Results for Point Group C2v



Characters of representations for molecular motions
Motion E C2.(z) σv.(xz) σd.(yz)
Cartesian 3N 156 0 14 14
Translation (x,y,z) 3 -1 1 1
Rotation (Rx,Ry,Rz) 3 -1 -1 -1
Vibration 150 2 14 14


Decomposition to irreducible representations
Motion A1 A2 B1 B2 Total
Cartesian 3N 46 32 39 39 156
Translation (x,y,z) 1 0 1 1 3
Rotation (Rx,Ry,Rz) 0 1 1 1 3
Vibration 45 31 37 37 150



Molecular parameter
Number of Atoms (N) 52
Number of internal coordinates 150
Number of independant internal coordinates 45
Number of vibrational modes 150


Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 Total
Linear (IR) 45 31 37 37 119 / 31
Quadratic (Raman) 45 31 37 37 150 / 0
IR + Raman 45 - - - - 37 37 119 / 0


Characters of force fields
(Symmetric powers of vibration representation)
Force field E C2.(z) σv.(xz) σd.(yz)
linear 150 2 14 14
quadratic 11.325 77 173 173
cubic 573.800 152 1.512 1.512
quartic 21.947.850 3.002 11.866 11.866
quintic 675.993.780 5.852 79.492 79.492
sextic 17.463.172.650 79.002 490.042 490.042


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A1 A2 B1 B2
linear 45 31 37 37
quadratic 2.937 2.764 2.812 2.812
cubic 144.244 142.732 143.412 143.412
quartic 5.493.646 5.481.780 5.486.212 5.486.212
quintic 169.039.654 168.960.162 168.996.982 168.996.982
sextic 4.366.057.934 4.365.567.892 4.365.773.412 4.365.773.412


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)
..1.035. A1A1...496. A2A2...703. B1B1...703. B2B2.
Subtotal: 2.937 / 4 / 4
Irrep combinations (i,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(B2)
Subtotal: 0 / 0 / 6
Total: 2.937 / 4 / 10


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A1) ≤ i ≤ pos(B2)
..16.215. A1A1A1.
Subtotal: 16.215 / 1 / 4
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(B2)
..22.320. A1A2A2...31.635. A1B1B1...31.635. A1B2B2.
Subtotal: 85.590 / 3 / 12
Irrep combinations (i,j,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(B2)
..42.439. A2B1B2.
Subtotal: 42.439 / 1 / 4
Total: 144.244 / 5 / 20


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A1) ≤ i ≤ pos(B2)
..194.580. A1A1A1A1...46.376. A2A2A2A2...91.390. B1B1B1B1...91.390. B2B2B2B2.
Subtotal: 423.736 / 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)
..513.360. A1A1A2A2...727.605. A1A1B1B1...727.605. A1A1B2B2...348.688. A2A2B1B1...348.688. A2A2B2B2...494.209. B1B1B2B2.
Subtotal: 3.160.155 / 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)
..1.909.755. A1A2B1B2.
Subtotal: 1.909.755 / 1 / 1
Total: 5.493.646 / 11 / 35


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Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement