Results for Point Group C3h



Characters of representations for molecular motions
Motion E C3 (C3)2 σh S3 (S3)5
Cartesian 3N 93 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 87 0 0 9 0 0


Decomposition to irreducible representations
Motion A' E'* A'' E''* Total
Cartesian 3N 17 17 14 14 62
Translation (x,y,z) 0 1 1 0 2
Rotation (Rx,Ry,Rz) 1 0 0 1 2
Vibration 16 16 13 13 58



Molecular parameter
Number of Atoms (N) 31
Number of internal coordinates 87
Number of independant internal coordinates 16
Number of vibrational modes 58

Force field analysis


Allowed / forbidden vibronational transitions
Operator A' E'* A'' E''* Total
Linear (IR) 16 16 13 13 29 / 29
Quadratic (Raman) 16 16 13 13 45 / 13
IR + Raman - - - - 16 - - - - - - - - 16 / 0


Characters of force fields
(Symmetric powers of vibration representation)
Force field E C3 (C3)2 σh S3 (S3)5
linear 87 0 0 9 0 0
quadratic 3.828 0 0 84 0 0
cubic 113.564 29 29 516 3 3
quartic 2.555.190 0 0 3.030 0 0
quintic 46.504.458 0 0 14.742 0 0
sextic 713.068.356 435 435 68.068 19 19


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A' E'* A'' E''*
linear 16 16 13 13
quadratic 652 652 624 624
cubic 19.024 19.008 18.850 18.837
quartic 426.370 426.370 425.360 425.360
quintic 7.753.200 7.753.200 7.748.286 7.748.286
sextic 118.856.222 118.855.995 118.833.520 118.833.312


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'')
..136. A'A'...256. E'E'...91. A''A''...169. E''E''.
Subtotal: 652 / 4 / 4
Irrep combinations (i,j) with indices: pos(A') ≤ i ≤ j ≤ pos(E'')
Subtotal: 0 / 0 / 6
Total: 652 / 4 / 10


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A') ≤ i ≤ pos(E'')
..816. A'A'A'...1.632. E'E'E'.
Subtotal: 2.448 / 2 / 4
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A') ≤ i ≤ j ≤ pos(E'')
..4.096. A'E'E'...1.456. A'A''A''...2.704. A'E''E''...2.912. E'E''E''.
Subtotal: 11.168 / 4 / 12
Irrep combinations (i,j,k) with indices: pos(A') ≤ i ≤ j ≤ k ≤ pos(E'')
..5.408. E'A''E''.
Subtotal: 5.408 / 1 / 4
Total: 19.024 / 7 / 20


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A') ≤ i ≤ pos(E'')
..3.876. A'A'A'A'...18.496. E'E'E'E'...1.820. A''A''A''A''...8.281. E''E''E''E''.
Subtotal: 32.473 / 4 / 4
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A') ≤ i ≤ j ≤ pos(E'')
..26.112. A'E'E'E'...11.830. A''E''E''E''.
Subtotal: 37.942 / 2 / 12
Irrep combinations (i,i,j,j) with indices: pos(A') ≤ i ≤ j ≤ pos(E'')
..34.816. A'A'E'E'...12.376. A'A'A''A''...22.984. A'A'E''E''...23.296. E'E'A''A''...68.016. E'E'E''E''...15.379. A''A''E''E''.
Subtotal: 176.867 / 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'')
..45.968. E'E'A''E''...46.592. A'E'E''E''.
Subtotal: 92.560 / 2 / 12
Irrep combinations (i,j,k,l) with indices: pos(A') ≤ i ≤ j ≤ k ≤ l ≤ pos(E'')
..86.528. A'E'A''E''.
Subtotal: 86.528 / 1 / 1
Total: 426.370 / 15 / 35


Calculate contributions to

A' E' A'' E''
Show only nonzero contributions Show all contributions
Up to quartic force fieldUp to quintic force fieldUp to sextic force field





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