Results for Point Group C3v



Characters of representations for molecular motions
Motion E 2C3 v
Cartesian 3N 24 0 4
Translation (x,y,z) 3 0 1
Rotation (Rx,Ry,Rz) 3 0 -1
Vibration 18 0 4


Decomposition to irreducible representations
Motion A1 A2 E Total
Cartesian 3N 6 2 8 16
Translation (x,y,z) 1 0 1 2
Rotation (Rx,Ry,Rz) 0 1 1 2
Vibration 5 1 6 12



Molecular parameter
Number of Atoms (N) 8
Number of internal coordinates 18
Number of independant internal coordinates 5
Number of vibrational modes 12


Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 E Total
Linear (IR) 5 1 6 11 / 1
Quadratic (Raman) 5 1 6 11 / 1
IR + Raman 5 1 6 11 / 1


Characters of force fields
(Symmetric powers of vibration representation)
Force field E 2C3 v
linear 18 0 4
quadratic 171 0 17
cubic 1.140 6 48
quartic 5.985 0 133
quintic 26.334 0 308
sextic 100.947 21 693


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A1 A2 E
linear 5 1 6
quadratic 37 20 57
cubic 216 168 378
quartic 1.064 931 1.995
quintic 4.543 4.235 8.778
sextic 17.178 16.485 33.642


Further Reading



Contributions to nonvanishing force field constants


pos(X) : Position of irreducible representation (irrep) X in character table of C3v

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(A1) ≤ i ≤ pos(E)
..15. A1A1...1. A2A2...21. EE.
Subtotal: 37 / 3 / 3
Irrep combinations (i,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
Subtotal: 0 / 0 / 3
Total: 37 / 3 / 6


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A1) ≤ i ≤ pos(E)
..35. A1A1A1...56. EEE.
Subtotal: 91 / 2 / 3
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
..5. A1A2A2...105. A1EE...15. A2EE.
Subtotal: 125 / 3 / 6
Irrep combinations (i,j,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(E)
Subtotal: 0 / 0 / 1
Total: 216 / 5 / 10


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A1) ≤ i ≤ pos(E)
..70. A1A1A1A1...1. A2A2A2A2...231. EEEE.
Subtotal: 302 / 3 / 3
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
..280. A1EEE...56. A2EEE.
Subtotal: 336 / 2 / 6
Irrep combinations (i,i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
..15. A1A1A2A2...315. A1A1EE...21. A2A2EE.
Subtotal: 351 / 3 / 3
Irrep combinations (i,i,j,k) (i,j,j,k) (i,j,k,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(E)
..75. A1A2EE.
Subtotal: 75 / 1 / 3
Irrep combinations (i,j,k,l) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ l ≤ pos(E)
Subtotal: 0 / 0 / 0
Total: 1.064 / 9 / 15


Calculate contributions to

A1 A2 E
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Last update January, 3rd 2020 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement