Direct sum of irreducible representation

A1	A2	B1	B2	E
3	0	0	3	3

Properties of derivatives and isotopomers by single substitution, h(D_2d)=8

Atom Set*	Site Symmetry**	h(Site Symmetry)	Identical Atoms***	Element	Chrial	Polar	Isotopomer
							Isotope	Mass	Abundance****
1	Cs	2	4	C	no	yes	13C	57.0660	4.2511
2	Cs	2	4	H	no	yes	2H	57.0689	0.059634
3	Cs	2	4	H	no	yes	2H	57.0689	0.059634
Total Number of Atoms:			12	✅ Correct Number of Atoms found

*Atom Orbit
**Subgroup of point group D_2d
***Calculated as h( D_2d)/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	0
Double	X2	9	6
Double	XY	15	9
Triple	X3	19	18
Triple	X2Y	39	63
Triple	XYZ	60	135
Quadruple	X4	33	51
Quadruple	X3Y	75	210
Quadruple	X2Y2	93	336
Quadruple	X2YZ	135	675
Quadruple	WXYZ	180	1.395
Quintuple	X5	42	78
Quintuple	VWXYZ	360	11.700
Sextuple	X6	46	100
Sextuple	UVWXYZ	360	82.980

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