Results for Point Group C3h



Characters of representations for molecular motions
Motion E C3 (C3)2 σh S3 (S3)5
Cartesian 3N 45 0 0 15 0 0
Translation (x,y,z) 3 0 0 1 -2 -2
Rotation (Rx,Ry,Rz) 3 0 0 -1 2 2
Vibration 39 0 0 15 0 0


Decomposition to irreducible representations
Motion A' E'* A'' E''* Total
Cartesian 3N 10 10 5 5 30
Translation (x,y,z) 0 1 1 0 2
Rotation (Rx,Ry,Rz) 1 0 0 1 2
Vibration 9 9 4 4 26



Molecular parameter
Number of Atoms (N) 15
Number of internal coordinates 39
Number of independant internal coordinates 9
Number of vibrational modes 26

Force field analysis


Allowed / forbidden vibronational transitions
Operator A' E'* A'' E''* Total
Linear (IR) 9 9 4 4 13 / 13
Quadratic (Raman) 9 9 4 4 22 / 4
IR + Raman - - - - 9 - - - - - - - - 9 / 0


Characters of force fields
(Symmetric powers of vibration representation)
Force field E C3 (C3)2 σh S3 (S3)5
linear 39 0 0 15 0 0
quadratic 780 0 0 132 0 0
cubic 10.660 13 13 860 5 5
quartic 111.930 0 0 4.578 0 0
quintic 962.598 0 0 20.958 0 0
sextic 7.059.052 91 91 85.204 19 19


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A' E'* A'' E''*
linear 9 9 4 4
quadratic 152 152 108 108
cubic 1.926 1.917 1.636 1.632
quartic 19.418 19.418 17.892 17.892
quintic 163.926 163.926 156.940 156.940
sextic 1.190.746 1.190.691 1.162.332 1.162.296


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'')
..45. A'A'...81. E'E'...10. A''A''...16. E''E''.
Subtotal: 152 / 4 / 4
Irrep combinations (i,j) with indices: pos(A') ≤ i ≤ j ≤ pos(E'')
Subtotal: 0 / 0 / 6
Total: 152 / 4 / 10


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A') ≤ i ≤ pos(E'')
..165. A'A'A'...330. E'E'E'.
Subtotal: 495 / 2 / 4
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A') ≤ i ≤ j ≤ pos(E'')
..729. A'E'E'...90. A'A''A''...144. A'E''E''...180. E'E''E''.
Subtotal: 1.143 / 4 / 12
Irrep combinations (i,j,k) with indices: pos(A') ≤ i ≤ j ≤ k ≤ pos(E'')
..288. E'A''E''.
Subtotal: 288 / 1 / 4
Total: 1.926 / 7 / 20


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A') ≤ i ≤ pos(E'')
..495. A'A'A'A'...2.025. E'E'E'E'...35. A''A''A''A''...100. E''E''E''E''.
Subtotal: 2.655 / 4 / 4
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A') ≤ i ≤ j ≤ pos(E'')
..2.970. A'E'E'E'...160. A''E''E''E''.
Subtotal: 3.130 / 2 / 12
Irrep combinations (i,i,j,j) with indices: pos(A') ≤ i ≤ j ≤ pos(E'')
..3.645. A'A'E'E'...450. A'A'A''A''...720. A'A'E''E''...810. E'E'A''A''...2.196. E'E'E''E''...160. A''A''E''E''.
Subtotal: 7.981 / 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'')
..1.440. E'E'A''E''...1.620. A'E'E''E''.
Subtotal: 3.060 / 2 / 12
Irrep combinations (i,j,k,l) with indices: pos(A') ≤ i ≤ j ≤ k ≤ l ≤ pos(E'')
..2.592. A'E'A''E''.
Subtotal: 2.592 / 1 / 1
Total: 19.418 / 15 / 35


Calculate contributions to

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