Direct sum of irreducible representation

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

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	43.0503	3.2248
2	Cs	2	6	H	no	yes	2H	43.0532	0.090474
Total Number of Atoms:			9	✅ 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	2	0
Double	X2	4	2
Double	XY	4	4
Triple	X3	7	5
Triple	X2Y	8	18
Triple	XYZ	4	40
Quadruple	X4	8	8
Quadruple	X3Y	12	36
Quadruple	X2Y2	16	58
Quadruple	X2YZ	12	120
Quadruple	WXYZ	0	252
Quintuple	X5	8	8
Quintuple	VWXYZ	0	1.260
Sextuple	X6	7	5
Sextuple	UVWXYZ	0	5.040

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