Grouptheoretical Analysis

Grouptheoretical Analysis

Composition Input Structure

Atomic Number	Atomic Symbol	Isotope	Isotope Mass	Isotope Abundance	Number Atoms	Mass
1	H	1	1.0078	99.9844	42	42.3287
6	C	12	12.0000	98.9000	42	504.0000
7	N	14	14.0031	99.6340	28	392.0861
8	O	16	15.9949	99.7620	14	223.9288

Total					126	1162.3435
Isotopomer Natural Abundance (%)					54.4907

Determined Point Group: D_7h

Representation Γ_N

**Characters of reducible representation**
E	2C₇	2(C₇)²	2(C₇)³	7C'₂	σ_h	2S₇	2(S₇)⁵	2(S₇)³	7σ_v
126	0.000	0.000	0.000	0	28	0.000	0.000	0.000	10

**Direct sum of irreducible representation**
A'₁	A'₂	E'₁	E'₂	E'₃	A''₁	A''₂	E''₁	E''₂	E''₃
8	3	11	11	11	1	6	7	7	7

**Properties of derivatives and isotopomers by single substitution, h(D_7h)=28**
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_s	2	14	C	no	yes	¹³C	1163.3469	8.4849
2	C_s	2	14	H	no	yes	²H	1163.3498	0.1190
3	C₁	1	28	N	yes	yes	¹⁵N	1163.3406	5.6047
4	C_s	2	14	C	no	yes	¹³C	1163.3469	8.4849
5	C_s	2	14	O	no	yes	¹⁸O ¹⁷O	1164.3478 1163.3477	1.5294 0.2906
6	C_s	2	14	C	no	yes	¹³C	1163.3469	8.4849
7	C_s	2	14	H	no	yes	²H	1163.3498	0.1190
8	C_s	2	14	H	no	yes	²H	1163.3498	0.1190
Total Number of Atoms:			126	✅ Correct Number of Atoms found

*Atom Orbit
**Subgroup of point group D_7h
***Calculated as h( D_7h)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %

**Numbers of isomers by substitution**
Replacement	Pattern	Achiral Isomers	Chiral Isomer Pairs
Single	X	7	1
Double	X₂	82	256
Double	XY	99	513
Triple	X₃	682	11.284
Triple	X₂Y	1.270	34.240
Triple	XYZ	1.764	68.868
Quadruple	X₄	5.106	355.404
Quadruple	X₃Y	11.526	1.424.112
Quadruple	X₂Y₂	16.482	2.137.548
Quadruple	X₂YZ	24.066	4.277.592
Quadruple	WXYZ	37.620	8.560.440
Quintuple	X₅	32.709	8.705.883
Quintuple	VWXYZ	857.520	1.046.239.740
Sextuple	X₆	190.456	175.813.156
Sextuple	UVWXYZ	19.450.800	126.637.163.100

Further Reading

P.W. Fowler, J. Chem. Soc. Faraday Trans. 91(15) 2241 (1995)
Isomer Counting using Point Group Symmetry

Representation Γ_3N

**Characters of reducible representation**
E	2C₇	2(C₇)²	2(C₇)³	7C'₂	σ_h	2S₇	2(S₇)⁵	2(S₇)³	7σ_v
378	0.000	0.000	-0.000	0	28	0.000	-0.000	-0.000	10

**Direct sum of irreducible representation**
A'₁	A'₂	E'₁	E'₂	E'₃	A''₁	A''₂	E''₁	E''₂	E''₃
17	12	29	29	29	10	15	25	25	25

Molecular motions and force field analysis

Last update November, 13^th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement