Results for Point Group C3h



Characters of representations for molecular motions
Motion E C3 (C3)2 σh S3 (S3)5
Cartesian 3N 21 0 0 7 -2 -2
Translation (x,y,z) 3 0 0 1 -2 -2
Rotation (Rx,Ry,Rz) 3 0 0 -1 2 2
Vibration 15 0 0 7 -2 -2


Decomposition to irreducible representations
Motion A' E'* A'' E''* Total
Cartesian 3N 4 5 3 2 14
Translation (x,y,z) 0 1 1 0 2
Rotation (Rx,Ry,Rz) 1 0 0 1 2
Vibration 3 4 2 1 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 A' E'* A'' E''* Total
Linear (IR) 3 4 2 1 6 / 4
Quadratic (Raman) 3 4 2 1 8 / 2
IR + Raman - - - - 4 - - - - - - - - 4 / 0


Characters of force fields
(Symmetric powers of vibration representation)
Force field E C3 (C3)2 σh S3 (S3)5
linear 15 0 0 7 -2 -2
quadratic 120 0 0 32 2 2
cubic 680 5 5 112 1 1
quartic 3.060 0 0 332 -4 -4
quintic 11.628 0 0 868 4 4
sextic 38.760 15 15 2.064 3 3


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A' E'* A'' E''*
linear 3 4 2 1
quadratic 26 25 14 15
cubic 134 131 96 94
quartic 564 566 456 454
quintic 2.084 2.082 1.792 1.794
sextic 6.810 6.801 6.120 6.114


Further Reading


Contributions to nonvanishing force field constants


pos(X) : Position of irreducible representation (irrep) X in character table of C3h

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(A') ≤ i ≤ pos(E'')
..6. A'A'...16. E'E'...3. A''A''...1. E''E''.
Subtotal: 26 / 4 / 4
Irrep combinations (i,j) with indices: pos(A') ≤ i ≤ j ≤ pos(E'')
Subtotal: 0 / 0 / 6
Total: 26 / 4 / 10


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A') ≤ i ≤ pos(E'')
..10. A'A'A'...40. E'E'E'.
Subtotal: 50 / 2 / 4
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A') ≤ i ≤ j ≤ pos(E'')
..48. A'E'E'...9. A'A''A''...3. A'E''E''...8. E'E''E''.
Subtotal: 68 / 4 / 12
Irrep combinations (i,j,k) with indices: pos(A') ≤ i ≤ j ≤ k ≤ pos(E'')
..16. E'A''E''.
Subtotal: 16 / 1 / 4
Total: 134 / 7 / 20


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A') ≤ i ≤ pos(E'')
..15. A'A'A'A'...100. E'E'E'E'...5. A''A''A''A''...1. E''E''E''E''.
Subtotal: 121 / 4 / 4
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A') ≤ i ≤ j ≤ pos(E'')
..120. A'E'E'E'...4. A''E''E''E''.
Subtotal: 124 / 2 / 12
Irrep combinations (i,i,j,j) with indices: pos(A') ≤ i ≤ j ≤ pos(E'')
..96. A'A'E'E'...18. A'A'A''A''...6. A'A'E''E''...48. E'E'A''A''...36. E'E'E''E''...3. A''A''E''E''.
Subtotal: 207 / 6 / 6
Irrep combinations (i,i,j,k) (i,j,j,k) (i,j,k,k) with indices: pos(A') ≤ i ≤ j ≤ k ≤ pos(E'')
..40. E'E'A''E''...24. A'E'E''E''.
Subtotal: 64 / 2 / 12
Irrep combinations (i,j,k,l) with indices: pos(A') ≤ i ≤ j ≤ k ≤ l ≤ pos(E'')
..48. A'E'A''E''.
Subtotal: 48 / 1 / 1
Total: 564 / 15 / 35


Calculate contributions to

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