Results for Point Group C2v



Characters of representations for molecular motions
Motion E C2.(z) σv.(xz) σd.(yz)
Cartesian 3N 48 0 0 8
Translation (x,y,z) 3 -1 1 1
Rotation (Rx,Ry,Rz) 3 -1 -1 -1
Vibration 42 2 0 8


Decomposition to irreducible representations
Motion A1 A2 B1 B2 Total
Cartesian 3N 14 10 10 14 48
Translation (x,y,z) 1 0 1 1 3
Rotation (Rx,Ry,Rz) 0 1 1 1 3
Vibration 13 9 8 12 42



Molecular parameter
Number of Atoms (N) 16
Number of internal coordinates 42
Number of independant internal coordinates 13
Number of vibrational modes 42


Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 Total
Linear (IR) 13 9 8 12 33 / 9
Quadratic (Raman) 13 9 8 12 42 / 0
IR + Raman 13 - - - - 8 12 33 / 0


Characters of force fields
(Symmetric powers of vibration representation)
Force field E C2.(z) σv.(xz) σd.(yz)
linear 42 2 0 8
quadratic 903 23 21 53
cubic 13.244 44 0 256
quartic 148.995 275 231 1.095
quintic 1.370.754 506 0 4.056
sextic 10.737.573 2.277 1.771 13.803


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A1 A2 B1 B2
linear 13 9 8 12
quadratic 250 213 212 228
cubic 3.386 3.258 3.236 3.364
quartic 37.649 36.986 36.964 37.396
quintic 343.829 341.801 341.548 343.576
sextic 2.688.856 2.681.069 2.680.816 2.686.832


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)
..91. A1A1...45. A2A2...36. B1B1...78. B2B2.
Subtotal: 250 / 4 / 4
Irrep combinations (i,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(B2)
Subtotal: 0 / 0 / 6
Total: 250 / 4 / 10


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A1) ≤ i ≤ pos(B2)
..455. A1A1A1.
Subtotal: 455 / 1 / 4
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(B2)
..585. A1A2A2...468. A1B1B1...1.014. A1B2B2.
Subtotal: 2.067 / 3 / 12
Irrep combinations (i,j,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(B2)
..864. A2B1B2.
Subtotal: 864 / 1 / 4
Total: 3.386 / 5 / 20


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A1) ≤ i ≤ pos(B2)
..1.820. A1A1A1A1...495. A2A2A2A2...330. B1B1B1B1...1.365. B2B2B2B2.
Subtotal: 4.010 / 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)
..4.095. A1A1A2A2...3.276. A1A1B1B1...7.098. A1A1B2B2...1.620. A2A2B1B1...3.510. A2A2B2B2...2.808. B1B1B2B2.
Subtotal: 22.407 / 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)
..11.232. A1A2B1B2.
Subtotal: 11.232 / 1 / 1
Total: 37.649 / 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