Results for Point Group D2d



Characters of representations for molecular motions
Motion E 2S4 C2 2C'2 d
Cartesian 3N 36 0 -4 -4 4
Translation (x,y,z) 3 -1 -1 -1 1
Rotation (Rx,Ry,Rz) 3 1 -1 -1 -1
Vibration 30 0 -2 -2 4


Decomposition to irreducible representations
Motion A1 A2 B1 B2 E Total
Cartesian 3N 4 4 2 6 10 26
Translation (x,y,z) 0 0 0 1 1 2
Rotation (Rx,Ry,Rz) 0 1 0 0 1 2
Vibration 4 3 2 5 8 22



Molecular parameter
Number of Atoms (N) 12
Number of internal coordinates 30
Number of independant internal coordinates 4
Number of vibrational modes 22


Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 E Total
Linear (IR) 4 3 2 5 8 13 / 9
Quadratic (Raman) 4 3 2 5 8 19 / 3
IR + Raman - - - - 3 - - - - 5 8 13 / 3


Characters of force fields
(Symmetric powers of vibration representation)
Force field E 2S4 C2 2C'2 d
linear 30 0 -2 -2 4
quadratic 465 -1 17 17 23
cubic 4.960 0 -32 -32 72
quartic 40.920 8 152 152 256
quintic 278.256 0 -272 -272 680
sextic 1.623.160 -8 952 952 1.904


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A1 A2 B1 B2 E
linear 4 3 2 5 8
quadratic 70 50 59 62 112
cubic 626 606 590 642 1.248
quartic 5.238 5.034 5.106 5.158 10.192
quintic 34.850 34.646 34.510 34.986 69.632
sextic 203.726 202.298 202.778 203.254 405.552


Further Reading



Contributions to nonvanishing force field constants


pos(X) : Position of irreducible representation (irrep) X in character table of D2d

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(A1) ≤ i ≤ pos(E)
..10. A1A1...6. A2A2...3. B1B1...15. B2B2...36. EE.
Subtotal: 70 / 5 / 5
Irrep combinations (i,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
Subtotal: 0 / 0 / 10
Total: 70 / 5 / 15


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A1) ≤ i ≤ pos(E)
..20. A1A1A1.
Subtotal: 20 / 1 / 5
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
..24. A1A2A2...12. A1B1B1...60. A1B2B2...144. A1EE...84. A2EE...72. B1EE...180. B2EE.
Subtotal: 576 / 7 / 20
Irrep combinations (i,j,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(E)
..30. A2B1B2.
Subtotal: 30 / 1 / 10
Total: 626 / 9 / 35


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A1) ≤ i ≤ pos(E)
..35. A1A1A1A1...15. A2A2A2A2...5. B1B1B1B1...70. B2B2B2B2...996. EEEE.
Subtotal: 1.121 / 5 / 5
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
Subtotal: 0 / 0 / 20
Irrep combinations (i,i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
..60. A1A1A2A2...30. A1A1B1B1...150. A1A1B2B2...360. A1A1EE...18. A2A2B1B1...90. A2A2B2B2...216. A2A2EE...45. B1B1B2B2...108. B1B1EE...540. B2B2EE.
Subtotal: 1.617 / 10 / 10
Irrep combinations (i,i,j,k) (i,j,j,k) (i,j,k,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(E)
..336. A1A2EE...288. A1B1EE...720. A1B2EE...216. A2B1EE...540. A2B2EE...280. B1B2EE.
Subtotal: 2.380 / 6 / 30
Irrep combinations (i,j,k,l) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ l ≤ pos(E)
..120. A1A2B1B2.
Subtotal: 120 / 1 / 5
Total: 5.238 / 22 / 70


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A1 A2 B1 B2 E
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Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement