Direct sum of irreducible representation

A'	A''
9	6

Properties of derivatives and isotopomers by single substitution, h(C_s)=2

Atom Set*	Site Symmetry**	h(Site Symmetry)	Identical Atoms***	Element	Chrial	Polar	Isotopomer
							Isotope	Mass	Abundance****
1	Cs	2	1	C	no	yes	13C	71.0816	1.0508
2	Cs	2	1	H	no	yes	2H	71.0845	0.014740
3	Cs	2	1	H	no	yes	2H	71.0845	0.014740
4	C1	1	2	C	yes	yes	13C	71.0816	2.1015
5	C1	1	2	C	yes	yes	13C	71.0816	2.1015
6	C1	1	2	H	yes	yes	2H	71.0845	0.029480
7	C1	1	2	H	yes	yes	2H	71.0845	0.029480
8	C1	1	2	H	yes	yes	2H	71.0845	0.029480
9	C1	1	2	H	yes	yes	2H	71.0845	0.029480
Total Number of Atoms:			15	✅ Correct Number of Atoms found

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

Numbers of isomers by substitution

Replacement	Pattern	Achiral Isomers	Chiral Isomer Pairs
Single	X	3	6
Double	X2	9	48
Double	XY	6	102
Triple	X3	19	218
Triple	X2Y	21	672
Triple	XYZ	6	1.362
Quadruple	X4	33	666
Quadruple	X3Y	36	2.712
Quadruple	X2Y2	66	4.062
Quadruple	X2YZ	36	8.172
Quadruple	WXYZ	0	16.380
Quintuple	X5	51	1.476
Quintuple	VWXYZ	0	180.180
Sextuple	X6	65	2.470
Sextuple	UVWXYZ	0	1.801.800

Further Reading

• P.W. Fowler, J. Chem. Soc. Faraday Trans. 91(15) 2241 (1995)
  Isomer Counting using Point Group Symmetry
  
  

---

Representation Γ_3N