Point Group D2h

Results for Point Group D_2h

**Characters of representations for molecular motions**
Motion	E	C₂.(z)	C₂.(y)	C₂.(x)	i	σ.(xy)	σ.(xy)	σ.(xy)
Cartesian 3N	24	0	-2	-2	0	4	6	2
Translation (x,y,z)	3	-1	-1	-1	-3	1	1	1
Rotation (R_x,R_y,R_z)	3	-1	-1	-1	3	-1	-1	-1
Vibration	18	2	0	0	0	4	6	2

**Decomposition to irreducible representations**
Motion	A_1g	B_1g	B_2g	B_3g	A_1u	B_1u	B_2u	B_3u	Total
Cartesian 3N	4	3	3	2	1	4	3	4	24
Translation (x,y,z)	0	0	0	0	0	1	1	1	3
Rotation (R_x,R_y,R_z)	0	1	1	1	0	0	0	0	3
Vibration	4	2	2	1	1	3	2	3	18

**Molecular parameter**
Number of Atoms (N)	8
Number of internal coordinates	18
Number of independant internal coordinates	4
Number of vibrational modes	18

Force field analysis

**Allowed / forbidden vibronational transitions**
Operator	A_1g	B_1g	B_2g	B_3g	A_1u	B_1u	B_2u	B_3u	Total
Linear (IR)	4	2	2	1	1	3	2	3	8 / 10
Quadratic (Raman)	4	2	2	1	1	3	2	3	9 / 9
IR + Raman	- - - -	- - - -	- - - -	- - - -	1	- - - -	- - - -	- - - -	0^* / 1

* Parity Mutual Exclusion Principle

Characters of force fields
(Symmetric powers of vibration representation)
Force field	E	C₂.(z)	C₂.(y)	C₂.(x)	i	σ.(xy)	σ.(xy)	σ.(xy)
linear	18	2	0	0	0	4	6	2
quadratic	171	11	9	9	9	17	27	11
cubic	1.140	20	0	0	0	48	92	20
quartic	5.985	65	45	45	45	133	273	65
quintic	26.334	110	0	0	0	308	714	110
sextic	100.947	275	165	165	165	693	1.715	275

Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field	A_1g	B_1g	B_2g	B_3g	A_1u	B_1u	B_2u	B_3u
linear	4	2	2	1	1	3	2	3
quadratic	33	19	21	17	17	22	19	23
cubic	165	137	143	125	125	153	137	155
quartic	832	725	755	703	703	765	725	777
quintic	3.447	3.241	3.315	3.164	3.164	3.370	3.241	3.392
sextic	13.050	12.470	12.698	12.338	12.338	12.753	12.470	12.830

Contributions to nonvanishing force field constants

pos(X) : Position of irreducible representation (irrep) X in character table of D_2h

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(B_3u)
..10.	A_1gA_1g.	..3.	B_1gB_1g.	..3.	B_2gB_2g.	..1.	B_3gB_3g.	..1.	A_1uA_1u.	..6.	B_1uB_1u.	..3.	B_2uB_2u.	..6.	B_3uB_3u.
Subtotal: 33 / 8 / 8
Irrep combinations (i,j) with indices: pos(A_1g) ≤ i ≤ j ≤ pos(B_3u)
Subtotal: 0 / 0 / 28
Total: 33 / 8 / 36

**Contributions to nonvanishing cubic force field constants**
Irrep combinations (i,i,i) with indices: pos(A_1g) ≤ i ≤ pos(B_3u)
..20.	A_1gA_1gA_1g.
Subtotal: 20 / 1 / 8
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A_1g) ≤ i ≤ j ≤ pos(B_3u)
..12.	A_1gB_1gB_1g.	..12.	A_1gB_2gB_2g.	..4.	A_1gB_3gB_3g.	..4.	A_1gA_1uA_1u.	..24.	A_1gB_1uB_1u.	..12.	A_1gB_2uB_2u.	..24.	A_1gB_3uB_3u.
Subtotal: 92 / 7 / 56
Irrep combinations (i,j,k) with indices: pos(A_1g) ≤ i ≤ j ≤ k ≤ pos(B_3u)
..4.	B_1gB_2gB_3g.	..6.	B_1gA_1uB_1u.	..12.	B_1gB_2uB_3u.	..4.	B_2gA_1uB_2u.	..18.	B_2gB_1uB_3u.	..3.	B_3gA_1uB_3u.	..6.	B_3gB_1uB_2u.
Subtotal: 53 / 7 / 56
Total: 165 / 15 / 120

