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 36 -4 -4 -4 0 8 8 8
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 30 -2 -2 -2 0 8 8 8


Decomposition to irreducible representations
Motion A1g B1g B2g B3g A1u B1u B2u B3u Total
Cartesian 3N 6 4 4 4 0 6 6 6 36
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 6 3 3 3 0 5 5 5 30



Molecular parameter
Number of Atoms (N) 12
Number of internal coordinates 30
Number of independant internal coordinates 6
Number of vibrational modes 30

Force field analysis


Allowed / forbidden vibronational transitions
Operator A1g B1g B2g B3g A1u B1u B2u B3u Total
Linear (IR) 6 3 3 3 0 5 5 5 15 / 15
Quadratic (Raman) 6 3 3 3 0 5 5 5 15 / 15
IR + Raman - - - - - - - - - - - - - - - - 0 - - - - - - - - - - - - 0* / 0
* 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 30 -2 -2 -2 0 8 8 8
quadratic 465 17 17 17 15 47 47 47
cubic 4.960 -32 -32 -32 0 208 208 208
quartic 40.920 152 152 152 120 792 792 792
quintic 278.256 -272 -272 -272 0 2.640 2.640 2.640
sextic 1.623.160 952 952 952 680 8.008 8.008 8.008


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A1g B1g B2g B3g A1u B1u B2u B3u
linear 6 3 3 3 0 5 5 5
quadratic 84 52 52 52 45 60 60 60
cubic 686 598 598 598 530 650 650 650
quartic 5.484 5.012 5.012 5.012 4.860 5.180 5.180 5.180
quintic 35.670 34.486 34.486 34.486 33.690 35.146 35.146 35.146
sextic 206.340 201.860 201.860 201.860 200.164 203.692 203.692 203.692


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)
..21. A1gA1g...6. B1gB1g...6. B2gB2g...6. B3gB3g...15. B1uB1u...15. B2uB2u...15. B3uB3u.
Subtotal: 84 / 7 / 8
Irrep combinations (i,j) with indices: pos(A1g) ≤ i ≤ j ≤ pos(B3u)
Subtotal: 0 / 0 / 28
Total: 84 / 7 / 36


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A1g) ≤ i ≤ pos(B3u)
..56. A1gA1gA1g.
Subtotal: 56 / 1 / 8
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A1g) ≤ i ≤ j ≤ pos(B3u)
..36. A1gB1gB1g...36. A1gB2gB2g...36. A1gB3gB3g...90. A1gB1uB1u...90. A1gB2uB2u...90. A1gB3uB3u.
Subtotal: 378 / 6 / 56
Irrep combinations (i,j,k) with indices: pos(A1g) ≤ i ≤ j ≤ k ≤ pos(B3u)
..27. B1gB2gB3g...75. B1gB2uB3u...75. B2gB1uB3u...75. B3gB1uB2u.
Subtotal: 252 / 4 / 56
Total: 686 / 11 / 120


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A1g) ≤ i ≤ pos(B3u)
..126. A1gA1gA1gA1g...15. B1gB1gB1gB1g...15. B2gB2gB2gB2g...15. B3gB3gB3gB3g...70. B1uB1uB1uB1u...70. B2uB2uB2uB2u...70. B3uB3uB3uB3u.
Subtotal: 381 / 7 / 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)
..126. A1gA1gB1gB1g...126. A1gA1gB2gB2g...126. A1gA1gB3gB3g...315. A1gA1gB1uB1u...315. A1gA1gB2uB2u...315. A1gA1gB3uB3u...36. B1gB1gB2gB2g...36. B1gB1gB3gB3g...90. B1gB1gB1uB1u...90. B1gB1gB2uB2u.
..90. B1gB1gB3uB3u...36. B2gB2gB3gB3g...90. B2gB2gB1uB1u...90. B2gB2gB2uB2u...90. B2gB2gB3uB3u...90. B3gB3gB1uB1u...90. B3gB3gB2uB2u...90. B3gB3gB3uB3u...225. B1uB1uB2uB2u...225. B1uB1uB3uB3u.
..225. B2uB2uB3uB3u.
Subtotal: 2.916 / 21 / 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)
..162. A1gB1gB2gB3g...450. A1gB1gB2uB3u...450. A1gB2gB1uB3u...450. A1gB3gB1uB2u...225. B1gB2gB1uB2u...225. B1gB3gB1uB3u...225. B2gB3gB2uB3u.
Subtotal: 2.187 / 7 / 70
Total: 5.484 / 35 / 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