Results for Point Group C2v



Characters of representations for molecular motions
Motion E C2.(z) σv.(xz) σd.(yz)
Cartesian 3N 12 -2 4 2
Translation (x,y,z) 3 -1 1 1
Rotation (Rx,Ry,Rz) 3 -1 -1 -1
Vibration 6 0 4 2


Decomposition to irreducible representations
Motion A1 A2 B1 B2 Total
Cartesian 3N 4 1 4 3 12
Translation (x,y,z) 1 0 1 1 3
Rotation (Rx,Ry,Rz) 0 1 1 1 3
Vibration 3 0 2 1 6



Molecular parameter
Number of Atoms (N) 4
Number of internal coordinates 6
Number of independant internal coordinates 3
Number of vibrational modes 6


Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 Total
Linear (IR) 3 0 2 1 6 / 0
Quadratic (Raman) 3 0 2 1 6 / 0
IR + Raman 3 - - - - 2 1 6 / 0


Characters of force fields
(Symmetric powers of vibration representation)
Force field E C2.(z) σv.(xz) σd.(yz)
linear 6 0 4 2
quadratic 21 3 11 5
cubic 56 0 24 8
quartic 126 6 46 14
quintic 252 0 80 20
sextic 462 10 130 30


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A1 A2 B1 B2
linear 3 0 2 1
quadratic 10 2 6 3
cubic 22 6 18 10
quartic 48 18 38 22
quintic 88 38 78 48
sextic 158 78 138 88


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)
..6. A1A1...3. B1B1...1. B2B2.
Subtotal: 10 / 3 / 4
Irrep combinations (i,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(B2)
Subtotal: 0 / 0 / 6
Total: 10 / 3 / 10


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A1) ≤ i ≤ pos(B2)
..10. A1A1A1.
Subtotal: 10 / 1 / 4
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(B2)
..9. A1B1B1...3. A1B2B2.
Subtotal: 12 / 2 / 12
Irrep combinations (i,j,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(B2)
Subtotal: 0 / 0 / 4
Total: 22 / 3 / 20


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A1) ≤ i ≤ pos(B2)
..15. A1A1A1A1...5. B1B1B1B1...1. B2B2B2B2.
Subtotal: 21 / 3 / 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)
..18. A1A1B1B1...6. A1A1B2B2...3. B1B1B2B2.
Subtotal: 27 / 3 / 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)
Subtotal: 0 / 0 / 1
Total: 48 / 6 / 35


Calculate contributions to

A1 A2 B1 B2
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Last update January, 3rd 2020 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement