Results for Point Group D3



Characters of representations for molecular motions
Motion E 2C3 3C'2
Cartesian 3N 36 0 0
Translation (x,y,z) 3 0 -1
Rotation (Rx,Ry,Rz) 3 0 -1
Vibration 30 0 2


Decomposition to irreducible representations
Motion A1 A2 E Total
Cartesian 3N 6 6 12 24
Translation (x,y,z) 0 1 1 2
Rotation (Rx,Ry,Rz) 0 1 1 2
Vibration 6 4 10 20



Molecular parameter
Number of Atoms (N) 12
Number of internal coordinates 30
Number of independant internal coordinates 6
Number of vibrational modes 20


Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 E Total
Linear (IR) 6 4 10 14 / 6
Quadratic (Raman) 6 4 10 16 / 4
IR + Raman - - - - - - - - 10 10 / 0


Characters of force fields
(Symmetric powers of vibration representation)
Force field E 2C3 3C'2
linear 30 0 2
quadratic 465 0 17
cubic 4.960 10 32
quartic 40.920 0 152
quintic 278.256 0 272
sextic 1.623.160 55 952


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A1 A2 E
linear 6 4 10
quadratic 86 69 155
cubic 846 814 1.650
quartic 6.896 6.744 13.640
quintic 46.512 46.240 92.752
sextic 271.021 270.069 541.035


Further Reading



Contributions to nonvanishing force field constants


pos(X) : Position of irreducible representation (irrep) X in character table of D3

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...10. A2A2...55. EE.
Subtotal: 86 / 3 / 3
Irrep combinations (i,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
Subtotal: 0 / 0 / 3
Total: 86 / 3 / 6


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A1) ≤ i ≤ pos(E)
..56. A1A1A1...220. EEE.
Subtotal: 276 / 2 / 3
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
..60. A1A2A2...330. A1EE...180. A2EE.
Subtotal: 570 / 3 / 6
Irrep combinations (i,j,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(E)
Subtotal: 0 / 0 / 1
Total: 846 / 5 / 10


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A1) ≤ i ≤ pos(E)
..126. A1A1A1A1...35. A2A2A2A2...1.540. EEEE.
Subtotal: 1.701 / 3 / 3
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
..1.320. A1EEE...880. A2EEE.
Subtotal: 2.200 / 2 / 6
Irrep combinations (i,i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
..210. A1A1A2A2...1.155. A1A1EE...550. A2A2EE.
Subtotal: 1.915 / 3 / 3
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.
Subtotal: 1.080 / 1 / 3
Irrep combinations (i,j,k,l) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ l ≤ pos(E)
Subtotal: 0 / 0 / 0
Total: 6.896 / 9 / 15


Calculate contributions to

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