Results for Point Group D2d



Characters of representations for molecular motions
Motion E 2S4 C2 2C'2 2σd
Cartesian 3N 39 -1 -5 -1 9
Translation (x,y,z) 3 -1 -1 -1 1
Rotation (Rx,Ry,Rz) 3 1 -1 -1 -1
Vibration 33 -1 -3 1 9


Decomposition to irreducible representations
Motion A1 A2 B1 B2 E Total
Cartesian 3N 6 2 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 6 1 2 6 9 24



Molecular parameter
Number of Atoms (N) 13
Number of internal coordinates 33
Number of independant internal coordinates 6
Number of vibrational modes 24

Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 E Total
Linear (IR) 6 1 2 6 9 15 / 9
Quadratic (Raman) 6 1 2 6 9 23 / 1
IR + Raman - - - - 1 - - - - 6 9 15 / 1


Characters of force fields
(Symmetric powers of vibration representation)
Force field E 2S4 C2 2C'2 2σd
linear 33 -1 -3 1 9
quadratic 561 -1 21 17 57
cubic 6.545 1 -55 17 273
quartic 58.905 9 225 153 1.113
quintic 435.897 -9 -531 153 3.969
sextic 2.760.681 -9 1.653 969 12.817


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A1 A2 B1 B2 E
linear 6 1 2 6 9
quadratic 91 54 63 83 135
cubic 884 739 747 875 1.650
quartic 7.710 7.077 7.149 7.629 14.670
quintic 55.449 53.388 53.469 55.377 109.107
sextic 348.736 341.843 342.332 348.256 689.757


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)
..21. A1A1...1. A2A2...3. B1B1...21. B2B2...45. EE.
Subtotal: 91 / 5 / 5
Irrep combinations (i,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
Subtotal: 0 / 0 / 10
Total: 91 / 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)
..6. A1A2A2...18. A1B1B1...126. A1B2B2...270. A1EE...36. A2EE...90. B1EE...270. B2EE.
Subtotal: 816 / 7 / 20
Irrep combinations (i,j,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(E)
..12. A2B1B2.
Subtotal: 12 / 1 / 10
Total: 884 / 9 / 35


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A1) ≤ i ≤ pos(E)
..126. A1A1A1A1...1. A2A2A2A2...5. B1B1B1B1...126. B2B2B2B2...1.530. EEEE.
Subtotal: 1.788 / 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)
..21. A1A1A2A2...63. A1A1B1B1...441. A1A1B2B2...945. A1A1EE...3. A2A2B1B1...21. A2A2B2B2...45. A2A2EE...63. B1B1B2B2...135. B1B1EE...945. B2B2EE.
Subtotal: 2.682 / 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)
..216. A1A2EE...540. A1B1EE...1.620. A1B2EE...90. A2B1EE...270. A2B2EE...432. B1B2EE.
Subtotal: 3.168 / 6 / 30
Irrep combinations (i,j,k,l) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ l ≤ pos(E)
..72. A1A2B1B2.
Subtotal: 72 / 1 / 5
Total: 7.710 / 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