Results for Point Group Cs



Characters of representations for molecular motions
Motion E σh
Cartesian 3N 51 17
Translation (x,y,z) 3 1
Rotation (Rx,Ry,Rz) 3 -1
Vibration 45 17


Decomposition to irreducible representations
Motion A' A'' Total
Cartesian 3N 34 17 51
Translation (x,y,z) 2 1 3
Rotation (Rx,Ry,Rz) 1 2 3
Vibration 31 14 45



Molecular parameter
Number of Atoms (N) 17
Number of internal coordinates 45
Number of independant internal coordinates 31
Number of vibrational modes 45


Force field analysis


Allowed / forbidden vibronational transitions
Operator A' A'' Total
Linear (IR) 31 14 45 / 0
Quadratic (Raman) 31 14 45 / 0
IR + Raman 31 14 45 / 0


Characters of force fields
(Symmetric powers of vibration representation)
Force field E σh
linear 45 17
quadratic 1.035 167
cubic 16.215 1.207
quartic 194.580 7.092
quintic 1.906.884 35.700
sextic 15.890.700 159.068


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A' A''
linear 31 14
quadratic 601 434
cubic 8.711 7.504
quartic 100.836 93.744
quintic 971.292 935.592
sextic 8.024.884 7.865.816


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'')
..496. A'A'...105. A''A''.
Subtotal: 601 / 2 / 2
Irrep combinations (i,j) with indices: pos(A') ≤ i ≤ j ≤ pos(A'')
Subtotal: 0 / 0 / 1
Total: 601 / 2 / 3


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A') ≤ i ≤ pos(A'')
..5.456. A'A'A'.
Subtotal: 5.456 / 1 / 2
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A') ≤ i ≤ j ≤ pos(A'')
..3.255. A'A''A''.
Subtotal: 3.255 / 1 / 2
Irrep combinations (i,j,k) with indices: pos(A') ≤ i ≤ j ≤ k ≤ pos(A'')
Subtotal: 0 / 0 / 0
Total: 8.711 / 2 / 4


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A') ≤ i ≤ pos(A'')
..46.376. A'A'A'A'...2.380. A''A''A''A''.
Subtotal: 48.756 / 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'')
..52.080. A'A'A''A''.
Subtotal: 52.080 / 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: 100.836 / 3 / 5


Calculate contributions to

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






Last update January, 3rd 2020 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement