Point Group D8h

Results for Point Group D_8h

**Characters of representations for molecular motions**
Motion	E	2C₈	2C₄	2(C₈)³	C₂	4C'₂	4C''₂	i	2(S₈)³	2S₄	2S₈	σ_h	4σ_v	4σ_d
Cartesian 3N	72	0.000	0	-0.000	0	-4	-2	0	-0.000	0	0.000	24	4	2
Translation (x,y,z)	3	2.414	1	-0.414	-1	-1	-1	-3	-2.414	-1	0.414	1	1	1
Rotation (R_x,R_y,R_z)	3	2.414	1	-0.414	-1	-1	-1	3	2.414	1	-0.414	-1	-1	-1
Vibration	66	-4.828	-2	0.828	2	-2	0	0	0.000	0	0.000	24	4	2

**Decomposition to irreducible representations**
Motion	A_1g	A_2g	B_1g	B_2g	E_1g	E_2g	E_3g	A_2u	B_1u	B_2u	E_1u	E_2u	E_3u	Total
Cartesian 3N	3	3	3	3	3	6	3	3	1	2	6	3	6	45
Translation (x,y,z)	0	0	0	0	0	0	0	1	0	0	1	0	0	2
Rotation (R_x,R_y,R_z)	0	1	0	0	1	0	0	0	0	0	0	0	0	2
Vibration	3	2	3	3	2	6	3	2	1	2	5	3	6	41

**Molecular parameter**
Number of Atoms (N)	24
Number of internal coordinates	66
Number of independant internal coordinates	3
Number of vibrational modes	41

Force field analysis

**Allowed / forbidden vibronational transitions**
Operator	A_1g	A_2g	B_1g	B_2g	E_1g	E_2g	E_3g	A_2u	B_1u	B_2u	E_1u	E_2u	E_3u	Total
Linear (IR)	3	2	3	3	2	6	3	2	1	2	5	3	6	7 / 34
Quadratic (Raman)	3	2	3	3	2	6	3	2	1	2	5	3	6	11 / 30
IR + Raman	- - - -	2	3	3	- - - -	- - - -	3	- - - -	1	2	- - - -	3	6	0^* / 23

* Parity Mutual Exclusion Principle

Characters of force fields
(Symmetric powers of vibration representation)
Force field	E	2C₈	2C₄	2(C₈)³	C₂	4C'₂	4C''₂	i	2(S₈)³	2S₄	2S₈	σ_h	4σ_v	4σ_d
linear	66	-4.828	-2	0.828	2	-2	0	0	0.000	0	0.000	24	4	2
quadratic	2.211	10.657	3	-0.657	35	35	33	33	-1.000	1	-1.000	321	41	35
cubic	50.116	-13.657	-4	-2.343	68	-68	0	0	0.000	0	0.000	3.104	144	68
quartic	864.501	10.657	21	-0.657	629	629	561	561	1.000	17	1.000	24.081	841	629
quintic	12.103.014	-4.828	-38	0.828	1.190	-1.190	0	0	0.000	0	0.000	158.424	2.660	1.190
sextic	143.218.999	1.000	55	1.000	7.735	7.735	6.545	6.545	-1.000	17	-1.000	914.641	11.585	7.735

Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field	A_1g	A_2g	B_1g	B_2g	E_1g	E_2g	E_3g	A_1u	A_2u	B_1u	B_2u	E_1u	E_2u	E_3u
linear	3	2	3	3	2	6	3	0	2	1	2	5	3	6
quadratic	100	64	82	80	119	162	117	59	61	58	59	155	118	153
cubic	1.682	1.646	1.667	1.665	2.933	3.331	2.935	1.435	1.505	1.454	1.490	3.321	2.943	3.323
quartic	28.141	27.476	27.842	27.772	52.523	55.606	52.521	26.231	26.301	26.247	26.283	55.463	52.530	55.461
quintic	383.537	382.872	383.240	383.170	746.462	766.419	746.463	372.673	373.933	372.971	373.636	766.265	746.616	766.266
sextic	4.508.827	4.500.427	4.505.257	4.503.997	8.893.948	9.009.236	8.893.948	4.446.421	4.447.681	4.446.718	4.447.383	9.007.460	8.894.092	9.007.460

