Direct sum of irreducible representation

A1g	A2g	Eg	T1g	T2g	A1u	A2u	Eu	T1u	T2u
3	0	2	0	0	0	0	0	2	0

Properties of derivatives and isotopomers by single substitution, h(O_h)=48

Atom Set*	Site Symmetry**	h(Site Symmetry)	Identical Atoms***	Element	Chrial	Polar	Isotopomer
							Isotope	Mass	Abundance****
1	Oh	48	1	W	no	no	186W 182W 183W 180W	353.9239 349.9177 350.9197 347.9162	26.3836 24.2619 13.1918 0.1199
2	C4v	8	6	C	no	yes	13C	352.9238	1.8881
3	C4v	8	6	O	no	yes	18O 17O	353.9247 352.9246	0.3403 0.064662
Total Number of Atoms:			13	✅ Correct Number of Atoms found

*Atom Orbit
**Subgroup of point group O_h
***Calculated as h( O_h)/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	0
Double	XY	14	0
Triple	X3	21	0
Triple	X2Y	47	2
Triple	XYZ	78	8
Quadruple	X4	39	2
Quadruple	X3Y	106	16
Quadruple	X2Y2	145	32
Quadruple	X2YZ	242	74
Quadruple	WXYZ	408	176
Quintuple	X5	57	6
Quintuple	VWXYZ	1.920	2.280
Sextuple	X6	70	12
Sextuple	UVWXYZ	7.560	21.960

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