Results for Point Group C4v



Characters of representations for molecular motions
Motion E 2C4 C2 v d
Cartesian 3N 21 3 -3 5 3
Translation (x,y,z) 3 1 -1 1 1
Rotation (Rx,Ry,Rz) 3 1 -1 -1 -1
Vibration 15 1 -1 5 3


Decomposition to irreducible representations
Motion A1 A2 B1 B2 E Total
Cartesian 3N 5 1 2 1 6 15
Translation (x,y,z) 1 0 0 0 1 2
Rotation (Rx,Ry,Rz) 0 1 0 0 1 2
Vibration 4 0 2 1 4 11



Molecular parameter
Number of Atoms (N) 7
Number of internal coordinates 15
Number of independant internal coordinates 4
Number of vibrational modes 11


Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 E Total
Linear (IR) 4 0 2 1 4 8 / 3
Quadratic (Raman) 4 0 2 1 4 11 / 0
IR + Raman 4 0 - - - - - - - - 4 8 / 0


Characters of force fields
(Symmetric powers of vibration representation)
Force field E 2C4 C2 v d
linear 15 1 -1 5 3
quadratic 120 0 8 20 12
cubic 680 0 -8 60 28
quartic 3.060 4 36 160 72
quintic 11.628 4 -36 376 144
sextic 38.760 0 120 820 300


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A1 A2 B1 B2 E
linear 4 0 2 1 4
quadratic 24 8 18 14 28
cubic 106 62 92 76 172
quartic 446 330 408 364 756
quintic 1.580 1.320 1.506 1.390 2.916
sextic 5.140 4.580 4.990 4.730 9.660


Further Reading



Contributions to nonvanishing force field constants


pos(X) : Position of irreducible representation (irrep) X in character table of C4v

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(E)
..10. A1A1...3. B1B1...1. B2B2...10. EE.
Subtotal: 24 / 4 / 5
Irrep combinations (i,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
Subtotal: 0 / 0 / 10
Total: 24 / 4 / 15


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A1) ≤ i ≤ pos(E)
..20. A1A1A1.
Subtotal: 20 / 1 / 5
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
..12. A1B1B1...4. A1B2B2...40. A1EE...20. B1EE...10. B2EE.
Subtotal: 86 / 5 / 20
Irrep combinations (i,j,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(E)
Subtotal: 0 / 0 / 10
Total: 106 / 6 / 35


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A1) ≤ i ≤ pos(E)
..35. A1A1A1A1...5. B1B1B1B1...1. B2B2B2B2...90. EEEE.
Subtotal: 131 / 4 / 5
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
Subtotal: 0 / 0 / 20
Irrep combinations (i,i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
..30. A1A1B1B1...10. A1A1B2B2...100. A1A1EE...3. B1B1B2B2...30. B1B1EE...10. B2B2EE.
Subtotal: 183 / 6 / 10
Irrep combinations (i,i,j,k) (i,j,j,k) (i,j,k,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(E)
..80. A1B1EE...40. A1B2EE...12. B1B2EE.
Subtotal: 132 / 3 / 30
Irrep combinations (i,j,k,l) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ l ≤ pos(E)
Subtotal: 0 / 0 / 5
Total: 446 / 13 / 70


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