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	60	0	0	0	0	12	8	0
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	54	2	2	2	0	12	8	0

**Decomposition to irreducible representations**
Motion	A_1g	B_1g	B_2g	B_3g	A_1u	B_1u	B_2u	B_3u	Total
Cartesian 3N	10	8	7	5	5	7	8	10	60
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	10	7	6	4	5	6	7	9	54

**Molecular parameter**
Number of Atoms (N)	20
Number of internal coordinates	54
Number of independant internal coordinates	10
Number of vibrational modes	54

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)	10	7	6	4	5	6	7	9	22 / 32
Quadratic (Raman)	10	7	6	4	5	6	7	9	27 / 27
IR + Raman	- - - -	- - - -	- - - -	- - - -	5	- - - -	- - - -	- - - -	0^* / 5

* 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	54	2	2	2	0	12	8	0
quadratic	1.485	29	29	29	27	99	59	27
cubic	27.720	56	56	56	0	616	304	0
quartic	395.010	434	434	434	378	3.234	1.434	378
quintic	4.582.116	812	812	812	0	14.784	5.760	0
sextic	45.057.474	4.466	4.466	4.466	3.654	60.830	21.542	3.654

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	10	7	6	4	5	6	7	9
quadratic	223	187	177	169	170	177	187	195
cubic	3.601	3.497	3.419	3.343	3.371	3.419	3.497	3.573
quartic	50.217	49.547	49.097	48.833	48.861	49.097	49.547	49.811
quintic	575.637	573.791	571.535	570.095	570.501	571.535	573.791	575.231
sextic	5.645.069	5.636.537	5.626.715	5.622.243	5.622.649	5.626.715	5.636.537	5.641.009

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)
..55.	A_1gA_1g.	..28.	B_1gB_1g.	..21.	B_2gB_2g.	..10.	B_3gB_3g.	..15.	A_1uA_1u.	..21.	B_1uB_1u.	..28.	B_2uB_2u.	..45.	B_3uB_3u.
Subtotal: 223 / 8 / 8
Irrep combinations (i,j) with indices: pos(A_1g) ≤ i ≤ j ≤ pos(B_3u)
Subtotal: 0 / 0 / 28
Total: 223 / 8 / 36

**Contributions to nonvanishing cubic force field constants**
Irrep combinations (i,i,i) with indices: pos(A_1g) ≤ i ≤ pos(B_3u)
..220.	A_1gA_1gA_1g.
Subtotal: 220 / 1 / 8
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A_1g) ≤ i ≤ j ≤ pos(B_3u)
..280.	A_1gB_1gB_1g.	..210.	A_1gB_2gB_2g.	..100.	A_1gB_3gB_3g.	..150.	A_1gA_1uA_1u.	..210.	A_1gB_1uB_1u.	..280.	A_1gB_2uB_2u.	..450.	A_1gB_3uB_3u.
Subtotal: 1.680 / 7 / 56
Irrep combinations (i,j,k) with indices: pos(A_1g) ≤ i ≤ j ≤ k ≤ pos(B_3u)
..168.	B_1gB_2gB_3g.	..210.	B_1gA_1uB_1u.	..441.	B_1gB_2uB_3u.	..210.	B_2gA_1uB_2u.	..324.	B_2gB_1uB_3u.	..180.	B_3gA_1uB_3u.	..168.	B_3gB_1uB_2u.
Subtotal: 1.701 / 7 / 56
Total: 3.601 / 15 / 120

**Contributions to nonvanishing quartic force field constants**
Irrep combinations (i,i,i,i) with indices: pos(A_1g) ≤ i ≤ pos(B_3u)
..715.	A_1gA_1gA_1gA_1g.	..210.	B_1gB_1gB_1gB_1g.	..126.	B_2gB_2gB_2gB_2g.	..35.	B_3gB_3gB_3gB_3g.	..70.	A_1uA_1uA_1uA_1u.	..126.	B_1uB_1uB_1uB_1u.	..210.	B_2uB_2uB_2uB_2u.	..495.	B_3uB_3uB_3uB_3u.
Subtotal: 1.987 / 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)
..1.540.	A_1gA_1gB_1gB_1g.	..1.155.	A_1gA_1gB_2gB_2g.	..550.	A_1gA_1gB_3gB_3g.	..825.	A_1gA_1gA_1uA_1u.	..1.155.	A_1gA_1gB_1uB_1u.	..1.540.	A_1gA_1gB_2uB_2u.	..2.475.	A_1gA_1gB_3uB_3u.	..588.	B_1gB_1gB_2gB_2g.	..280.	B_1gB_1gB_3gB_3g.	..420.	B_1gB_1gA_1uA_1u.
..588.	B_1gB_1gB_1uB_1u.	..784.	B_1gB_1gB_2uB_2u.	..1.260.	B_1gB_1gB_3uB_3u.	..210.	B_2gB_2gB_3gB_3g.	..315.	B_2gB_2gA_1uA_1u.	..441.	B_2gB_2gB_1uB_1u.	..588.	B_2gB_2gB_2uB_2u.	..945.	B_2gB_2gB_3uB_3u.	..150.	B_3gB_3gA_1uA_1u.	..210.	B_3gB_3gB_1uB_1u.
..280.	B_3gB_3gB_2uB_2u.	..450.	B_3gB_3gB_3uB_3u.	..315.	A_1uA_1uB_1uB_1u.	..420.	A_1uA_1uB_2uB_2u.	..675.	A_1uA_1uB_3uB_3u.	..588.	B_1uB_1uB_2uB_2u.	..945.	B_1uB_1uB_3uB_3u.	..1.260.	B_2uB_2uB_3uB_3u.
Subtotal: 20.952 / 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)
..1.680.	A_1gB_1gB_2gB_3g.	..2.100.	A_1gB_1gA_1uB_1u.	..4.410.	A_1gB_1gB_2uB_3u.	..2.100.	A_1gB_2gA_1uB_2u.	..3.240.	A_1gB_2gB_1uB_3u.	..1.800.	A_1gB_3gA_1uB_3u.	..1.680.	A_1gB_3gB_1uB_2u.	..1.890.	B_1gB_2gA_1uB_3u.	..1.764.	B_1gB_2gB_1uB_2u.	..980.	B_1gB_3gA_1uB_2u.
..1.512.	B_1gB_3gB_1uB_3u.	..720.	B_2gB_3gA_1uB_1u.	..1.512.	B_2gB_3gB_2uB_3u.	..1.890.	A_1uB_1uB_2uB_3u.
Subtotal: 27.278 / 14 / 70
Total: 50.217 / 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