Direct sum of irreducible representation

Ag	Bg	Au	Bu
5	2	2	5

Properties of derivatives and isotopomers by single substitution, h(C_2h)=4

Atom Set*	Site Symmetry**	h(Site Symmetry)	Identical Atoms***	Element	Chrial	Polar	Isotopomer
							Isotope	Mass	Abundance****
1	Cs	2	2	C	no	yes	13C	59.0816	2.1249
2	Cs	2	2	C	no	yes	13C	59.0816	2.1249
3	Cs	2	2	H	no	yes	2H	59.0845	0.029808
4	C1	1	4	H	yes	yes	2H	59.0845	0.059616
5	C1	1	4	H	yes	yes	2H	59.0845	0.059616
Total Number of Atoms:			14	✅ Correct Number of Atoms found

*Atom Orbit
**Subgroup of point group C_2h
***Calculated as h( C_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	3	2
Double	X2	13	18
Double	XY	15	38
Triple	X3	22	80
Triple	X2Y	42	252
Triple	XYZ	60	516
Quadruple	X4	51	230
Quadruple	X3Y	90	956
Quadruple	X2Y2	132	1.446
Quadruple	X2YZ	150	2.928
Quadruple	WXYZ	180	5.916
Quintuple	X5	61	470
Quintuple	VWXYZ	360	59.880
Sextuple	X6	95	712
Sextuple	UVWXYZ	360	540.360

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