Grouptheoretical Analysis

Grouptheoretical Analysis

Composition Input Structure

Atomic Number	Atomic Symbol	Isotope	Isotope Mass	Isotope Abundance	Number Atoms	Mass
5	B	11	11.0093	80.1000	7	77.0651
35	Br	79	78.9183	50.6900	7	552.4284

Total					14	629.4935
Isotopomer Natural Abundance (%)					0.1819

Determined Point Group: D_5h

Representation Γ_N

**Characters of reducible representation**
E	2C₅	2(C₅)²	5C'₂	σ_h	2S₅	2(S₅)³	5σ_v
14	4.000	4.000	2	10	0.000	0.000	6

**Direct sum of irreducible representation**
A'₁	A'₂	E'₁	E'₂	A''₁	A''₂	E''₁	E''₂
4	0	2	2	0	2	0	0

**Properties of derivatives and isotopomers by single substitution, h(D_5h)=20**
Atom Set^*	Site Symmetry^**	h(Site Symmetry)	Identical Atoms^***	Element	Chrial	Polar	Isotopomer
Atom Set^*	Site Symmetry^**	h(Site Symmetry)	Identical Atoms^***	Element	Chrial	Polar	Isotope	Mass	Abundance^****
1	C_2v	4	5	B	no	yes	¹⁰B	628.4971	0.2260
2	C_5v	10	2	B	no	yes	¹⁰B	628.4971	0.090393
3	C_5v	10	2	Br	no	yes	⁸¹Br	631.4915	0.3539
4	C_2v	4	5	Br	no	yes	⁸¹Br	631.4915	0.8848
Total Number of Atoms:			14	✅ Correct Number of Atoms found

*Atom Orbit
**Subgroup of point group D_5h
***Calculated as h( D_5h)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %

Error: Reduction failed

Reduction to integer numbers for irreducible representations failed.
Error Code: 1

**Numbers of isomers by substitution**
Replacement	Pattern	Achiral Isomers	Chiral Isomer Pairs
Single	X	4	0
Double	X₂	15	0
Double	XY	24	0
Triple	X₃	36	4
Triple	X₂Y	80	20
Triple	XYZ	132	48
Quadruple	X₄	71	20
Quadruple	X₃Y	192	108
Quadruple	X₂Y₂	256	184
Quadruple	X₂YZ	420	396
Quadruple	WXYZ	684	864
Quintuple	X₅	112	52
Quintuple	VWXYZ	3.384	10.320
Sextuple	X₆	145	88
Sextuple	UVWXYZ

**Characters of reducible representation**
E	2C₅	2(C₅)²	5C'₂	σ_h	2S₅	2(S₅)³	5σ_v
2.162.160	13.152.000	13.152.000	0	151.200	0.000	0.000	720