Results for Point Group C2v



Characters of representations for molecular motions
Motion E C2.(z) σv.(xz) σd.(yz)
Cartesian 3N 39 -5 9 9
Translation (x,y,z) 3 -1 1 1
Rotation (Rx,Ry,Rz) 3 -1 -1 -1
Vibration 33 -3 9 9


Decomposition to irreducible representations
Motion A1 A2 B1 B2 Total
Cartesian 3N 13 4 11 11 39
Translation (x,y,z) 1 0 1 1 3
Rotation (Rx,Ry,Rz) 0 1 1 1 3
Vibration 12 3 9 9 33



Molecular parameter
Number of Atoms (N) 13
Number of internal coordinates 33
Number of independant internal coordinates 12
Number of vibrational modes 33


Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 Total
Linear (IR) 12 3 9 9 30 / 3
Quadratic (Raman) 12 3 9 9 33 / 0
IR + Raman 12 - - - - 9 9 30 / 0


Characters of force fields
(Symmetric powers of vibration representation)
Force field E C2.(z) σv.(xz) σd.(yz)
linear 33 -3 9 9
quadratic 561 21 57 57
cubic 6.545 -55 273 273
quartic 58.905 225 1.113 1.113
quintic 435.897 -531 3.969 3.969
sextic 2.760.681 1.653 12.817 12.817


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A1 A2 B1 B2
linear 12 3 9 9
quadratic 174 117 135 135
cubic 1.759 1.486 1.650 1.650
quartic 15.339 14.226 14.670 14.670
quintic 110.826 106.857 109.107 109.107
sextic 696.992 684.175 689.757 689.757


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)
..78. A1A1...6. A2A2...45. B1B1...45. B2B2.
Subtotal: 174 / 4 / 4
Irrep combinations (i,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(B2)
Subtotal: 0 / 0 / 6
Total: 174 / 4 / 10


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A1) ≤ i ≤ pos(B2)
..364. A1A1A1.
Subtotal: 364 / 1 / 4
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(B2)
..72. A1A2A2...540. A1B1B1...540. A1B2B2.
Subtotal: 1.152 / 3 / 12
Irrep combinations (i,j,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(B2)
..243. A2B1B2.
Subtotal: 243 / 1 / 4
Total: 1.759 / 5 / 20


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A1) ≤ i ≤ pos(B2)
..1.365. A1A1A1A1...15. A2A2A2A2...495. B1B1B1B1...495. B2B2B2B2.
Subtotal: 2.370 / 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)
..468. A1A1A2A2...3.510. A1A1B1B1...3.510. A1A1B2B2...270. A2A2B1B1...270. A2A2B2B2...2.025. B1B1B2B2.
Subtotal: 10.053 / 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)
..2.916. A1A2B1B2.
Subtotal: 2.916 / 1 / 1
Total: 15.339 / 11 / 35


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