Contributions to nonvanishing force field constants

pos(X) : Position of irreducible representation (irrep) X in character table of D_8h

Subtotal: <Number of nonvanishing force constants in subsection> / <number of nonzero irrep combinations in subsection> / <number of irrep combinations in subsection>
Total: <Number of nonvanishing force constants in force field> / <number of nonzero irrep combinations in force field> / <number of irrep combinations in force field>

**Contributions to nonvanishing quadratic force field constants**
Irrep combinations (i,i) with indices: pos(A_1g) ≤ i ≤ pos(E_3u)
..6.	A_1gA_1g.	..3.	A_2gA_2g.	..6.	B_1gB_1g.	..6.	B_2gB_2g.	..3.	E_1gE_1g.	..21.	E_2gE_2g.	..6.	E_3gE_3g.	..3.	A_2uA_2u.	..1.	B_1uB_1u.	..3.	B_2uB_2u.
..15.	E_1uE_1u.	..6.	E_2uE_2u.	..21.	E_3uE_3u.
Subtotal: 100 / 13 / 14
Irrep combinations (i,j) with indices: pos(A_1g) ≤ i ≤ j ≤ pos(E_3u)
Subtotal: 0 / 0 / 91
Total: 100 / 13 / 105

**Contributions to nonvanishing cubic force field constants**
Irrep combinations (i,i,i) with indices: pos(A_1g) ≤ i ≤ pos(E_3u)
..10.	A_1gA_1gA_1g.
Subtotal: 10 / 1 / 14
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A_1g) ≤ i ≤ j ≤ pos(E_3u)
..18.	E_1gE_1gE_2g.	..9.	A_1gA_2gA_2g.	..18.	A_1gB_1gB_1g.	..18.	A_1gB_2gB_2g.	..9.	A_1gE_1gE_1g.	..63.	A_1gE_2gE_2g.	..18.	A_1gE_3gE_3g.	..9.	A_1gA_2uA_2u.	..3.	A_1gB_1uB_1u.	..9.	A_1gB_2uB_2u.
..45.	A_1gE_1uE_1u.	..18.	A_1gE_2uE_2u.	..63.	A_1gE_3uE_3u.	..2.	A_2gE_1gE_1g.	..30.	A_2gE_2gE_2g.	..6.	A_2gE_3gE_3g.	..20.	A_2gE_1uE_1u.	..6.	A_2gE_2uE_2u.	..30.	A_2gE_3uE_3u.	..63.	B_1gE_2gE_2g.
..18.	B_1gE_2uE_2u.	..63.	B_2gE_2gE_2g.	..18.	B_2gE_2uE_2u.	..36.	E_2gE_3gE_3g.	..90.	E_2gE_1uE_1u.	..126.	E_2gE_3uE_3u.
Subtotal: 808 / 26 / 182
Irrep combinations (i,j,k) with indices: pos(A_1g) ≤ i ≤ j ≤ k ≤ pos(E_3u)
..18.	A_2gB_1gB_2g.	..4.	A_2gB_1uB_2u.	..18.	B_1gE_1gE_3g.	..12.	B_1gA_2uB_2u.	..90.	B_1gE_1uE_3u.	..18.	B_2gE_1gE_3g.	..6.	B_2gA_2uB_1u.	..90.	B_2gE_1uE_3u.	..36.	E_1gE_2gE_3g.	..20.	E_1gA_2uE_1u.
..12.	E_1gB_1uE_3u.	..24.	E_1gB_2uE_3u.	..30.	E_1gE_1uE_2u.	..36.	E_1gE_2uE_3u.	..36.	E_2gA_2uE_2u.	..18.	E_2gB_1uE_2u.	..36.	E_2gB_2uE_2u.	..180.	E_2gE_1uE_3u.	..36.	E_3gA_2uE_3u.	..15.	E_3gB_1uE_1u.
..30.	E_3gB_2uE_1u.	..45.	E_3gE_1uE_2u.	..54.	E_3gE_2uE_3u.
Subtotal: 864 / 23 / 364
Total: 1.682 / 50 / 560

