Direct sum of irreducible representation

A1	A2	E
4	0	1

Properties of derivatives and isotopomers by single substitution, h(C_3v)=6

Atom Set*	Site Symmetry**	h(Site Symmetry)	Identical Atoms***	Element	Chrial	Polar	Isotopomer
							Isotope	Mass	Abundance****
1	C3v	6	1	C	no	yes	13C	42.0299	1.0834
2	C3v	6	1	C	no	yes	13C	42.0299	1.0834
3	C3v	6	1	N	no	yes	15N	42.0236	0.3578
4	Cs	2	3	H	no	yes	2H	42.0328	0.045594
Total Number of Atoms:			6	✅ Correct Number of Atoms found

*Atom Orbit
**Subgroup of point group C_3v
***Calculated as h( C_3v)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %

Numbers of isomers by substitution

Replacement	Pattern	Achiral Isomers	Chiral Isomer Pairs
Single	X	4	0
Double	X2	7	0
Double	XY	12	1
Triple	X3	8	0
Triple	X2Y	16	3
Triple	XYZ	24	10
Quadruple	X4	7	0
Quadruple	X3Y	16	3
Quadruple	X2Y2	18	6
Quadruple	X2YZ	24	18
Quadruple	WXYZ	24	48
Quintuple	X5	4	0
Quintuple	VWXYZ	0	120
Sextuple	X6	1	0
Sextuple	UVWXYZ	0	120

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