Direct sum of irreducible representation

A1	A2	E
7	2	6

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	112.1082	1.0235
2	C3v	6	1	H	no	yes	2H	112.1111	0.014358
3	C3v	6	1	N	no	yes	15N	112.1018	0.3380
4	Cs	2	3	C	no	yes	13C	112.1082	3.0706
5	Cs	2	3	C	no	yes	13C	112.1082	3.0706
6	C1	1	6	H	yes	yes	2H	112.1111	0.086148
7	C1	1	6	H	yes	yes	2H	112.1111	0.086148
Total Number of Atoms:			21	✅ 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	5	2
Double	X2	18	27
Double	XY	20	62
Triple	X3	50	199
Triple	X2Y	70	631
Triple	XYZ	60	1.302
Quadruple	X4	113	947
Quadruple	X3Y	180	3.906
Quadruple	X2Y2	246	5.862
Quadruple	X2YZ	220	11.860
Quadruple	WXYZ	120	23.880
Quintuple	X5	221	3.287
Quintuple	VWXYZ	120	406.920
Sextuple	X6	376	8.863
Sextuple	UVWXYZ	0	6.511.680

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