Results for Point Group C3h



Characters of representations for molecular motions
Motion E C3 (C3)2 σh S3 (S3)5
Cartesian 3N 87 0 0 9 0 0
Translation (x,y,z) 3 0 0 1 -2 -2
Rotation (Rx,Ry,Rz) 3 0 0 -1 2 2
Vibration 81 0 0 9 0 0


Decomposition to irreducible representations
Motion A' E'* A'' E''* Total
Cartesian 3N 16 16 13 13 58
Translation (x,y,z) 0 1 1 0 2
Rotation (Rx,Ry,Rz) 1 0 0 1 2
Vibration 15 15 12 12 54



Molecular parameter
Number of Atoms (N) 29
Number of internal coordinates 81
Number of independant internal coordinates 15
Number of vibrational modes 54

Force field analysis


Allowed / forbidden vibronational transitions
Operator A' E'* A'' E''* Total
Linear (IR) 15 15 12 12 27 / 27
Quadratic (Raman) 15 15 12 12 42 / 12
IR + Raman - - - - 15 - - - - - - - - 15 / 0


Characters of force fields
(Symmetric powers of vibration representation)
Force field E C3 (C3)2 σh S3 (S3)5
linear 81 0 0 9 0 0
quadratic 3.321 0 0 81 0 0
cubic 91.881 27 27 489 3 3
quartic 1.929.501 0 0 2.781 0 0
quintic 32.801.517 0 0 13.221 0 0
sextic 470.155.077 378 378 59.229 18 18


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A' E'* A'' E''*
linear 15 15 12 12
quadratic 567 567 540 540
cubic 15.405 15.390 15.240 15.228
quartic 322.047 322.047 321.120 321.120
quintic 5.469.123 5.469.123 5.464.716 5.464.716
sextic 78.369.183 78.368.985 78.349.428 78.349.248


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'')
..120. A'A'...225. E'E'...78. A''A''...144. E''E''.
Subtotal: 567 / 4 / 4
Irrep combinations (i,j) with indices: pos(A') ≤ i ≤ j ≤ pos(E'')
Subtotal: 0 / 0 / 6
Total: 567 / 4 / 10


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A') ≤ i ≤ pos(E'')
..680. A'A'A'...1.360. E'E'E'.
Subtotal: 2.040 / 2 / 4
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A') ≤ i ≤ j ≤ pos(E'')
..3.375. A'E'E'...1.170. A'A''A''...2.160. A'E''E''...2.340. E'E''E''.
Subtotal: 9.045 / 4 / 12
Irrep combinations (i,j,k) with indices: pos(A') ≤ i ≤ j ≤ k ≤ pos(E'')
..4.320. E'A''E''.
Subtotal: 4.320 / 1 / 4
Total: 15.405 / 7 / 20


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A') ≤ i ≤ pos(E'')
..3.060. A'A'A'A'...14.400. E'E'E'E'...1.365. A''A''A''A''...6.084. E''E''E''E''.
Subtotal: 24.909 / 4 / 4
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A') ≤ i ≤ j ≤ pos(E'')
..20.400. A'E'E'E'...8.736. A''E''E''E''.
Subtotal: 29.136 / 2 / 12
Irrep combinations (i,i,j,j) with indices: pos(A') ≤ i ≤ j ≤ pos(E'')
..27.000. A'A'E'E'...9.360. A'A'A''A''...17.280. A'A'E''E''...17.550. E'E'A''A''...51.120. E'E'E''E''...11.232. A''A''E''E''.
Subtotal: 133.542 / 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'')
..34.560. E'E'A''E''...35.100. A'E'E''E''.
Subtotal: 69.660 / 2 / 12
Irrep combinations (i,j,k,l) with indices: pos(A') ≤ i ≤ j ≤ k ≤ l ≤ pos(E'')
..64.800. A'E'A''E''.
Subtotal: 64.800 / 1 / 1
Total: 322.047 / 15 / 35


Calculate contributions to

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