Direct sum of irreducible representation

A1g	A2g	Eg	T1g	T2g	A1u	A2u	Eu	T1u	T2u
4	0	2	1	5	0	3	1	5	2

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	C3v	6	8	Si	no	yes	29Si 30Si	536.9418 537.9390	18.8452 12.4374
2	C2v	4	12	O	no	yes	18O 17O	537.9464 536.9464	1.1155 0.2120
3	C3v	6	8	C	no	yes	13C	536.9455	4.1260
4	Cs	2	24	H	no	yes	2H	536.9485	0.1736
Total Number of Atoms:			52	✅ 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	4	0
Double	X2	33	17
Double	XY	47	34
Triple	X3	170	385
Triple	X2Y	353	1.213
Triple	XYZ	549	2.492
Quadruple	X4	795	5.316
Quadruple	X3Y	1.902	21.627
Quadruple	X2Y2	2.585	32.671
Quadruple	X2YZ	3.905	65.737
Quadruple	WXYZ	6.009	132.362
Quintuple	X5	2.978	52.747
Quintuple	VWXYZ	60.060	6.467.370
Sextuple	X6	10.212	419.548
Sextuple	UVWXYZ	540.540	305.107.530

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