Results for Point Group C4v



Characters of representations for molecular motions
Motion E 2C4 C2 2σv 2σd
Cartesian 3N 39 5 -5 9 5
Translation (x,y,z) 3 1 -1 1 1
Rotation (Rx,Ry,Rz) 3 1 -1 -1 -1
Vibration 33 3 -3 9 5


Decomposition to irreducible representations
Motion A1 A2 B1 B2 E Total
Cartesian 3N 9 2 4 2 11 28
Translation (x,y,z) 1 0 0 0 1 2
Rotation (Rx,Ry,Rz) 0 1 0 0 1 2
Vibration 8 1 4 2 9 24



Molecular parameter
Number of Atoms (N) 13
Number of internal coordinates 33
Number of independant internal coordinates 8
Number of vibrational modes 24

Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 E Total
Linear (IR) 8 1 4 2 9 17 / 7
Quadratic (Raman) 8 1 4 2 9 23 / 1
IR + Raman 8 1 - - - - - - - - 9 17 / 1


Characters of force fields
(Symmetric powers of vibration representation)
Force field E 2C4 C2 2σv 2σd
linear 33 3 -3 9 5
quadratic 561 3 21 57 29
cubic 6.545 1 -55 273 105
quartic 58.905 9 225 1.113 385
quintic 435.897 27 -531 3.969 1.141
sextic 2.760.681 27 1.653 12.817 3.325


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A1 A2 B1 B2 E
linear 8 1 4 2 9
quadratic 95 52 79 65 135
cubic 906 717 853 769 1.650
quartic 7.768 7.019 7.571 7.207 14.670
quintic 55.705 53.150 55.121 53.707 109.107
sextic 349.334 341.263 347.658 342.912 689.757


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)
..36. A1A1...1. A2A2...10. B1B1...3. B2B2...45. EE.
Subtotal: 95 / 5 / 5
Irrep combinations (i,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
Subtotal: 0 / 0 / 10
Total: 95 / 5 / 15


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A1) ≤ i ≤ pos(E)
..120. A1A1A1.
Subtotal: 120 / 1 / 5
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
..8. A1A2A2...80. A1B1B1...24. A1B2B2...360. A1EE...36. A2EE...180. B1EE...90. B2EE.
Subtotal: 778 / 7 / 20
Irrep combinations (i,j,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(E)
..8. A2B1B2.
Subtotal: 8 / 1 / 10
Total: 906 / 9 / 35


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A1) ≤ i ≤ pos(E)
..330. A1A1A1A1...1. A2A2A2A2...35. B1B1B1B1...5. B2B2B2B2...1.530. EEEE.
Subtotal: 1.901 / 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)
..36. A1A1A2A2...360. A1A1B1B1...108. A1A1B2B2...1.620. A1A1EE...10. A2A2B1B1...3. A2A2B2B2...45. A2A2EE...30. B1B1B2B2...450. B1B1EE...135. B2B2EE.
Subtotal: 2.797 / 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)
..288. A1A2EE...1.440. A1B1EE...720. A1B2EE...180. A2B1EE...90. A2B2EE...288. B1B2EE.
Subtotal: 3.006 / 6 / 30
Irrep combinations (i,j,k,l) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ l ≤ pos(E)
..64. A1A2B1B2.
Subtotal: 64 / 1 / 5
Total: 7.768 / 22 / 70


Calculate contributions to

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