**Contributions to nonvanishing quartic force field constants**
Irrep combinations (i,i,i,i) with indices: pos(A_1g) ≤ i ≤ pos(E_3u)
..15.	A_1gA_1gA_1gA_1g.	..5.	A_2gA_2gA_2gA_2g.	..15.	B_1gB_1gB_1gB_1g.	..15.	B_2gB_2gB_2gB_2g.	..6.	E_1gE_1gE_1gE_1g.	..357.	E_2gE_2gE_2gE_2g.	..21.	E_3gE_3gE_3gE_3g.	..5.	A_2uA_2uA_2uA_2u.	..1.	B_1uB_1uB_1uB_1u.	..5.	B_2uB_2uB_2uB_2u.
..120.	E_1uE_1uE_1uE_1u.	..36.	E_2uE_2uE_2uE_2u.	..231.	E_3uE_3uE_3uE_3u.
Subtotal: 832 / 13 / 14
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A_1g) ≤ i ≤ j ≤ pos(E_3u)
..12.	E_1gE_1gE_1gE_3g.	..210.	E_1uE_1uE_1uE_3u.	..20.	E_1gE_3gE_3gE_3g.	..280.	E_1uE_3uE_3uE_3u.
Subtotal: 522 / 4 / 182
Irrep combinations (i,i,j,j) with indices: pos(A_1g) ≤ i ≤ j ≤ pos(E_3u)
..18.	A_1gA_1gA_2gA_2g.	..36.	A_1gA_1gB_1gB_1g.	..36.	A_1gA_1gB_2gB_2g.	..18.	A_1gA_1gE_1gE_1g.	..126.	A_1gA_1gE_2gE_2g.	..36.	A_1gA_1gE_3gE_3g.	..18.	A_1gA_1gA_2uA_2u.	..6.	A_1gA_1gB_1uB_1u.	..18.	A_1gA_1gB_2uB_2u.	..90.	A_1gA_1gE_1uE_1u.
..36.	A_1gA_1gE_2uE_2u.	..126.	A_1gA_1gE_3uE_3u.	..18.	A_2gA_2gB_1gB_1g.	..18.	A_2gA_2gB_2gB_2g.	..9.	A_2gA_2gE_1gE_1g.	..63.	A_2gA_2gE_2gE_2g.	..18.	A_2gA_2gE_3gE_3g.	..9.	A_2gA_2gA_2uA_2u.	..3.	A_2gA_2gB_1uB_1u.	..9.	A_2gA_2gB_2uB_2u.
..45.	A_2gA_2gE_1uE_1u.	..18.	A_2gA_2gE_2uE_2u.	..63.	A_2gA_2gE_3uE_3u.	..36.	B_1gB_1gB_2gB_2g.	..18.	B_1gB_1gE_1gE_1g.	..126.	B_1gB_1gE_2gE_2g.	..36.	B_1gB_1gE_3gE_3g.	..18.	B_1gB_1gA_2uA_2u.	..6.	B_1gB_1gB_1uB_1u.	..18.	B_1gB_1gB_2uB_2u.
..90.	B_1gB_1gE_1uE_1u.	..36.	B_1gB_1gE_2uE_2u.	..126.	B_1gB_1gE_3uE_3u.	..18.	B_2gB_2gE_1gE_1g.	..126.	B_2gB_2gE_2gE_2g.	..36.	B_2gB_2gE_3gE_3g.	..18.	B_2gB_2gA_2uA_2u.	..6.	B_2gB_2gB_1uB_1u.	..18.	B_2gB_2gB_2uB_2u.	..90.	B_2gB_2gE_1uE_1u.
