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	48	0	0	0	0	0	0	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	42	2	2	2	0	0	0	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	6	6	6	6	6	6	6	6	48
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	6	5	5	5	6	5	5	5	42

**Molecular parameter**
Number of Atoms (N)	16
Number of internal coordinates	42
Number of independant internal coordinates	6
Number of vibrational modes	42

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)	6	5	5	5	6	5	5	5	15 / 27
Quadratic (Raman)	6	5	5	5	6	5	5	5	21 / 21
IR + Raman	- - - -	- - - -	- - - -	- - - -	6	- - - -	- - - -	- - - -	0^* / 6

* 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	42	2	2	2	0	0	0	0
quadratic	903	23	23	23	21	21	21	21
cubic	13.244	44	44	44	0	0	0	0
quartic	148.995	275	275	275	231	231	231	231
quintic	1.370.754	506	506	506	0	0	0	0
sextic	10.737.573	2.277	2.277	2.277	1.771	1.771	1.771	1.771

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	6	5	5	5	6	5	5	5
quadratic	132	110	110	110	111	110	110	110
cubic	1.672	1.650	1.650	1.650	1.672	1.650	1.650	1.650
quartic	18.843	18.590	18.590	18.590	18.612	18.590	18.590	18.590
quintic	171.534	171.281	171.281	171.281	171.534	171.281	171.281	171.281
sextic	1.343.936	1.341.912	1.341.912	1.341.912	1.342.165	1.341.912	1.341.912	1.341.912

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)
..21.	A_1gA_1g.	..15.	B_1gB_1g.	..15.	B_2gB_2g.	..15.	B_3gB_3g.	..21.	A_1uA_1u.	..15.	B_1uB_1u.	..15.	B_2uB_2u.	..15.	B_3uB_3u.
Subtotal: 132 / 8 / 8
Irrep combinations (i,j) with indices: pos(A_1g) ≤ i ≤ j ≤ pos(B_3u)
Subtotal: 0 / 0 / 28
Total: 132 / 8 / 36

**Contributions to nonvanishing cubic force field constants**
Irrep combinations (i,i,i) with indices: pos(A_1g) ≤ i ≤ pos(B_3u)
..56.	A_1gA_1gA_1g.
Subtotal: 56 / 1 / 8
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A_1g) ≤ i ≤ j ≤ pos(B_3u)
..90.	A_1gB_1gB_1g.	..90.	A_1gB_2gB_2g.	..90.	A_1gB_3gB_3g.	..126.	A_1gA_1uA_1u.	..90.	A_1gB_1uB_1u.	..90.	A_1gB_2uB_2u.	..90.	A_1gB_3uB_3u.
Subtotal: 666 / 7 / 56
Irrep combinations (i,j,k) with indices: pos(A_1g) ≤ i ≤ j ≤ k ≤ pos(B_3u)
..125.	B_1gB_2gB_3g.	..150.	B_1gA_1uB_1u.	..125.	B_1gB_2uB_3u.	..150.	B_2gA_1uB_2u.	..125.	B_2gB_1uB_3u.	..150.	B_3gA_1uB_3u.	..125.	B_3gB_1uB_2u.
Subtotal: 950 / 7 / 56
Total: 1.672 / 15 / 120

**Contributions to nonvanishing quartic force field constants**
Irrep combinations (i,i,i,i) with indices: pos(A_1g) ≤ i ≤ pos(B_3u)
..126.	A_1gA_1gA_1gA_1g.	..70.	B_1gB_1gB_1gB_1g.	..70.	B_2gB_2gB_2gB_2g.	..70.	B_3gB_3gB_3gB_3g.	..126.	A_1uA_1uA_1uA_1u.	..70.	B_1uB_1uB_1uB_1u.	..70.	B_2uB_2uB_2uB_2u.	..70.	B_3uB_3uB_3uB_3u.
Subtotal: 672 / 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)
..315.	A_1gA_1gB_1gB_1g.	..315.	A_1gA_1gB_2gB_2g.	..315.	A_1gA_1gB_3gB_3g.	..441.	A_1gA_1gA_1uA_1u.	..315.	A_1gA_1gB_1uB_1u.	..315.	A_1gA_1gB_2uB_2u.	..315.	A_1gA_1gB_3uB_3u.	..225.	B_1gB_1gB_2gB_2g.	..225.	B_1gB_1gB_3gB_3g.	..315.	B_1gB_1gA_1uA_1u.
..225.	B_1gB_1gB_1uB_1u.	..225.	B_1gB_1gB_2uB_2u.	..225.	B_1gB_1gB_3uB_3u.	..225.	B_2gB_2gB_3gB_3g.	..315.	B_2gB_2gA_1uA_1u.	..225.	B_2gB_2gB_1uB_1u.	..225.	B_2gB_2gB_2uB_2u.	..225.	B_2gB_2gB_3uB_3u.	..315.	B_3gB_3gA_1uA_1u.	..225.	B_3gB_3gB_1uB_1u.
..225.	B_3gB_3gB_2uB_2u.	..225.	B_3gB_3gB_3uB_3u.	..315.	A_1uA_1uB_1uB_1u.	..315.	A_1uA_1uB_2uB_2u.	..315.	A_1uA_1uB_3uB_3u.	..225.	B_1uB_1uB_2uB_2u.	..225.	B_1uB_1uB_3uB_3u.	..225.	B_2uB_2uB_3uB_3u.
Subtotal: 7.596 / 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)
..750.	A_1gB_1gB_2gB_3g.	..900.	A_1gB_1gA_1uB_1u.	..750.	A_1gB_1gB_2uB_3u.	..900.	A_1gB_2gA_1uB_2u.	..750.	A_1gB_2gB_1uB_3u.	..900.	A_1gB_3gA_1uB_3u.	..750.	A_1gB_3gB_1uB_2u.	..750.	B_1gB_2gA_1uB_3u.	..625.	B_1gB_2gB_1uB_2u.	..750.	B_1gB_3gA_1uB_2u.
..625.	B_1gB_3gB_1uB_3u.	..750.	B_2gB_3gA_1uB_1u.	..625.	B_2gB_3gB_2uB_3u.	..750.	A_1uB_1uB_2uB_3u.
Subtotal: 10.575 / 14 / 70
Total: 18.843 / 50 / 330

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Results for Point Group D2h

Force field analysis

Further Reading

Contributions to nonvanishing force field constants

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Results for Point Group D_2h