Results for Point Group C2v



Characters of representations for molecular motions
Motion E C2.(z) σv.(xz) σd.(yz)
Cartesian 3N 33 -1 5 3
Translation (x,y,z) 3 -1 1 1
Rotation (Rx,Ry,Rz) 3 -1 -1 -1
Vibration 27 1 5 3


Decomposition to irreducible representations
Motion A1 A2 B1 B2 Total
Cartesian 3N 10 6 9 8 33
Translation (x,y,z) 1 0 1 1 3
Rotation (Rx,Ry,Rz) 0 1 1 1 3
Vibration 9 5 7 6 27



Molecular parameter
Number of Atoms (N) 11
Number of internal coordinates 27
Number of independant internal coordinates 9
Number of vibrational modes 27


Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 Total
Linear (IR) 9 5 7 6 22 / 5
Quadratic (Raman) 9 5 7 6 27 / 0
IR + Raman 9 - - - - 7 6 22 / 0


Characters of force fields
(Symmetric powers of vibration representation)
Force field E C2.(z) σv.(xz) σd.(yz)
linear 27 1 5 3
quadratic 378 14 26 18
cubic 3.654 14 90 46
quartic 27.405 105 301 165
quintic 169.911 105 841 375
sextic 906.192 560 2.256 1.040


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A1 A2 B1 B2
linear 9 5 7 6
quadratic 109 87 93 89
cubic 951 883 921 899
quartic 6.994 6.761 6.859 6.791
quintic 42.808 42.200 42.568 42.335
sextic 227.512 225.864 226.712 226.104


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)
..45. A1A1...15. A2A2...28. B1B1...21. B2B2.
Subtotal: 109 / 4 / 4
Irrep combinations (i,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(B2)
Subtotal: 0 / 0 / 6
Total: 109 / 4 / 10


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A1) ≤ i ≤ pos(B2)
..165. A1A1A1.
Subtotal: 165 / 1 / 4
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(B2)
..135. A1A2A2...252. A1B1B1...189. A1B2B2.
Subtotal: 576 / 3 / 12
Irrep combinations (i,j,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(B2)
..210. A2B1B2.
Subtotal: 210 / 1 / 4
Total: 951 / 5 / 20


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A1) ≤ i ≤ pos(B2)
..495. A1A1A1A1...70. A2A2A2A2...210. B1B1B1B1...126. B2B2B2B2.
Subtotal: 901 / 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)
..675. A1A1A2A2...1.260. A1A1B1B1...945. A1A1B2B2...420. A2A2B1B1...315. A2A2B2B2...588. B1B1B2B2.
Subtotal: 4.203 / 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)
..1.890. A1A2B1B2.
Subtotal: 1.890 / 1 / 1
Total: 6.994 / 11 / 35


Calculate contributions to

A1 A2 B1 B2
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