O	no	yes	18O 17O	197.9138 196.9137	0.5160 0.098033
5	C3v	6	2	O	no	yes	18O 17O	197.9138 196.9137	0.3440 0.065355
Total Number of Atoms:			11	✅ 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	16	0
Double	XY	28	0
Triple	X3	34	2
Triple	X2Y	80	10
Triple	XYZ	140	24
Quadruple	X4	53	8
Quadruple	X3Y	150	46
Quadruple	X2Y2	198	80
Quadruple	X2YZ	336	178
Quadruple	WXYZ	560	400
Quintuple	X5	67	14
Quintuple	VWXYZ	1.680	3.800
Sextuple	X6	67	14
Sextuple	UVWXYZ	3.360	26.040

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