Direct sum of irreducible representation

A1	A2	B1	B2
4	0	3	0

Properties of derivatives and isotopomers by single substitution, h(C_2v)=4

Atom Set*	Site Symmetry**	h(Site Symmetry)	Identical Atoms***	Element	Chrial	Polar	Isotopomer
							Isotope	Mass	Abundance****
1	C2v	4	1	S	no	yes	34S 33S 36S	157.9080 156.9116 159.9072	3.7887 0.6686 0.008915
2	Cs	2	2	N	no	yes	15N	156.9092	0.6221
3	Cs	2	2	S	no	yes	34S 33S 36S	157.9080 156.9116 159.9072	7.5774 1.3372 0.017829
4	Cs	2	2	O	no	yes	18O 17O	157.9164 156.9164	0.3395 0.064510
Total Number of Atoms:			7	✅ Correct Number of Atoms found

*Atom Orbit
**Subgroup of point group C_2v
***Calculated as h( C_2v)/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	12	0
Double	XY	21	0
Triple	X3	19	0
Triple	X2Y	54	0
Triple	XYZ	105	0
Quadruple	X4	19	0
Quadruple	X3Y	70	0
Quadruple	X2Y2	108	0
Quadruple	X2YZ	210	0
Quadruple	WXYZ	420	0
Quintuple	X5	12	0
Quintuple	VWXYZ	1.260	0
Sextuple	X6	4	0
Sextuple	UVWXYZ	2.520	0

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