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	48	0.000	0	-0.000	0	-4	0	0	-0.000	0	0.000	16	4	0
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	42	-4.828	-2	0.828	2	-2	2	0	-0.000	0	-0.000	16	4	0

**Decomposition to irreducible representations**
Motion	A_1g	A_2g	B_1g	B_2g	E_1g	E_2g	E_3g	A_2u	B_2u	E_1u	E_2u	E_3u	Total
Cartesian 3N	2	2	2	2	2	4	2	2	2	4	2	4	30
Translation (x,y,z)	0	0	0	0	0	0	0	1	0	1	0	0	2
Rotation (R_x,R_y,R_z)	0	1	0	0	1	0	0	0	0	0	0	0	2
Vibration	2	1	2	2	1	4	2	1	2	3	2	4	26

**Molecular parameter**
Number of Atoms (N)	16
Number of internal coordinates	42
Number of independant internal coordinates	2
Number of vibrational modes	26

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_2u	E_1u	E_2u	E_3u	Total
Linear (IR)	2	1	2	2	1	4	2	1	2	3	2	4	4 / 22
Quadratic (Raman)	2	1	2	2	1	4	2	1	2	3	2	4	7 / 19
IR + Raman	- - - -	1	2	2	- - - -	- - - -	2	- - - -	2	- - - -	2	4	0^* / 15

* 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	42	-4.828	-2	0.828	2	-2	2	0	-0.000	0	-0.000	16	4	0
quadratic	903	10.657	3	-0.657	23	23	23	21	-1.000	1	-1.000	149	29	21
cubic	13.244	-13.657	-4	-2.343	44	-44	44	0	0.000	0	0.000	1.024	96	0
quartic	148.995	10.657	15	-0.657	275	275	275	231	1.000	11	1.000	5.735	415	231
quintic	1.370.754	-4.828	-26	0.828	506	-506	506	0	-0.000	0	-0.000	27.568	1.196	0
sextic	10.737.573	1.000	37	1.000	2.277	2.277	2.277	1.771	-1.000	11	-1.000	117.483	3.979	1.771

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	2	1	2	2	1	4	2	0	1	0	2	3	2	4
quadratic	47	23	35	33	48	68	46	24	25	22	24	64	47	62
cubic	458	434	449	447	760	895	762	370	394	361	407	888	767	890
quartic	5.003	4.704	4.875	4.829	8.952	9.699	8.950	4.467	4.491	4.455	4.501	9.640	8.956	9.638
quintic	43.861	43.562	43.735	43.689	83.917	87.430	83.918	41.839	42.138	41.713	42.265	87.363	83.984	87.364
sextic	340.638	338.062	339.626	339.074	663.724	678.688	663.724	331.746	332.045	331.619	332.171	678.188	663.784	678.188

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)
..3.	A_1gA_1g.	..1.	A_2gA_2g.	..3.	B_1gB_1g.	..3.	B_2gB_2g.	..1.	E_1gE_1g.	..10.	E_2gE_2g.	..3.	E_3gE_3g.	..1.	A_2uA_2u.	..3.	B_2uB_2u.	..6.	E_1uE_1u.
..3.	E_2uE_2u.	..10.	E_3uE_3u.
Subtotal: 47 / 12 / 14
Irrep combinations (i,j) with indices: pos(A_1g) ≤ i ≤ j ≤ pos(E_3u)
Subtotal: 0 / 0 / 91
Total: 47 / 12 / 105

**Contributions to nonvanishing cubic force field constants**
Irrep combinations (i,i,i) with indices: pos(A_1g) ≤ i ≤ pos(E_3u)
..4.	A_1gA_1gA_1g.
Subtotal: 4 / 1 / 14
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A_1g) ≤ i ≤ j ≤ pos(E_3u)
..4.	E_1gE_1gE_2g.	..2.	A_1gA_2gA_2g.	..6.	A_1gB_1gB_1g.	..6.	A_1gB_2gB_2g.	..2.	A_1gE_1gE_1g.	..20.	A_1gE_2gE_2g.	..6.	A_1gE_3gE_3g.	..2.	A_1gA_2uA_2u.	..6.	A_1gB_2uB_2u.	..12.	A_1gE_1uE_1u.
..6.	A_1gE_2uE_2u.	..20.	A_1gE_3uE_3u.	..6.	A_2gE_2gE_2g.	..1.	A_2gE_3gE_3g.	..3.	A_2gE_1uE_1u.	..1.	A_2gE_2uE_2u.	..6.	A_2gE_3uE_3u.	..20.	B_1gE_2gE_2g.	..6.	B_1gE_2uE_2u.	..20.	B_2gE_2gE_2g.
..6.	B_2gE_2uE_2u.	..12.	E_2gE_3gE_3g.	..24.	E_2gE_1uE_1u.	..40.	E_2gE_3uE_3u.
Subtotal: 237 / 24 / 182
Irrep combinations (i,j,k) with indices: pos(A_1g) ≤ i ≤ j ≤ k ≤ pos(E_3u)
..4.	A_2gB_1gB_2g.	..4.	B_1gE_1gE_3g.	..4.	B_1gA_2uB_2u.	..24.	B_1gE_1uE_3u.	..4.	B_2gE_1gE_3g.	..24.	B_2gE_1uE_3u.	..8.	E_1gE_2gE_3g.	..3.	E_1gA_2uE_1u.	..8.	E_1gB_2uE_3u.	..6.	E_1gE_1uE_2u.
..8.	E_1gE_2uE_3u.	..8.	E_2gA_2uE_2u.	..16.	E_2gB_2uE_2u.	..48.	E_2gE_1uE_3u.	..8.	E_3gA_2uE_3u.	..12.	E_3gB_2uE_1u.	..12.	E_3gE_1uE_2u.	..16.	E_3gE_2uE_3u.
Subtotal: 217 / 18 / 364
Total: 458 / 43 / 560

**Contributions to nonvanishing quartic force field constants**
Irrep combinations (i,i,i,i) with indices: pos(A_1g) ≤ i ≤ pos(E_3u)
..5.	A_1gA_1gA_1gA_1g.	..1.	A_2gA_2gA_2gA_2g.	..5.	B_1gB_1gB_1gB_1g.	..5.	B_2gB_2gB_2gB_2g.	..1.	E_1gE_1gE_1gE_1g.	..90.	E_2gE_2gE_2gE_2g.	..6.	E_3gE_3gE_3gE_3g.	..1.	A_2uA_2uA_2uA_2u.	..5.	B_2uB_2uB_2uB_2u.	..21.	E_1uE_1uE_1uE_1u.
..11.	E_2uE_2uE_2uE_2u.	..55.	E_3uE_3uE_3uE_3u.
Subtotal: 206 / 12 / 14
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A_1g) ≤ i ≤ j ≤ pos(E_3u)
..2.	E_1gE_1gE_1gE_3g.	..40.	E_1uE_1uE_1uE_3u.	..4.	E_1gE_3gE_3gE_3g.	..60.	E_1uE_3uE_3uE_3u.
Subtotal: 106 / 4 / 182
Irrep combinations (i,i,j,j) with indices: pos(A_1g) ≤ i ≤ j ≤ pos(E_3u)
..3.	A_1gA_1gA_2gA_2g.	..9.	A_1gA_1gB_1gB_1g.	..9.	A_1gA_1gB_2gB_2g.	..3.	A_1gA_1gE_1gE_1g.	..30.	A_1gA_1gE_2gE_2g.	..9.	A_1gA_1gE_3gE_3g.	..3.	A_1gA_1gA_2uA_2u.	..9.	A_1gA_1gB_2uB_2u.	..18.	A_1gA_1gE_1uE_1u.	..9.	A_1gA_1gE_2uE_2u.
..30.	A_1gA_1gE_3uE_3u.	..3.	A_2gA_2gB_1gB_1g.	..3.	A_2gA_2gB_2gB_2g.	..1.	A_2gA_2gE_1gE_1g.	..10.	A_2gA_2gE_2gE_2g.	..3.	A_2gA_2gE_3gE_3g.	..1.	A_2gA_2gA_2uA_2u.	..3.	A_2gA_2gB_2uB_2u.	..6.	A_2gA_2gE_1uE_1u.	..3.	A_2gA_2gE_2uE_2u.
..10.	A_2gA_2gE_3uE_3u.	..9.	B_1gB_1gB_2gB_2g.	..3.	B_1gB_1gE_1gE_1g.	..30.	B_1gB_1gE_2gE_2g.	..9.	B_1gB_1gE_3gE_3g.	..3.	B_1gB_1gA_2uA_2u.	..9.	B_1gB_1gB_2uB_2u.	..18.	B_1gB_1gE_1uE_1u.	..9.	B_1gB_1gE_2uE_2u.	..30.	B_1gB_1gE_3uE_3u.
..3.	B_2gB_2gE_1gE_1g.	..30.	B_2gB_2gE_2gE_2g.	..9.	B_2gB_2gE_3gE_3g.	..3.	B_2gB_2gA_2uA_2u.	..9.	B_2gB_2gB_2uB_2u.	..18.	B_2gB_2gE_1uE_1u.	..9.	B_2gB_2gE_2uE_2u.	..30.	B_2gB_2gE_3uE_3u.	..10.	E_1gE_1gE_2gE_2g.	..6.	E_1gE_1gE_3gE_3g.
..1.	E_1gE_1gA_2uA_2u.	..3.	E_1gE_1gB_2uB_2u.	..12.	E_1gE_1gE_1uE_1u.	..3.	E_1gE_1gE_2uE_2u.	..20.	E_1gE_1gE_3uE_3u.	..36.	E_2gE_2gE_3gE_3g.	..10.	E_2gE_2gA_2uA_2u.	..30.	E_2gE_2gB_2uB_2u.	..78.	E_2gE_2gE_1uE_1u.	..96.	E_2gE_2gE_2uE_2u.
..136.	E_2gE_2gE_3uE_3u.	..3.	E_3gE_3gA_2uA_2u.	..9.	E_3gE_3gB_2uB_2u.	..39.	E_3gE_3gE_1uE_1u.	..10.	E_3gE_3gE_2uE_2u.	..66.	E_3gE_3gE_3uE_3u.	..3.	A_2uA_2uB_2uB_2u.	..6.	A_2uA_2uE_1uE_1u.	..3.	A_2uA_2uE_2uE_2u.	..10.	A_2uA_2uE_3uE_3u.
..18.	B_2uB_2uE_1uE_1u.	..9.	B_2uB_2uE_2uE_2u.	..30.	B_2uB_2uE_3uE_3u.	..21.	E_1uE_1uE_2uE_2u.	..138.	E_1uE_1uE_3uE_3u.	..36.	E_2uE_2uE_3uE_3u.
Subtotal: 1.248 / 66 / 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)
..2.	E_1gE_1gA_2uE_2u.	..4.	E_1gE_1gB_2uE_2u.	..12.	E_1gE_1gE_1uE_3u.	..20.	E_2gE_2gA_2uB_2u.	..240.	E_2gE_2gE_1uE_3u.	..6.	E_3gE_3gA_2uE_2u.	..12.	E_3gE_3gB_2uE_2u.	..36.	E_3gE_3gE_1uE_3u.	..8.	A_1gE_1gE_1gE_2g.	..4.	A_2gE_1gE_1gE_2g.
..8.	B_1gE_1gE_1gE_2g.	..8.	B_2gE_1gE_1gE_2g.	..40.	E_1gE_2gE_2gE_3g.	..12.	A_2uE_1uE_1uE_2u.	..24.	B_2uE_1uE_1uE_2u.	..72.	E_1uE_2uE_2uE_3u.	..12.	A_1gA_2gE_2gE_2g.	..2.	A_1gA_2gE_3gE_3g.	..6.	A_1gA_2gE_1uE_1u.	..2.	A_1gA_2gE_2uE_2u.
