Results for Point Group D4



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


Decomposition to irreducible representations
Motion A1 A2 B1 B2 E Total
Cartesian 3N 4 7 2 4 11 28
Translation (x,y,z) 0 1 0 0 1 2
Rotation (Rx,Ry,Rz) 0 1 0 0 1 2
Vibration 4 5 2 4 9 24



Molecular parameter
Number of Atoms (N) 13
Number of internal coordinates 33
Number of independant internal coordinates 4
Number of vibrational modes 24

Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 E Total
Linear (IR) 4 5 2 4 9 14 / 10
Quadratic (Raman) 4 5 2 4 9 19 / 5
IR + Raman - - - - - - - - - - - - - - - - 9 9 / 0


Characters of force fields
(Symmetric powers of vibration representation)
Force field E 2C4 C2 2C'2 2C''2
linear 33 3 -3 -3 1
quadratic 561 3 21 21 17
cubic 6.545 1 -55 -55 17
quartic 58.905 9 225 225 153
quintic 435.897 27 -531 -531 153
sextic 2.760.681 27 1.653 1.653 969


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A1 A2 B1 B2 E
linear 4 5 2 4 9
quadratic 83 64 73 71 135
cubic 802 821 793 829 1.650
quartic 7.488 7.299 7.407 7.371 14.670
quintic 54.333 54.522 54.243 54.585 109.107
sextic 345.954 344.643 345.456 345.114 689.757


Further Reading


Contributions to nonvanishing force field constants


pos(X) : Position of irreducible representation (irrep) X in character table of D4

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...15. A2A2...3. B1B1...10. B2B2...45. EE.
Subtotal: 83 / 5 / 5
Irrep combinations (i,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
Subtotal: 0 / 0 / 10
Total: 83 / 5 / 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)
..60. A1A2A2...12. A1B1B1...40. A1B2B2...180. A1EE...180. A2EE...90. B1EE...180. B2EE.
Subtotal: 742 / 7 / 20
Irrep combinations (i,j,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(E)
..40. A2B1B2.
Subtotal: 40 / 1 / 10
Total: 802 / 9 / 35


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A1) ≤ i ≤ pos(E)
..35. A1A1A1A1...70. A2A2A2A2...5. B1B1B1B1...35. B2B2B2B2...1.530. EEEE.
Subtotal: 1.675 / 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)
..150. A1A1A2A2...30. A1A1B1B1...100. A1A1B2B2...450. A1A1EE...45. A2A2B1B1...150. A2A2B2B2...675. A2A2EE...30. B1B1B2B2...135. B1B1EE...450. B2B2EE.
Subtotal: 2.215 / 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)
..720. A1A2EE...360. A1B1EE...720. A1B2EE...450. A2B1EE...900. A2B2EE...288. B1B2EE.
Subtotal: 3.438 / 6 / 30
Irrep combinations (i,j,k,l) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ l ≤ pos(E)
..160. A1A2B1B2.
Subtotal: 160 / 1 / 5
Total: 7.488 / 22 / 70


Calculate contributions to

A1 A2 B1 B2 E
Show only nonzero contributions Show all contributions
Up to quartic force fieldUp to quintic force fieldUp to sextic force field





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