Results for Point Group C2v



Characters of representations for molecular motions
Motion E C2.(z) σv.(xz) σd.(yz)
Cartesian 3N 30 0 10 0
Translation (x,y,z) 3 -1 1 1
Rotation (Rx,Ry,Rz) 3 -1 -1 -1
Vibration 24 2 10 0


Decomposition to irreducible representations
Motion A1 A2 B1 B2 Total
Cartesian 3N 10 5 10 5 30
Translation (x,y,z) 1 0 1 1 3
Rotation (Rx,Ry,Rz) 0 1 1 1 3
Vibration 9 4 8 3 24



Molecular parameter
Number of Atoms (N) 10
Number of internal coordinates 24
Number of independant internal coordinates 9
Number of vibrational modes 24


Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 Total
Linear (IR) 9 4 8 3 20 / 4
Quadratic (Raman) 9 4 8 3 24 / 0
IR + Raman 9 - - - - 8 3 20 / 0


Characters of force fields
(Symmetric powers of vibration representation)
Force field E C2.(z) σv.(xz) σd.(yz)
linear 24 2 10 0
quadratic 300 14 62 12
cubic 2.600 26 290 0
quartic 17.550 104 1.128 78
quintic 98.280 182 3.822 0
sextic 475.020 546 11.634 364


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A1 A2 B1 B2
linear 9 4 8 3
quadratic 97 60 84 59
cubic 729 584 716 571
quartic 4.715 4.112 4.624 4.099
quintic 25.571 23.660 25.480 23.569
sextic 121.891 115.892 121.436 115.801


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...10. A2A2...36. B1B1...6. B2B2.
Subtotal: 97 / 4 / 4
Irrep combinations (i,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(B2)
Subtotal: 0 / 0 / 6
Total: 97 / 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)
..90. A1A2A2...324. A1B1B1...54. A1B2B2.
Subtotal: 468 / 3 / 12
Irrep combinations (i,j,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(B2)
..96. A2B1B2.
Subtotal: 96 / 1 / 4
Total: 729 / 5 / 20


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A1) ≤ i ≤ pos(B2)
..495. A1A1A1A1...35. A2A2A2A2...330. B1B1B1B1...15. B2B2B2B2.
Subtotal: 875 / 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)
..450. A1A1A2A2...1.620. A1A1B1B1...270. A1A1B2B2...360. A2A2B1B1...60. A2A2B2B2...216. B1B1B2B2.
Subtotal: 2.976 / 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)
..864. A1A2B1B2.
Subtotal: 864 / 1 / 1
Total: 4.715 / 11 / 35


Calculate contributions to

A1 A2 B1 B2
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