..12.	A_1gA_2gE_3uE_3u.	..40.	A_1gB_1gE_2gE_2g.	..12.	A_1gB_1gE_2uE_2u.	..40.	A_1gB_2gE_2gE_2g.	..12.	A_1gB_2gE_2uE_2u.	..24.	A_1gE_2gE_3gE_3g.	..48.	A_1gE_2gE_1uE_1u.	..80.	A_1gE_2gE_3uE_3u.	..20.	A_2gB_1gE_2gE_2g.	..6.	A_2gB_1gE_2uE_2u.
..20.	A_2gB_2gE_2gE_2g.	..6.	A_2gB_2gE_2uE_2u.	..12.	A_2gE_2gE_3gE_3g.	..24.	A_2gE_2gE_1uE_1u.	..40.	A_2gE_2gE_3uE_3u.	..24.	B_1gB_2gE_2gE_2g.	..4.	B_1gB_2gE_3gE_3g.	..12.	B_1gB_2gE_1uE_1u.	..4.	B_1gB_2gE_2uE_2u.	..24.	B_1gB_2gE_3uE_3u.
..24.	B_1gE_2gE_3gE_3g.	..48.	B_1gE_2gE_1uE_1u.	..80.	B_1gE_2gE_3uE_3u.	..24.	B_2gE_2gE_3gE_3g.	..48.	B_2gE_2gE_1uE_1u.	..80.	B_2gE_2gE_3uE_3u.	..12.	E_1gE_3gE_1uE_1u.	..12.	E_1gE_3gE_2uE_2u.	..20.	E_1gE_3gE_3uE_3u.	..6.	A_2uB_2uE_2uE_2u.
..20.	A_2uE_2uE_3uE_3u.	..40.	B_2uE_2uE_3uE_3u.
Subtotal: 1.408 / 52 / 1.092
Irrep combinations (i,j,k,l) with indices: pos(A_1g) ≤ i ≤ j ≤ k ≤ l ≤ pos(E_3u)
..8.	A_1gA_2gB_1gB_2g.	..8.	A_1gB_1gE_1gE_3g.	..8.	A_1gB_1gA_2uB_2u.	..48.	A_1gB_1gE_1uE_3u.	..8.	A_1gB_2gE_1gE_3g.	..48.	A_1gB_2gE_1uE_3u.	..16.	A_1gE_1gE_2gE_3g.	..6.	A_1gE_1gA_2uE_1u.	..16.	A_1gE_1gB_2uE_3u.	..12.	A_1gE_1gE_1uE_2u.
..16.	A_1gE_1gE_2uE_3u.	..16.	A_1gE_2gA_2uE_2u.	..32.	A_1gE_2gB_2uE_2u.	..96.	A_1gE_2gE_1uE_3u.	..16.	A_1gE_3gA_2uE_3u.	..24.	A_1gE_3gB_2uE_1u.	..24.	A_1gE_3gE_1uE_2u.	..32.	A_1gE_3gE_2uE_3u.	..4.	A_2gB_1gE_1gE_3g.	..24.	A_2gB_1gE_1uE_3u.
..4.	A_2gB_2gE_1gE_3g.	..4.	A_2gB_2gA_2uB_2u.	..24.	A_2gB_2gE_1uE_3u.	..8.	A_2gE_1gE_2gE_3g.	..3.	A_2gE_1gA_2uE_1u.	..8.	A_2gE_1gB_2uE_3u.	..6.	A_2gE_1gE_1uE_2u.	..8.	A_2gE_1gE_2uE_3u.	..8.	A_2gE_2gA_2uE_2u.	..16.	A_2gE_2gB_2uE_2u.
..48.	A_2gE_2gE_1uE_3u.	..8.	A_2gE_3gA_2uE_3u.	..12.	A_2gE_3gB_2uE_1u.	..12.	A_2gE_3gE_1uE_2u.	..16.	A_2gE_3gE_2uE_3u.	..16.	B_1gE_1gE_2gE_3g.	..8.	B_1gE_1gA_2uE_3u.	..12.	B_1gE_1gB_2uE_1u.	..12.	B_1gE_1gE_1uE_2u.	..16.	B_1gE_1gE_2uE_3u.
..16.	B_1gE_2gA_2uE_2u.	..32.	B_1gE_2gB_2uE_2u.	..96.	B_1gE_2gE_1uE_3u.	..12.	B_1gE_3gA_2uE_1u.	..32.	B_1gE_3gB_2uE_3u.	..24.	B_1gE_3gE_1uE_2u.	..32.	B_1gE_3gE_2uE_3u.	..16.	B_2gE_1gE_2gE_3g.	..8.	B_2gE_1gA_2uE_3u.	..12.	B_2gE_1gB_2uE_1u.
..12.	B_2gE_1gE_1uE_2u.	..16.	B_2gE_1gE_2uE_3u.	..16.	B_2gE_2gA_2uE_2u.	..32.	B_2gE_2gB_2uE_2u.	..96.	B_2gE_2gE_1uE_3u.	..12.	B_2gE_3gA_2uE_1u.	..32.	B_2gE_3gB_2uE_3u.	..24.	B_2gE_3gE_1uE_2u.	..32.	B_2gE_3gE_2uE_3u.	..12.	E_1gE_2gA_2uE_1u.
..16.	E_1gE_2gA_2uE_3u.	..24.	E_1gE_2gB_2uE_1u.	..32.	E_1gE_2gB_2uE_3u.	..48.	E_1gE_2gE_1uE_2u.	..64.	E_1gE_2gE_2uE_3u.	..4.	E_1gE_3gA_2uB_2u.	..4.	E_1gE_3gA_2uE_2u.	..8.	E_1gE_3gB_2uE_2u.	..72.	E_1gE_3gE_1uE_3u.	..24.	E_2gE_3gA_2uE_1u.
..32.	E_2gE_3gA_2uE_3u.	..48.	E_2gE_3gB_2uE_1u.	..64.	E_2gE_3gB_2uE_3u.	..96.	E_2gE_3gE_1uE_2u.	..128.	E_2gE_3gE_2uE_3u.	..24.	A_2uB_2uE_1uE_3u.	..24.	A_2uE_1uE_2uE_3u.	..48.	B_2uE_1uE_2uE_3u.
Subtotal: 2.035 / 78 / 1.001
Total: 5.003 / 212 / 2.380

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Results for Point Group D8h

Force field analysis

Further Reading

Contributions to nonvanishing force field constants

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Results for Point Group D_8h