Direct sum of irreducible representation

A'1	A'2	E'	A''1	A''2	E''
2	0	1	0	2	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	C3v	6	2	C	no	yes	13C	31.0503	2.1738
2	Cs	2	6	H	no	yes	2H	31.0532	0.091481
Total Number of Atoms:			8	✅ 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	5	1
Double	XY	6	2
Triple	X3	6	2
Triple	X2Y	10	9
Triple	XYZ	12	22
Quadruple	X4	8	4
Quadruple	X3Y	14	17
Quadruple	X2Y2	18	29
Quadruple	X2YZ	18	61
Quadruple	WXYZ	12	134
Quintuple	X5	6	2
Quintuple	VWXYZ	0	560
Sextuple	X6	5	1
Sextuple	UVWXYZ	0	1.680

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