Direct sum of irreducible representation

Ag	Bg	Au	Bu
5	0	0	5

Properties of derivatives and isotopomers by single substitution, h(C_2h)=4

Atom Set*	Site Symmetry**	h(Site Symmetry)	Identical Atoms***	Element	Chrial	Polar	Isotopomer
							Isotope	Mass	Abundance****
1	Cs	2	2	C	no	yes	13C	55.0503	2.1262
2	Cs	2	2	C	no	yes	13C	55.0503	2.1262
3	Cs	2	2	H	no	yes	2H	55.0532	0.029826
4	Cs	2	2	H	no	yes	2H	55.0532	0.029826
5	Cs	2	2	H	no	yes	2H	55.0532	0.029826
Total Number of Atoms:			10	✅ Correct Number of Atoms found

*Atom Orbit
**Subgroup of point group C_2h
***Calculated as h( C_2h)/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	0
Double	X2	25	0
Double	XY	45	0
Triple	X3	60	0
Triple	X2Y	180	0
Triple	XYZ	360	0
Quadruple	X4	110	0
Quadruple	X3Y	420	0
Quadruple	X2Y2	640	0
Quadruple	X2YZ	1.260	0
Quadruple	WXYZ	2.520	0
Quintuple	X5	126	0
Quintuple	VWXYZ	15.120	0
Sextuple	X6	110	0
Sextuple	UVWXYZ	75.600	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