Results for Point Group D2h



Characters of representations for molecular motions
Motion E C2.(z) C2.(y) C2.(x) i σ.(xy) σ.(xy) σ.(xy)
Cartesian 3N 21 -3 -1 -1 -3 5 3 3
Translation (x,y,z) 3 -1 -1 -1 -3 1 1 1
Rotation (Rx,Ry,Rz) 3 -1 -1 -1 3 -1 -1 -1
Vibration 15 -1 1 1 -3 5 3 3


Decomposition to irreducible representations
Motion A1g B1g B2g B3g A1u B1u B2u B3u Total
Cartesian 3N 3 2 2 2 1 3 4 4 21
Translation (x,y,z) 0 0 0 0 0 1 1 1 3
Rotation (Rx,Ry,Rz) 0 1 1 1 0 0 0 0 3
Vibration 3 1 1 1 1 2 3 3 15



Molecular parameter
Number of Atoms (N) 7
Number of internal coordinates 15
Number of independant internal coordinates 3
Number of vibrational modes 15

Force field analysis


Allowed / forbidden vibronational transitions
Operator A1g B1g B2g B3g A1u B1u B2u B3u Total
Linear (IR) 3 1 1 1 1 2 3 3 8 / 7
Quadratic (Raman) 3 1 1 1 1 2 3 3 6 / 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 15 -1 1 1 -3 5 3 3
quadratic 120 8 8 8 12 20 12 12
cubic 680 -8 8 8 -28 60 28 28
quartic 3.060 36 36 36 72 160 72 72
quintic 11.628 -36 36 36 -144 376 144 144
sextic 38.760 120 120 120 300 820 300 300


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A1g B1g B2g B3g A1u B1u B2u B3u
linear 3 1 1 1 1 2 3 3
quadratic 25 15 13 13 11 13 15 15
cubic 97 79 75 75 75 85 97 97
quartic 443 389 367 367 349 367 389 389
quintic 1.523 1.433 1.393 1.393 1.393 1.447 1.523 1.523
sextic 5.105 4.895 4.765 4.765 4.675 4.765 4.895 4.895


Further Reading


Contributions to nonvanishing force field constants


pos(X) : Position of irreducible representation (irrep) X in character table of D2h

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(A1g) ≤ i ≤ pos(B3u)
..6. A1gA1g...1. B1gB1g...1. B2gB2g...1. B3gB3g...1. A1uA1u...3. B1uB1u...6. B2uB2u...6. B3uB3u.
Subtotal: 25 / 8 / 8
Irrep combinations (i,j) with indices: pos(A1g) ≤ i ≤ j ≤ pos(B3u)
Subtotal: 0 / 0 / 28
Total: 25 / 8 / 36


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A1g) ≤ i ≤ pos(B3u)
..10. A1gA1gA1g.
Subtotal: 10 / 1 / 8
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A1g) ≤ i ≤ j ≤ pos(B3u)
..3. A1gB1gB1g...3. A1gB2gB2g...3. A1gB3gB3g...3. A1gA1uA1u...9. A1gB1uB1u...18. A1gB2uB2u...18. A1gB3uB3u.
Subtotal: 57 / 7 / 56
Irrep combinations (i,j,k) with indices: pos(A1g) ≤ i ≤ j ≤ k ≤ pos(B3u)
..1. B1gB2gB3g...2. B1gA1uB1u...9. B1gB2uB3u...3. B2gA1uB2u...6. B2gB1uB3u...3. B3gA1uB3u...6. B3gB1uB2u.
Subtotal: 30 / 7 / 56
Total: 97 / 15 / 120


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A1g) ≤ i ≤ pos(B3u)
..15. A1gA1gA1gA1g...1. B1gB1gB1gB1g...1. B2gB2gB2gB2g...1. B3gB3gB3gB3g...1. A1uA1uA1uA1u...5. B1uB1uB1uB1u...15. B2uB2uB2uB2u...15. B3uB3uB3uB3u.
Subtotal: 54 / 8 / 8
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A1g) ≤ i ≤ j ≤ pos(B3u)
Subtotal: 0 / 0 / 56
Irrep combinations (i,i,j,j) with indices: pos(A1g) ≤ i ≤ j ≤ pos(B3u)
..6. A1gA1gB1gB1g...6. A1gA1gB2gB2g...6. A1gA1gB3gB3g...6. A1gA1gA1uA1u...18. A1gA1gB1uB1u...36. A1gA1gB2uB2u...36. A1gA1gB3uB3u...1. B1gB1gB2gB2g...1. B1gB1gB3gB3g...1. B1gB1gA1uA1u.
..3. B1gB1gB1uB1u...6. B1gB1gB2uB2u...6. B1gB1gB3uB3u...1. B2gB2gB3gB3g...1. B2gB2gA1uA1u...3. B2gB2gB1uB1u...6. B2gB2gB2uB2u...6. B2gB2gB3uB3u...1. B3gB3gA1uA1u...3. B3gB3gB1uB1u.
..6. B3gB3gB2uB2u...6. B3gB3gB3uB3u...3. A1uA1uB1uB1u...6. A1uA1uB2uB2u...6. A1uA1uB3uB3u...18. B1uB1uB2uB2u...18. B1uB1uB3uB3u...36. B2uB2uB3uB3u.
Subtotal: 252 / 28 / 28
Irrep combinations (i,i,j,k) (i,j,j,k) (i,j,k,k) with indices: pos(A1g) ≤ i ≤ j ≤ k ≤ pos(B3u)
Subtotal: 0 / 0 / 168
Irrep combinations (i,j,k,l) with indices: pos(A1g) ≤ i ≤ j ≤ k ≤ l ≤ pos(B3u)
..3. A1gB1gB2gB3g...6. A1gB1gA1uB1u...27. A1gB1gB2uB3u...9. A1gB2gA1uB2u...18. A1gB2gB1uB3u...9. A1gB3gA1uB3u...18. A1gB3gB1uB2u...3. B1gB2gA1uB3u...6. B1gB2gB1uB2u...3. B1gB3gA1uB2u.
..6. B1gB3gB1uB3u...2. B2gB3gA1uB1u...9. B2gB3gB2uB3u...18. A1uB1uB2uB3u.
Subtotal: 137 / 14 / 70
Total: 443 / 50 / 330


Calculate contributions to

A1g B1g B2g B3g A1u B1u B2u B3u
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Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement