Direct sum of irreducible representation

A1	A2	E	T1	T2
3	0	2	2	5

Properties of derivatives and isotopomers by single substitution, h(T_d)=24

Atom Set*	Site Symmetry**	h(Site Symmetry)	Identical Atoms***	Element	Chrial	Polar	Isotopomer
							Isotope	Mass	Abundance****
1	C3v	6	4	Ir	no	yes	191Ir	1105.7883	31.2974
2	Cs	2	12	C	no	yes	13C	1108.7940	1.7554
3	Cs	2	12	O	no	yes	18O 17O	1109.7949 1108.7949	0.3164 0.060118
Total Number of Atoms:			28	✅ Correct Number of Atoms found

*Atom Orbit
**Subgroup of point group T_d
***Calculated as h( T_d)/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	13	11
Double	XY	15	24
Triple	X3	43	118
Triple	X2Y	63	378
Triple	XYZ	60	789
Quadruple	X4	121	807
Quadruple	X3Y	195	3.318
Quadruple	X2Y2	265	5.009
Quadruple	X2YZ	255	10.110
Quadruple	WXYZ	180	20.385
Quintuple	X5	278	3.956
Quintuple	VWXYZ	360	491.220
Sextuple	X6	578	15.466
Sextuple	UVWXYZ	360	11.302.020

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