Results for Point Group O



Characters of representations for molecular motions
Motion E 8C3 6C2 6C4 3C2
Cartesian 3N 39 0 -1 5 -5
Translation (x,y,z) 3 0 -1 1 -1
Rotation (Rx,Ry,Rz) 3 0 -1 1 -1
Vibration 33 0 1 3 -3


Decomposition to irreducible representations
Motion A1 A2 E T1 T2 Total
Cartesian 3N 2 0 2 7 4 15
Translation (x,y,z) 0 0 0 1 0 1
Rotation (Rx,Ry,Rz) 0 0 0 1 0 1
Vibration 2 0 2 5 4 13



Molecular parameter
Number of Atoms (N) 13
Number of internal coordinates 33
Number of independant internal coordinates 2
Number of vibrational modes 13

Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 E T1 T2 Total
Linear (IR) 2 0 2 5 4 5 / 8
Quadratic (Raman) 2 0 2 5 4 8 / 5
IR + Raman - - - - 0 - - - - - - - - - - - - 0 / 0


Characters of force fields
(Symmetric powers of vibration representation)
Force field E 8C3 6C2 6C4 3C2
linear 33 0 1 3 -3
quadratic 561 0 17 3 21
cubic 6.545 11 17 1 -55
quartic 58.905 0 153 9 225
quintic 435.897 0 153 27 -531
sextic 2.760.681 66 969 27 1.653


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A1 A2 E T1 T2
linear 2 0 2 5 4
quadratic 31 21 52 64 71
cubic 274 265 528 821 829
quartic 2.523 2.442 4.965 7.299 7.371
quintic 18.141 18.051 36.192 54.522 54.585
sextic 115.506 115.008 230.448 344.643 345.114


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...15. T1T1...10. T2T2.
Subtotal: 31 / 4 / 5
Irrep combinations (i,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(T2)
Subtotal: 0 / 0 / 10
Total: 31 / 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...10. T1T1T1...20. T2T2T2.
Subtotal: 38 / 4 / 5
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(T2)
..60. T1T1T2...6. A1EE...30. A1T1T1...20. A1T2T2...30. ET1T1...20. ET2T2...30. T1T2T2.
Subtotal: 196 / 7 / 20
Irrep combinations (i,j,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(T2)
..40. ET1T2.
Subtotal: 40 / 1 / 10
Total: 274 / 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...190. T1T1T1T1...90. T2T2T2T2.
Subtotal: 291 / 4 / 5
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(T2)
..300. T1T1T1T2...8. A1EEE...20. A1T1T1T1...40. A1T2T2T2...80. ET1T1T1...40. ET2T2T2...200. T1T2T2T2.
Subtotal: 688 / 7 / 20
Irrep combinations (i,i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(T2)
..9. A1A1EE...45. A1A1T1T1...30. A1A1T2T2...90. EET1T1...60. EET2T2...510. T1T1T2T2.
Subtotal: 744 / 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)
..80. EET1T2...120. A1T1T1T2...200. ET1T1T2...60. A1ET1T1...40. A1ET2T2...60. A1T1T2T2...160. ET1T2T2.
Subtotal: 720 / 7 / 30
Irrep combinations (i,j,k,l) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ l ≤ pos(T2)
..80. A1ET1T2.
Subtotal: 80 / 1 / 5
Total: 2.523 / 25 / 70


Calculate contributions to

A1 A2 E T1 T2
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Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement