Results for Point Group D2d



Characters of representations for molecular motions
Motion E 2S4 C2 2C'2 2σd
Cartesian 3N 39 -1 -5 -5 5
Translation (x,y,z) 3 -1 -1 -1 1
Rotation (Rx,Ry,Rz) 3 1 -1 -1 -1
Vibration 33 -1 -3 -3 5


Decomposition to irreducible representations
Motion A1 A2 B1 B2 E Total
Cartesian 3N 4 4 2 7 11 28
Translation (x,y,z) 0 0 0 1 1 2
Rotation (Rx,Ry,Rz) 0 1 0 0 1 2
Vibration 4 3 2 6 9 24



Molecular parameter
Number of Atoms (N) 13
Number of internal coordinates 33
Number of independant internal coordinates 4
Number of vibrational modes 24

Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 E Total
Linear (IR) 4 3 2 6 9 15 / 9
Quadratic (Raman) 4 3 2 6 9 21 / 3
IR + Raman - - - - 3 - - - - 6 9 15 / 3


Characters of force fields
(Symmetric powers of vibration representation)
Force field E 2S4 C2 2C'2 2σd
linear 33 -1 -3 -3 5
quadratic 561 -1 21 21 29
cubic 6.545 1 -55 -55 105
quartic 58.905 9 225 225 385
quintic 435.897 -9 -531 -531 1.141
sextic 2.760.681 -9 1.653 1.653 3.325


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A1 A2 B1 B2 E
linear 4 3 2 6 9
quadratic 85 60 71 75 135
cubic 824 799 771 851 1.650
quartic 7.546 7.241 7.349 7.429 14.670
quintic 54.571 54.266 54.005 54.841 109.107
sextic 346.534 344.045 344.876 345.712 689.757


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...21. B2B2...45. EE.
Subtotal: 85 / 5 / 5
Irrep combinations (i,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
Subtotal: 0 / 0 / 10
Total: 85 / 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...84. A1B2B2...180. A1EE...108. A2EE...90. B1EE...270. B2EE.
Subtotal: 768 / 7 / 20
Irrep combinations (i,j,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(E)
..36. A2B1B2.
Subtotal: 36 / 1 / 10
Total: 824 / 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...126. B2B2B2B2...1.530. EEEE.
Subtotal: 1.711 / 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...210. A1A1B2B2...450. A1A1EE...18. A2A2B1B1...126. A2A2B2B2...270. A2A2EE...63. B1B1B2B2...135. B1B1EE...945. B2B2EE.
Subtotal: 2.307 / 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)
..432. A1A2EE...360. A1B1EE...1.080. A1B2EE...270. A2B1EE...810. A2B2EE...432. B1B2EE.
Subtotal: 3.384 / 6 / 30
Irrep combinations (i,j,k,l) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ l ≤ pos(E)
..144. A1A2B1B2.
Subtotal: 144 / 1 / 5
Total: 7.546 / 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