..36.	B_2gB_2gE_2uE_2u.	..126.	B_2gB_2gE_3uE_3u.	..78.	E_1gE_1gE_2gE_2g.	..39.	E_1gE_1gE_3gE_3g.	..9.	E_1gE_1gA_2uA_2u.	..3.	E_1gE_1gB_1uB_1u.	..9.	E_1gE_1gB_2uB_2u.	..100.	E_1gE_1gE_1uE_1u.	..21.	E_1gE_1gE_2uE_2u.	..141.	E_1gE_1gE_3uE_3u.
..171.	E_2gE_2gE_3gE_3g.	..63.	E_2gE_2gA_2uA_2u.	..21.	E_2gE_2gB_1uB_1u.	..63.	E_2gE_2gB_2uB_2u.	..465.	E_2gE_2gE_1uE_1u.	..423.	E_2gE_2gE_2uE_2u.	..666.	E_2gE_2gE_3uE_3u.	..18.	E_3gE_3gA_2uA_2u.	..6.	E_3gE_3gB_1uB_1u.	..18.	E_3gE_3gB_2uB_2u.
..210.	E_3gE_3gE_1uE_1u.	..45.	E_3gE_3gE_2uE_2u.	..297.	E_3gE_3gE_3uE_3u.	..3.	A_2uA_2uB_1uB_1u.	..9.	A_2uA_2uB_2uB_2u.	..45.	A_2uA_2uE_1uE_1u.	..18.	A_2uA_2uE_2uE_2u.	..63.	A_2uA_2uE_3uE_3u.	..3.	B_1uB_1uB_2uB_2u.	..15.	B_1uB_1uE_1uE_1u.
..6.	B_1uB_1uE_2uE_2u.	..21.	B_1uB_1uE_3uE_3u.	..45.	B_2uB_2uE_1uE_1u.	..18.	B_2uB_2uE_2uE_2u.	..63.	B_2uB_2uE_3uE_3u.	..120.	E_1uE_1uE_2uE_2u.	..780.	E_1uE_1uE_3uE_3u.	..171.	E_2uE_2uE_3uE_3u.
Subtotal: 6.067 / 78 / 91
Irrep combinations (i,i,j,k) (i,j,j,k) (i,j,k,k) with indices: pos(A_1g) ≤ i ≤ j ≤ k ≤ pos(E_3u)
..18.	E_1gE_1gA_2uE_2u.	..2.	E_1gE_1gB_1uB_2u.	..9.	E_1gE_1gB_1uE_2u.	..18.	E_1gE_1gB_2uE_2u.	..90.	E_1gE_1gE_1uE_3u.	..42.	E_2gE_2gA_2uB_1u.	..84.	E_2gE_2gA_2uB_2u.	..30.	E_2gE_2gB_1uB_2u.	..1.260.	E_2gE_2gE_1uE_3u.	..36.	E_3gE_3gA_2uE_2u.
..6.	E_3gE_3gB_1uB_2u.	..18.	E_3gE_3gB_1uE_2u.	..36.	E_3gE_3gB_2uE_2u.	..180.	E_3gE_3gE_1uE_3u.	..54.	A_1gE_1gE_1gE_2g.	..36.	A_2gE_1gE_1gE_2g.	..54.	B_1gE_1gE_1gE_2g.	..54.	B_2gE_1gE_1gE_2g.	..252.	E_1gE_2gE_2gE_3g.	..90.	A_2uE_1uE_1uE_2u.
..45.	B_1uE_1uE_1uE_2u.	..90.	B_2uE_1uE_1uE_2u.	..360.	E_1uE_2uE_2uE_3u.	..6.	A_1gA_2gE_1gE_1g.	..90.	A_1gA_2gE_2gE_2g.	..18.	A_1gA_2gE_3gE_3g.	..60.	A_1gA_2gE_1uE_1u.	..18.	A_1gA_2gE_2uE_2u.	..90.	A_1gA_2gE_3uE_3u.	..189.	A_1gB_1gE_2gE_2g.
..54.	A_1gB_1gE_2uE_2u.	..189.	A_1gB_2gE_2gE_2g.	..54.	A_1gB_2gE_2uE_2u.	..108.	A_1gE_2gE_3gE_3g.	..270.	A_1gE_2gE_1uE_1u.	..378.	A_1gE_2gE_3uE_3u.	..126.	A_2gB_1gE_2gE_2g.	..36.	A_2gB_1gE_2uE_2u.	..126.	A_2gB_2gE_2gE_2g.	..36.	A_2gB_2gE_2uE_2u.
..72.	A_2gE_2gE_3gE_3g.	..180.	A_2gE_2gE_1uE_1u.	..252.	A_2gE_2gE_3uE_3u.	..9.	B_1gB_2gE_1gE_1g.	..135.	B_1gB_2gE_2gE_2g.	..27.	B_1gB_2gE_3gE_3g.	..90.	B_1gB_2gE_1uE_1u.	..27.	B_1gB_2gE_2uE_2u.	..135.	B_1gB_2gE_3uE_3u.	..108.	B_1gE_2gE_3gE_3g.
..270.	B_1gE_2gE_1uE_1u.	..378.	B_1gE_2gE_3uE_3u.	..108.	B_2gE_2gE_3gE_3g.	..270.	B_2gE_2gE_1uE_1u.	..378.	B_2gE_2gE_3uE_3u.	..90.	E_1gE_3gE_1uE_1u.	..72.	E_1gE_3gE_2uE_2u.	..126.	E_1gE_3gE_3uE_3u.	..12.	A_2uB_1uE_2uE_2u.	..24.	A_2uB_2uE_2uE_2u.
..126.	A_2uE_2uE_3uE_3u.	..20.	B_1uB_2uE_1uE_1u.	..6.	B_1uB_2uE_2uE_2u.	..30.	B_1uB_2uE_3uE_3u.	..63.	B_1uE_2uE_3uE_3u.	..126.	B_2uE_2uE_3uE_3u.
Subtotal: 7.846 / 66 / 1.092
Irrep combinations (i,j,k,l) with indices: pos(A_1g) ≤ i ≤ j ≤ k ≤ l ≤ pos(E_3u)
..54.	A_1gA_2gB_1gB_2g.	..12.	A_1gA_2gB_1uB_2u.	..54.	A_1gB_1gE_1gE_3g.	..36.	A_1gB_1gA_2uB_2u.	..270.	A_1gB_1gE_1uE_3u.	..54.	A_1gB_2gE_1gE_3g.	..18.	A_1gB_2gA_2uB_1u.	..270.	A_1gB_2gE_1uE_3u.	..108.	A_1gE_1gE_2gE_3g.	..60.	A_1gE_1gA_2uE_1u.
..36.	A_1gE_1gB_1uE_3u.	..72.	A_1gE_1gB_2uE_3u.	..90.	A_1gE_1gE_1uE_2u.	..108.	A_1gE_1gE_2uE_3u.	..108.	A_1gE_2gA_2uE_2u.	..54.	A_1gE_2gB_1uE_2u.	..108.	A_1gE_2gB_2uE_2u.	..540.	A_1gE_2gE_1uE_3u.	..108.	A_1gE_3gA_2uE_3u.	..45.	A_1gE_3gB_1uE_1u.
..90.	A_1gE_3gB_2uE_1u.	..135.	A_1gE_3gE_1uE_2u.	..162.	A_1gE_3gE_2uE_3u.	..36.	A_2gB_1gE_1gE_3g.	..12.	A_2gB_1gA_2uB_1u.	..180.	A_2gB_1gE_1uE_3u.	..36.	A_2gB_2gE_1gE_3g.	..24.	A_2gB_2gA_2uB_2u.	..180.	A_2gB_2gE_1uE_3u.	..72.	A_2gE_1gE_2gE_3g.
..40.	A_2gE_1gA_2uE_1u.	..24.	A_2gE_1gB_1uE_3u.	..48.	A_2gE_1gB_2uE_3u.	..60.	A_2gE_1gE_1uE_2u.	..72.	A_2gE_1gE_2uE_3u.	..72.	A_2gE_2gA_2uE_2u.	..36.	A_2gE_2gB_1uE_2u.	..72.	A_2gE_2gB_2uE_2u.	..360.	A_2gE_2gE_1uE_3u.	..72.	A_2gE_3gA_2uE_3u.
