Results for Point Group D3



Characters of representations for molecular motions
Motion E 2C3 3C'2
Cartesian 3N 21 0 -1
Translation (x,y,z) 3 0 -1
Rotation (Rx,Ry,Rz) 3 0 -1
Vibration 15 0 1


Decomposition to irreducible representations
Motion A1 A2 E Total
Cartesian 3N 3 4 7 14
Translation (x,y,z) 0 1 1 2
Rotation (Rx,Ry,Rz) 0 1 1 2
Vibration 3 2 5 10



Molecular parameter
Number of Atoms (N) 7
Number of internal coordinates 15
Number of independant internal coordinates 3
Number of vibrational modes 10


Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 E Total
Linear (IR) 3 2 5 7 / 3
Quadratic (Raman) 3 2 5 8 / 2
IR + Raman - - - - - - - - 5 5 / 0


Characters of force fields
(Symmetric powers of vibration representation)
Force field E 2C3 3C'2
linear 15 0 1
quadratic 120 0 8
cubic 680 5 8
quartic 3.060 0 36
quintic 11.628 0 36
sextic 38.760 15 120


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A1 A2 E
linear 3 2 5
quadratic 24 16 40
cubic 119 111 225
quartic 528 492 1.020
quintic 1.956 1.920 3.876
sextic 6.525 6.405 12.915


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)
..6. A1A1...3. A2A2...15. EE.
Subtotal: 24 / 3 / 3
Irrep combinations (i,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
Subtotal: 0 / 0 / 3
Total: 24 / 3 / 6


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A1) ≤ i ≤ pos(E)
..10. A1A1A1...35. EEE.
Subtotal: 45 / 2 / 3
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
..9. A1A2A2...45. A1EE...20. A2EE.
Subtotal: 74 / 3 / 6
Irrep combinations (i,j,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(E)
Subtotal: 0 / 0 / 1
Total: 119 / 5 / 10


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A1) ≤ i ≤ pos(E)
..15. A1A1A1A1...5. A2A2A2A2...120. EEEE.
Subtotal: 140 / 3 / 3
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
..105. A1EEE...70. A2EEE.
Subtotal: 175 / 2 / 6
Irrep combinations (i,i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
..18. A1A1A2A2...90. A1A1EE...45. A2A2EE.
Subtotal: 153 / 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)
..60. A1A2EE.
Subtotal: 60 / 1 / 3
Irrep combinations (i,j,k,l) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ l ≤ pos(E)
Subtotal: 0 / 0 / 0
Total: 528 / 9 / 15


Calculate contributions to

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