Direct sum of irreducible representation

A1g	B1g	B2g	B3g	A1u	B1u	B2u	B3u
4	2	0	0	0	0	3	3

Properties of derivatives and isotopomers by single substitution, h(D_2h)=8

Atom Set*	Site Symmetry**	h(Site Symmetry)	Identical Atoms***	Element	Chrial	Polar	Isotopomer
							Isotope	Mass	Abundance****
1	C2v	4	2	C	no	yes	13C	168.9728	2.0521
2	C2v	4	2	O	no	yes	18O 17O	169.9737 168.9737	0.3699 0.070278
3	Cs	2	4	C	no	yes	13C	168.9728	4.1042
4	Cs	2	4	O	no	yes	18O 17O	169.9737 168.9737	0.7398 0.1406
Total Number of Atoms:			12	✅ Correct Number of Atoms found

*Atom Orbit
**Subgroup of point group D_2h
***Calculated as h( D_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	4	0
Double	X2	21	0
Double	XY	34	0
Triple	X3	60	0
Triple	X2Y	170	0
Triple	XYZ	330	0
Quadruple	X4	135	0
Quadruple	X3Y	500	0
Quadruple	X2Y2	765	0
Quadruple	X2YZ	1.490	0
Quadruple	WXYZ	2.970	0
Quintuple	X5	208	0
Quintuple	VWXYZ	23.760	0
Sextuple	X6	246	0
Sextuple	UVWXYZ	166.320	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