..30.	A_2gE_3gB_1uE_1u.	..60.	A_2gE_3gB_2uE_1u.	..90.	A_2gE_3gE_1uE_2u.	..108.	A_2gE_3gE_2uE_3u.	..18.	B_1gB_2gB_1uB_2u.	..108.	B_1gE_1gE_2gE_3g.	..72.	B_1gE_1gA_2uE_3u.	..30.	B_1gE_1gB_1uE_1u.	..60.	B_1gE_1gB_2uE_1u.	..90.	B_1gE_1gE_1uE_2u.
..108.	B_1gE_1gE_2uE_3u.	..108.	B_1gE_2gA_2uE_2u.	..54.	B_1gE_2gB_1uE_2u.	..108.	B_1gE_2gB_2uE_2u.	..540.	B_1gE_2gE_1uE_3u.	..90.	B_1gE_3gA_2uE_1u.	..54.	B_1gE_3gB_1uE_3u.	..108.	B_1gE_3gB_2uE_3u.	..135.	B_1gE_3gE_1uE_2u.	..162.	B_1gE_3gE_2uE_3u.
..108.	B_2gE_1gE_2gE_3g.	..72.	B_2gE_1gA_2uE_3u.	..30.	B_2gE_1gB_1uE_1u.	..60.	B_2gE_1gB_2uE_1u.	..90.	B_2gE_1gE_1uE_2u.	..108.	B_2gE_1gE_2uE_3u.	..108.	B_2gE_2gA_2uE_2u.	..54.	B_2gE_2gB_1uE_2u.	..108.	B_2gE_2gB_2uE_2u.	..540.	B_2gE_2gE_1uE_3u.
..90.	B_2gE_3gA_2uE_1u.	..54.	B_2gE_3gB_1uE_3u.	..108.	B_2gE_3gB_2uE_3u.	..135.	B_2gE_3gE_1uE_2u.	..162.	B_2gE_3gE_2uE_3u.	..120.	E_1gE_2gA_2uE_1u.	..144.	E_1gE_2gA_2uE_3u.	..60.	E_1gE_2gB_1uE_1u.	..72.	E_1gE_2gB_1uE_3u.	..120.	E_1gE_2gB_2uE_1u.
..144.	E_1gE_2gB_2uE_3u.	..360.	E_1gE_2gE_1uE_2u.	..432.	E_1gE_2gE_2uE_3u.	..12.	E_1gE_3gA_2uB_1u.	..24.	E_1gE_3gA_2uB_2u.	..36.	E_1gE_3gA_2uE_2u.	..18.	E_1gE_3gB_1uE_2u.	..36.	E_1gE_3gB_2uE_2u.	..540.	E_1gE_3gE_1uE_3u.	..180.	E_2gE_3gA_2uE_1u.
..216.	E_2gE_3gA_2uE_3u.	..90.	E_2gE_3gB_1uE_1u.	..108.	E_2gE_3gB_1uE_3u.	..180.	E_2gE_3gB_2uE_1u.	..216.	E_2gE_3gB_2uE_3u.	..540.	E_2gE_3gE_1uE_2u.	..648.	E_2gE_3gE_2uE_3u.	..60.	A_2uB_1uE_1uE_3u.	..120.	A_2uB_2uE_1uE_3u.	..180.	A_2uE_1uE_2uE_3u.
..90.	B_1uE_1uE_2uE_3u.	..180.	B_2uE_1uE_2uE_3u.
Subtotal: 12.874 / 102 / 1.001
Total: 28.141 / 263 / 2.380

Calculate contributions to

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

Results for Point Group D8h

Force field analysis

Further Reading

Contributions to nonvanishing force field constants

Calculate contributions to

Results for Point Group D_8h