Results for Point Group C2v



Characters of representations for molecular motions
Motion E C2.(z) σv.(xz) σd.(yz)
Cartesian 3N 21 -1 5 3
Translation (x,y,z) 3 -1 1 1
Rotation (Rx,Ry,Rz) 3 -1 -1 -1
Vibration 15 1 5 3


Decomposition to irreducible representations
Motion A1 A2 B1 B2 Total
Cartesian 3N 7 3 6 5 21
Translation (x,y,z) 1 0 1 1 3
Rotation (Rx,Ry,Rz) 0 1 1 1 3
Vibration 6 2 4 3 15



Molecular parameter
Number of Atoms (N) 7
Number of internal coordinates 15
Number of independant internal coordinates 6
Number of vibrational modes 15


Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 Total
Linear (IR) 6 2 4 3 13 / 2
Quadratic (Raman) 6 2 4 3 15 / 0
IR + Raman 6 - - - - 4 3 13 / 0


Characters of force fields
(Symmetric powers of vibration representation)
Force field E C2.(z) σv.(xz) σd.(yz)
linear 15 1 5 3
quadratic 120 8 20 12
cubic 680 8 60 28
quartic 3.060 36 160 72
quintic 11.628 36 376 144
sextic 38.760 120 820 300


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A1 A2 B1 B2
linear 6 2 4 3
quadratic 40 24 30 26
cubic 194 150 176 160
quartic 832 716 778 734
quintic 3.046 2.786 2.956 2.840
sextic 10.000 9.440 9.790 9.530


Further Reading



Contributions to nonvanishing force field constants


pos(X) : Position of irreducible representation (irrep) X in character table of C2v

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(B2)
..21. A1A1...3. A2A2...10. B1B1...6. B2B2.
Subtotal: 40 / 4 / 4
Irrep combinations (i,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(B2)
Subtotal: 0 / 0 / 6
Total: 40 / 4 / 10


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A1) ≤ i ≤ pos(B2)
..56. A1A1A1.
Subtotal: 56 / 1 / 4
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(B2)
..18. A1A2A2...60. A1B1B1...36. A1B2B2.
Subtotal: 114 / 3 / 12
Irrep combinations (i,j,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(B2)
..24. A2B1B2.
Subtotal: 24 / 1 / 4
Total: 194 / 5 / 20


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A1) ≤ i ≤ pos(B2)
..126. A1A1A1A1...5. A2A2A2A2...35. B1B1B1B1...15. B2B2B2B2.
Subtotal: 181 / 4 / 4
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(B2)
Subtotal: 0 / 0 / 12
Irrep combinations (i,i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(B2)
..63. A1A1A2A2...210. A1A1B1B1...126. A1A1B2B2...30. A2A2B1B1...18. A2A2B2B2...60. B1B1B2B2.
Subtotal: 507 / 6 / 6
Irrep combinations (i,i,j,k) (i,j,j,k) (i,j,k,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(B2)
Subtotal: 0 / 0 / 12
Irrep combinations (i,j,k,l) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ l ≤ pos(B2)
..144. A1A2B1B2.
Subtotal: 144 / 1 / 1
Total: 832 / 11 / 35


Calculate contributions to

A1 A2 B1 B2
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Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement