Results for Point Group C3



Characters of representations for molecular motions
Motion E C3 (C3)2
Cartesian 3N 36 0 0
Translation (x,y,z) 3 0 0
Rotation (Rx,Ry,Rz) 3 0 0
Vibration 30 0 0


Decomposition to irreducible representations
Motion A E* Total
Cartesian 3N 12 12 24
Translation (x,y,z) 1 1 2
Rotation (Rx,Ry,Rz) 1 1 2
Vibration 10 10 20



Molecular parameter
Number of Atoms (N) 12
Number of internal coordinates 30
Number of independant internal coordinates 10
Number of vibrational modes 20


Force field analysis


Allowed / forbidden vibronational transitions
Operator A E* Total
Linear (IR) 10 10 20 / 0
Quadratic (Raman) 10 10 20 / 0
IR + Raman 10 10 20 / 0


Characters of force fields
(Symmetric powers of vibration representation)
Force field E C3 (C3)2
linear 30 0 0
quadratic 465 0 0
cubic 4.960 10 10
quartic 40.920 0 0
quintic 278.256 0 0
sextic 1.623.160 55 55


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A E*
linear 10 10
quadratic 155 155
cubic 1.660 1.650
quartic 13.640 13.640
quintic 92.752 92.752
sextic 541.090 541.035


Further Reading



Contributions to nonvanishing force field constants


pos(X) : Position of irreducible representation (irrep) X in character table of C3

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)
..55. AA...100. EE.
Subtotal: 155 / 2 / 2
Irrep combinations (i,j) with indices: pos(A) ≤ i ≤ j ≤ pos(E)
Subtotal: 0 / 0 / 1
Total: 155 / 2 / 3


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A) ≤ i ≤ pos(E)
..220. AAA...440. EEE.
Subtotal: 660 / 2 / 2
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A) ≤ i ≤ j ≤ pos(E)
..1.000. AEE.
Subtotal: 1.000 / 1 / 2
Irrep combinations (i,j,k) with indices: pos(A) ≤ i ≤ j ≤ k ≤ pos(E)
Subtotal: 0 / 0 / 0
Total: 1.660 / 3 / 4


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A) ≤ i ≤ pos(E)
..715. AAAA...3.025. EEEE.
Subtotal: 3.740 / 2 / 2
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A) ≤ i ≤ j ≤ pos(E)
..4.400. AEEE.
Subtotal: 4.400 / 1 / 2
Irrep combinations (i,i,j,j) with indices: pos(A) ≤ i ≤ j ≤ pos(E)
..5.500. AAEE.
Subtotal: 5.500 / 1 / 1
Irrep combinations (i,i,j,k) (i,j,j,k) (i,j,k,k) with indices: pos(A) ≤ i ≤ j ≤ k ≤ pos(E)
Subtotal: 0 / 0 / 0
Irrep combinations (i,j,k,l) with indices: pos(A) ≤ i ≤ j ≤ k ≤ l ≤ pos(E)
Subtotal: 0 / 0 / 0
Total: 13.640 / 4 / 5


Calculate contributions to

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