Direct sum of irreducible representation

A1g	B1g	B2g	B3g	A1u	B1u	B2u	B3u
6	2	0	0	0	0	4	4

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	224.9627	1.9976
2	C2v	4	2	C	no	yes	13C	224.9627	1.9976
3	C2v	4	2	O	no	yes	18O 17O	225.9636 224.9635	0.3601 0.068413
4	C2v	4	2	O	no	yes	18O 17O	225.9636 224.9635	0.3601 0.068413
5	Cs	2	4	C	no	yes	13C	224.9627	3.9953
6	Cs	2	4	O	no	yes	18O 17O	225.9636 224.9635	0.7201 0.1368
Total Number of Atoms:			16	✅ 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	6	0
Double	X2	38	0
Double	XY	66	0
Triple	X3	154	0
Triple	X2Y	438	0
Triple	XYZ	852	0
Quadruple	X4	488	0
Quadruple	X3Y	1.858	0
Quadruple	X2Y2	2.798	0
Quadruple	X2YZ	5.502	0
Quadruple	WXYZ	10.932	0
Quintuple	X5	1.134	0
Quintuple	VWXYZ	131.040	0
Sextuple	X6	2.074	0
Sextuple	UVWXYZ	1.441.440	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