Results for Point Group Cs



Characters of representations for molecular motions
Motion E σh
Cartesian 3N 36 8
Translation (x,y,z) 3 1
Rotation (Rx,Ry,Rz) 3 -1
Vibration 30 8


Decomposition to irreducible representations
Motion A' A'' Total
Cartesian 3N 22 14 36
Translation (x,y,z) 2 1 3
Rotation (Rx,Ry,Rz) 1 2 3
Vibration 19 11 30



Molecular parameter
Number of Atoms (N) 12
Number of internal coordinates 30
Number of independant internal coordinates 19
Number of vibrational modes 30


Force field analysis


Allowed / forbidden vibronational transitions
Operator A' A'' Total
Linear (IR) 19 11 30 / 0
Quadratic (Raman) 19 11 30 / 0
IR + Raman 19 11 30 / 0


Characters of force fields
(Symmetric powers of vibration representation)
Force field E σh
linear 30 8
quadratic 465 47
cubic 4.960 208
quartic 40.920 792
quintic 278.256 2.640
sextic 1.623.160 8.008


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A' A''
linear 19 11
quadratic 256 209
cubic 2.584 2.376
quartic 20.856 20.064
quintic 140.448 137.808
sextic 815.584 807.576


Further Reading



Contributions to nonvanishing force field constants


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

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(A'')
..190. A'A'...66. A''A''.
Subtotal: 256 / 2 / 2
Irrep combinations (i,j) with indices: pos(A') ≤ i ≤ j ≤ pos(A'')
Subtotal: 0 / 0 / 1
Total: 256 / 2 / 3


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A') ≤ i ≤ pos(A'')
..1.330. A'A'A'.
Subtotal: 1.330 / 1 / 2
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A') ≤ i ≤ j ≤ pos(A'')
..1.254. A'A''A''.
Subtotal: 1.254 / 1 / 2
Irrep combinations (i,j,k) with indices: pos(A') ≤ i ≤ j ≤ k ≤ pos(A'')
Subtotal: 0 / 0 / 0
Total: 2.584 / 2 / 4


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A') ≤ i ≤ pos(A'')
..7.315. A'A'A'A'...1.001. A''A''A''A''.
Subtotal: 8.316 / 2 / 2
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A') ≤ i ≤ j ≤ pos(A'')
Subtotal: 0 / 0 / 2
Irrep combinations (i,i,j,j) with indices: pos(A') ≤ i ≤ j ≤ pos(A'')
..12.540. A'A'A''A''.
Subtotal: 12.540 / 1 / 1
Irrep combinations (i,i,j,k) (i,j,j,k) (i,j,k,k) with indices: pos(A') ≤ i ≤ j ≤ k ≤ pos(A'')
Subtotal: 0 / 0 / 0
Irrep combinations (i,j,k,l) with indices: pos(A') ≤ i ≤ j ≤ k ≤ l ≤ pos(A'')
Subtotal: 0 / 0 / 0
Total: 20.856 / 3 / 5


Calculate contributions to

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