Results for Point Group D4



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


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



Molecular parameter
Number of Atoms (N) 7
Number of internal coordinates 15
Number of independant internal coordinates 2
Number of vibrational modes 11

Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 E Total
Linear (IR) 2 2 1 2 4 6 / 5
Quadratic (Raman) 2 2 1 2 4 9 / 2
IR + Raman - - - - - - - - - - - - - - - - 4 4 / 0


Characters of force fields
(Symmetric powers of vibration representation)
Force field E 2C4 C2 2C'2 2C''2
linear 15 1 -1 -1 1
quadratic 120 0 8 8 8
cubic 680 0 -8 -8 8
quartic 3.060 4 36 36 36
quintic 11.628 4 -36 -36 36
sextic 38.760 0 120 120 120


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A1 A2 B1 B2 E
linear 2 2 1 2 4
quadratic 20 12 16 16 28
cubic 84 84 80 88 172
quartic 406 370 386 386 756
quintic 1.450 1.450 1.430 1.466 2.916
sextic 4.920 4.800 4.860 4.860 9.660


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)
..3. A1A1...3. A2A2...1. B1B1...3. B2B2...10. EE.
Subtotal: 20 / 5 / 5
Irrep combinations (i,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
Subtotal: 0 / 0 / 10
Total: 20 / 5 / 15


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A1) ≤ i ≤ pos(E)
..4. A1A1A1.
Subtotal: 4 / 1 / 5
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
..6. A1A2A2...2. A1B1B1...6. A1B2B2...20. A1EE...12. A2EE...10. B1EE...20. B2EE.
Subtotal: 76 / 7 / 20
Irrep combinations (i,j,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(E)
..4. A2B1B2.
Subtotal: 4 / 1 / 10
Total: 84 / 9 / 35


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A1) ≤ i ≤ pos(E)
..5. A1A1A1A1...5. A2A2A2A2...1. B1B1B1B1...5. B2B2B2B2...90. EEEE.
Subtotal: 106 / 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)
..9. A1A1A2A2...3. A1A1B1B1...9. A1A1B2B2...30. A1A1EE...3. A2A2B1B1...9. A2A2B2B2...30. A2A2EE...3. B1B1B2B2...10. B1B1EE...30. B2B2EE.
Subtotal: 136 / 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)
..24. A1A2EE...20. A1B1EE...40. A1B2EE...20. A2B1EE...40. A2B2EE...12. B1B2EE.
Subtotal: 156 / 6 / 30
Irrep combinations (i,j,k,l) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ l ≤ pos(E)
..8. A1A2B1B2.
Subtotal: 8 / 1 / 5
Total: 406 / 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