Results for Point Group C2



Characters of representations for molecular motions
Motion E C2
Cartesian 3N 45 -1
Translation (x,y,z) 3 -1
Rotation (Rx,Ry,Rz) 3 -1
Vibration 39 1


Decomposition to irreducible representations
Motion A B Total
Cartesian 3N 22 23 45
Translation (x,y,z) 1 2 3
Rotation (Rx,Ry,Rz) 1 2 3
Vibration 20 19 39



Molecular parameter
Number of Atoms (N) 15
Number of internal coordinates 39
Number of independant internal coordinates 20
Number of vibrational modes 39


Force field analysis


Allowed / forbidden vibronational transitions
Operator A B Total
Linear (IR) 20 19 39 / 0
Quadratic (Raman) 20 19 39 / 0
IR + Raman 20 19 39 / 0


Characters of force fields
(Symmetric powers of vibration representation)
Force field E C2
linear 39 1
quadratic 780 20
cubic 10.660 20
quartic 111.930 210
quintic 962.598 210
sextic 7.059.052 1.540


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A B
linear 20 19
quadratic 400 380
cubic 5.340 5.320
quartic 56.070 55.860
quintic 481.404 481.194
sextic 3.530.296 3.528.756


Further Reading



Contributions to nonvanishing force field constants


pos(X) : Position of irreducible representation (irrep) X in character table of C2

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(B)
..210. AA...190. BB.
Subtotal: 400 / 2 / 2
Irrep combinations (i,j) with indices: pos(A) ≤ i ≤ j ≤ pos(B)
Subtotal: 0 / 0 / 1
Total: 400 / 2 / 3


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A) ≤ i ≤ pos(B)
..1.540. AAA.
Subtotal: 1.540 / 1 / 2
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A) ≤ i ≤ j ≤ pos(B)
..3.800. ABB.
Subtotal: 3.800 / 1 / 2
Irrep combinations (i,j,k) with indices: pos(A) ≤ i ≤ j ≤ k ≤ pos(B)
Subtotal: 0 / 0 / 0
Total: 5.340 / 2 / 4


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A) ≤ i ≤ pos(B)
..8.855. AAAA...7.315. BBBB.
Subtotal: 16.170 / 2 / 2
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A) ≤ i ≤ j ≤ pos(B)
Subtotal: 0 / 0 / 2
Irrep combinations (i,i,j,j) with indices: pos(A) ≤ i ≤ j ≤ pos(B)
..39.900. AABB.
Subtotal: 39.900 / 1 / 1
Irrep combinations (i,i,j,k) (i,j,j,k) (i,j,k,k) with indices: pos(A) ≤ i ≤ j ≤ k ≤ pos(B)
Subtotal: 0 / 0 / 0
Irrep combinations (i,j,k,l) with indices: pos(A) ≤ i ≤ j ≤ k ≤ l ≤ pos(B)
Subtotal: 0 / 0 / 0
Total: 56.070 / 3 / 5


Calculate contributions to

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