Results for Point Group D2d



Characters of representations for molecular motions
Motion E 2S4 C2 2C'2 2σd
Cartesian 3N 36 0 0 0 6
Translation (x,y,z) 3 -1 -1 -1 1
Rotation (Rx,Ry,Rz) 3 1 -1 -1 -1
Vibration 30 0 2 2 6


Decomposition to irreducible representations
Motion A1 A2 B1 B2 E Total
Cartesian 3N 6 3 3 6 9 27
Translation (x,y,z) 0 0 0 1 1 2
Rotation (Rx,Ry,Rz) 0 1 0 0 1 2
Vibration 6 2 3 5 7 23



Molecular parameter
Number of Atoms (N) 12
Number of internal coordinates 30
Number of independant internal coordinates 6
Number of vibrational modes 23

Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 E Total
Linear (IR) 6 2 3 5 7 12 / 11
Quadratic (Raman) 6 2 3 5 7 21 / 2
IR + Raman - - - - 2 - - - - 5 7 12 / 2


Characters of force fields
(Symmetric powers of vibration representation)
Force field E 2S4 C2 2C'2 2σd
linear 30 0 2 2 6
quadratic 465 1 17 17 33
cubic 4.960 0 32 32 128
quartic 40.920 8 152 152 456
quintic 278.256 0 272 272 1.392
sextic 1.623.160 8 952 952 3.976


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A1 A2 B1 B2 E
linear 6 2 3 5 7
quadratic 73 48 56 64 112
cubic 664 584 600 648 1.232
quartic 5.288 4.984 5.056 5.208 10.192
quintic 35.232 34.400 34.536 35.096 69.496
sextic 204.248 201.784 202.256 203.768 405.552


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)
..21. A1A1...3. A2A2...6. B1B1...15. B2B2...28. EE.
Subtotal: 73 / 5 / 5
Irrep combinations (i,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
Subtotal: 0 / 0 / 10
Total: 73 / 5 / 15


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A1) ≤ i ≤ pos(E)
..56. A1A1A1.
Subtotal: 56 / 1 / 5
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
..18. A1A2A2...36. A1B1B1...90. A1B2B2...168. A1EE...42. A2EE...84. B1EE...140. B2EE.
Subtotal: 578 / 7 / 20
Irrep combinations (i,j,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(E)
..30. A2B1B2.
Subtotal: 30 / 1 / 10
Total: 664 / 9 / 35


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A1) ≤ i ≤ pos(E)
..126. A1A1A1A1...5. A2A2A2A2...15. B1B1B1B1...70. B2B2B2B2...616. EEEE.
Subtotal: 832 / 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)
..63. A1A1A2A2...126. A1A1B1B1...315. A1A1B2B2...588. A1A1EE...18. A2A2B1B1...45. A2A2B2B2...84. A2A2EE...90. B1B1B2B2...168. B1B1EE...420. B2B2EE.
Subtotal: 1.917 / 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)
..252. A1A2EE...504. A1B1EE...840. A1B2EE...168. A2B1EE...280. A2B2EE...315. B1B2EE.
Subtotal: 2.359 / 6 / 30
Irrep combinations (i,j,k,l) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ l ≤ pos(E)
..180. A1A2B1B2.
Subtotal: 180 / 1 / 5
Total: 5.288 / 22 / 70


Calculate contributions to

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