**Contributions to nonvanishing quartic force field constants**
Irrep combinations (i,i,i,i) with indices: pos(A_1g) ≤ i ≤ pos(B_3u)
..35.	A_1gA_1gA_1gA_1g.	..5.	B_1gB_1gB_1gB_1g.	..5.	B_2gB_2gB_2gB_2g.	..1.	B_3gB_3gB_3gB_3g.	..1.	A_1uA_1uA_1uA_1u.	..15.	B_1uB_1uB_1uB_1u.	..5.	B_2uB_2uB_2uB_2u.	..15.	B_3uB_3uB_3uB_3u.
Subtotal: 82 / 8 / 8
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A_1g) ≤ i ≤ j ≤ pos(B_3u)
Subtotal: 0 / 0 / 56
Irrep combinations (i,i,j,j) with indices: pos(A_1g) ≤ i ≤ j ≤ pos(B_3u)
..30.	A_1gA_1gB_1gB_1g.	..30.	A_1gA_1gB_2gB_2g.	..10.	A_1gA_1gB_3gB_3g.	..10.	A_1gA_1gA_1uA_1u.	..60.	A_1gA_1gB_1uB_1u.	..30.	A_1gA_1gB_2uB_2u.	..60.	A_1gA_1gB_3uB_3u.	..9.	B_1gB_1gB_2gB_2g.	..3.	B_1gB_1gB_3gB_3g.	..3.	B_1gB_1gA_1uA_1u.
..18.	B_1gB_1gB_1uB_1u.	..9.	B_1gB_1gB_2uB_2u.	..18.	B_1gB_1gB_3uB_3u.	..3.	B_2gB_2gB_3gB_3g.	..3.	B_2gB_2gA_1uA_1u.	..18.	B_2gB_2gB_1uB_1u.	..9.	B_2gB_2gB_2uB_2u.	..18.	B_2gB_2gB_3uB_3u.	..1.	B_3gB_3gA_1uA_1u.	..6.	B_3gB_3gB_1uB_1u.
..3.	B_3gB_3gB_2uB_2u.	..6.	B_3gB_3gB_3uB_3u.	..6.	A_1uA_1uB_1uB_1u.	..3.	A_1uA_1uB_2uB_2u.	..6.	A_1uA_1uB_3uB_3u.	..18.	B_1uB_1uB_2uB_2u.	..36.	B_1uB_1uB_3uB_3u.	..18.	B_2uB_2uB_3uB_3u.
Subtotal: 444 / 28 / 28
Irrep combinations (i,i,j,k) (i,j,j,k) (i,j,k,k) with indices: pos(A_1g) ≤ i ≤ j ≤ k ≤ pos(B_3u)
Subtotal: 0 / 0 / 168
Irrep combinations (i,j,k,l) with indices: pos(A_1g) ≤ i ≤ j ≤ k ≤ l ≤ pos(B_3u)
..16.	A_1gB_1gB_2gB_3g.	..24.	A_1gB_1gA_1uB_1u.	..48.	A_1gB_1gB_2uB_3u.	..16.	A_1gB_2gA_1uB_2u.	..72.	A_1gB_2gB_1uB_3u.	..12.	A_1gB_3gA_1uB_3u.	..24.	A_1gB_3gB_1uB_2u.	..12.	B_1gB_2gA_1uB_3u.	..24.	B_1gB_2gB_1uB_2u.	..4.	B_1gB_3gA_1uB_2u.
..18.	B_1gB_3gB_1uB_3u.	..6.	B_2gB_3gA_1uB_1u.	..12.	B_2gB_3gB_2uB_3u.	..18.	A_1uB_1uB_2uB_3u.
Subtotal: 306 / 14 / 70
Total: 832 / 50 / 330

Calculate contributions to

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

Results for Point Group D2h

Force field analysis

Further Reading

Contributions to nonvanishing force field constants

Calculate contributions to

Results for Point Group D_2h