Results for Point Group D2d



Characters of representations for molecular motions
Motion E 2S4 C2 2C'2 2σd
Cartesian 3N 48 0 0 0 8
Translation (x,y,z) 3 -1 -1 -1 1
Rotation (Rx,Ry,Rz) 3 1 -1 -1 -1
Vibration 42 0 2 2 8


Decomposition to irreducible representations
Motion A1 A2 B1 B2 E Total
Cartesian 3N 8 4 4 8 12 36
Translation (x,y,z) 0 0 0 1 1 2
Rotation (Rx,Ry,Rz) 0 1 0 0 1 2
Vibration 8 3 4 7 10 32



Molecular parameter
Number of Atoms (N) 16
Number of internal coordinates 42
Number of independant internal coordinates 8
Number of vibrational modes 32

Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 E Total
Linear (IR) 8 3 4 7 10 17 / 15
Quadratic (Raman) 8 3 4 7 10 29 / 3
IR + Raman - - - - 3 - - - - 7 10 17 / 3


Characters of force fields
(Symmetric powers of vibration representation)
Force field E 2S4 C2 2C'2 2σd
linear 42 0 2 2 8
quadratic 903 1 23 23 53
cubic 13.244 0 44 44 256
quartic 148.995 11 275 275 1.095
quintic 1.370.754 0 506 506 4.056
sextic 10.737.573 11 2.277 2.277 13.803


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A1 A2 B1 B2 E
linear 8 3 4 7 10
quadratic 135 97 108 123 220
cubic 1.736 1.586 1.608 1.714 3.300
quartic 19.004 18.319 18.451 18.861 37.180
quintic 172.548 170.267 170.520 172.295 342.562
sextic 1.346.504 1.338.464 1.339.597 1.345.360 2.683.824


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)
..36. A1A1...6. A2A2...10. B1B1...28. B2B2...55. EE.
Subtotal: 135 / 5 / 5
Irrep combinations (i,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
Subtotal: 0 / 0 / 10
Total: 135 / 5 / 15


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A1) ≤ i ≤ pos(E)
..120. A1A1A1.
Subtotal: 120 / 1 / 5
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
..48. A1A2A2...80. A1B1B1...224. A1B2B2...440. A1EE...135. A2EE...220. B1EE...385. B2EE.
Subtotal: 1.532 / 7 / 20
Irrep combinations (i,j,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(E)
..84. A2B1B2.
Subtotal: 84 / 1 / 10
Total: 1.736 / 9 / 35


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A1) ≤ i ≤ pos(E)
..330. A1A1A1A1...15. A2A2A2A2...35. B1B1B1B1...210. B2B2B2B2...2.255. EEEE.
Subtotal: 2.845 / 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)
..216. A1A1A2A2...360. A1A1B1B1...1.008. A1A1B2B2...1.980. A1A1EE...60. A2A2B1B1...168. A2A2B2B2...330. A2A2EE...280. B1B1B2B2...550. B1B1EE...1.540. B2B2EE.
Subtotal: 6.492 / 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)
..1.080. A1A2EE...1.760. A1B1EE...3.080. A1B2EE...660. A2B1EE...1.155. A2B2EE...1.260. B1B2EE.
Subtotal: 8.995 / 6 / 30
Irrep combinations (i,j,k,l) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ l ≤ pos(E)
..672. A1A2B1B2.
Subtotal: 672 / 1 / 5
Total: 19.004 / 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