Results for Point Group C4v



Characters of representations for molecular motions
Motion E 2C4 C2 v d
Cartesian 3N 36 4 -4 8 4
Translation (x,y,z) 3 1 -1 1 1
Rotation (Rx,Ry,Rz) 3 1 -1 -1 -1
Vibration 30 2 -2 8 4


Decomposition to irreducible representations
Motion A1 A2 B1 B2 E Total
Cartesian 3N 8 2 4 2 10 26
Translation (x,y,z) 1 0 0 0 1 2
Rotation (Rx,Ry,Rz) 0 1 0 0 1 2
Vibration 7 1 4 2 8 22



Molecular parameter
Number of Atoms (N) 12
Number of internal coordinates 30
Number of independant internal coordinates 7
Number of vibrational modes 22


Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 E Total
Linear (IR) 7 1 4 2 8 15 / 7
Quadratic (Raman) 7 1 4 2 8 21 / 1
IR + Raman 7 1 - - - - - - - - 8 15 / 1


Characters of force fields
(Symmetric powers of vibration representation)
Force field E 2C4 C2 v d
linear 30 2 -2 8 4
quadratic 465 1 17 47 23
cubic 4.960 0 -32 208 72
quartic 40.920 8 152 792 256
quintic 278.256 16 -272 2.640 680
sextic 1.623.160 8 952 8.008 1.904


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A1 A2 B1 B2 E
linear 7 1 4 2 8
quadratic 78 43 66 54 112
cubic 686 546 650 582 1.248
quartic 5.398 4.874 5.266 4.998 10.192
quintic 35.582 33.922 35.234 34.254 69.632
sextic 205.494 200.538 204.538 201.486 405.552


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)
..28. A1A1...1. A2A2...10. B1B1...3. B2B2...36. EE.
Subtotal: 78 / 5 / 5
Irrep combinations (i,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
Subtotal: 0 / 0 / 10
Total: 78 / 5 / 15


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A1) ≤ i ≤ pos(E)
..84. A1A1A1.
Subtotal: 84 / 1 / 5
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
..7. A1A2A2...70. A1B1B1...21. A1B2B2...252. A1EE...28. A2EE...144. B1EE...72. B2EE.
Subtotal: 594 / 7 / 20
Irrep combinations (i,j,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(E)
..8. A2B1B2.
Subtotal: 8 / 1 / 10
Total: 686 / 9 / 35


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A1) ≤ i ≤ pos(E)
..210. A1A1A1A1...1. A2A2A2A2...35. B1B1B1B1...5. B2B2B2B2...996. EEEE.
Subtotal: 1.247 / 5 / 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)
..28. A1A1A2A2...280. A1A1B1B1...84. A1A1B2B2...1.008. A1A1EE...10. A2A2B1B1...3. A2A2B2B2...36. A2A2EE...30. B1B1B2B2...360. B1B1EE...108. B2B2EE.
Subtotal: 1.947 / 10 / 10
Irrep combinations (i,i,j,k) (i,j,j,k) (i,j,k,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(E)
..196. A1A2EE...1.008. A1B1EE...504. A1B2EE...144. A2B1EE...72. A2B2EE...224. B1B2EE.
Subtotal: 2.148 / 6 / 30
Irrep combinations (i,j,k,l) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ l ≤ pos(E)
..56. A1A2B1B2.
Subtotal: 56 / 1 / 5
Total: 5.398 / 22 / 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