Results for Point Group O



Characters of representations for molecular motions
Motion E 8C3 6C2 6C4 3C2
Cartesian 3N 36 0 0 4 -4
Translation (x,y,z) 3 0 -1 1 -1
Rotation (Rx,Ry,Rz) 3 0 -1 1 -1
Vibration 30 0 2 2 -2


Decomposition to irreducible representations
Motion A1 A2 E T1 T2 Total
Cartesian 3N 2 0 2 6 4 14
Translation (x,y,z) 0 0 0 1 0 1
Rotation (Rx,Ry,Rz) 0 0 0 1 0 1
Vibration 2 0 2 4 4 12



Molecular parameter
Number of Atoms (N) 12
Number of internal coordinates 30
Number of independant internal coordinates 2
Number of vibrational modes 12

Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 E T1 T2 Total
Linear (IR) 2 0 2 4 4 4 / 8
Quadratic (Raman) 2 0 2 4 4 8 / 4
IR + Raman - - - - 0 - - - - - - - - - - - - 0 / 0


Characters of force fields
(Symmetric powers of vibration representation)
Force field E 8C3 6C2 6C4 3C2
linear 30 0 2 2 -2
quadratic 465 0 17 1 17
cubic 4.960 10 32 0 -32
quartic 40.920 0 152 8 152
quintic 278.256 0 272 16 -272
sextic 1.623.160 55 952 8 952


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A1 A2 E T1 T2
linear 2 0 2 4 4
quadratic 26 17 43 52 60
cubic 214 198 402 616 632
quartic 1.764 1.684 3.448 5.060 5.132
quintic 11.632 11.488 23.120 34.752 34.880
sextic 68.009 67.529 135.483 202.540 203.012


Further Reading


Contributions to nonvanishing force field constants


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

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(T2)
..3. A1A1...3. EE...10. T1T1...10. T2T2.
Subtotal: 26 / 4 / 5
Irrep combinations (i,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(T2)
Subtotal: 0 / 0 / 10
Total: 26 / 4 / 15


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A1) ≤ i ≤ pos(T2)
..4. A1A1A1...4. EEE...4. T1T1T1...20. T2T2T2.
Subtotal: 32 / 4 / 5
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(T2)
..40. T1T1T2...6. A1EE...20. A1T1T1...20. A1T2T2...20. ET1T1...20. ET2T2...24. T1T2T2.
Subtotal: 150 / 7 / 20
Irrep combinations (i,j,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(T2)
..32. ET1T2.
Subtotal: 32 / 1 / 10
Total: 214 / 12 / 35


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A1) ≤ i ≤ pos(T2)
..5. A1A1A1A1...6. EEEE...90. T1T1T1T1...90. T2T2T2T2.
Subtotal: 191 / 4 / 5
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(T2)
..160. T1T1T1T2...8. A1EEE...8. A1T1T1T1...40. A1T2T2T2...40. ET1T1T1...40. ET2T2T2...160. T1T2T2T2.
Subtotal: 456 / 7 / 20
Irrep combinations (i,i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(T2)
..9. A1A1EE...30. A1A1T1T1...30. A1A1T2T2...60. EET1T1...60. EET2T2...336. T1T1T2T2.
Subtotal: 525 / 6 / 10
Irrep combinations (i,i,j,k) (i,j,j,k) (i,j,k,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(T2)
..64. EET1T2...80. A1T1T1T2...128. ET1T1T2...40. A1ET1T1...40. A1ET2T2...48. A1T1T2T2...128. ET1T2T2.
Subtotal: 528 / 7 / 30
Irrep combinations (i,j,k,l) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ l ≤ pos(T2)
..64. A1ET1T2.
Subtotal: 64 / 1 / 5
Total: 1.764 / 25 / 70


Calculate contributions to

A1 A2 E T1 T2
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