Results for Point Group Td



Characters of representations for molecular motions
Motion E 8C3 3C2 6S4 6σd
Cartesian 3N 30 0 -2 0 4
Translation (x,y,z) 3 0 -1 -1 1
Rotation (Rx,Ry,Rz) 3 0 -1 1 -1
Vibration 24 0 0 0 4


Decomposition to irreducible representations
Motion A1 A2 E T1 T2 Total
Cartesian 3N 2 0 2 3 5 12
Translation (x,y,z) 0 0 0 0 1 1
Rotation (Rx,Ry,Rz) 0 0 0 1 0 1
Vibration 2 0 2 2 4 10



Molecular parameter
Number of Atoms (N) 10
Number of internal coordinates 24
Number of independant internal coordinates 2
Number of vibrational modes 10

Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 E T1 T2 Total
Linear (IR) 2 0 2 2 4 4 / 6
Quadratic (Raman) 2 0 2 2 4 8 / 2
IR + Raman - - - - 0 - - - - 2 4 4 / 2


Characters of force fields
(Symmetric powers of vibration representation)
Force field E 8C3 3C2 6S4 6σd
linear 24 0 0 0 4
quadratic 300 0 12 0 20
cubic 2.600 8 0 0 60
quartic 17.550 0 78 6 190
quintic 98.280 0 0 0 476
sextic 475.020 36 364 0 1.204


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A1 A2 E T1 T2
linear 2 0 2 2 4
quadratic 19 9 28 31 41
cubic 126 96 214 310 340
quartic 790 692 1.482 2.138 2.230
quintic 4.214 3.976 8.190 12.166 12.404
sextic 20.151 19.549 39.664 59.031 59.633


Further Reading


Contributions to nonvanishing force field constants


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

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...3. T1T1...10. T2T2.
Subtotal: 19 / 4 / 5
Irrep combinations (i,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(T2)
Subtotal: 0 / 0 / 10
Total: 19 / 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...20. T2T2T2.
Subtotal: 28 / 3 / 5
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(T2)
..12. T1T1T2...6. A1EE...6. A1T1T1...20. A1T2T2...6. ET1T1...20. ET2T2...12. T1T2T2.
Subtotal: 82 / 7 / 20
Irrep combinations (i,j,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(T2)
..16. ET1T2.
Subtotal: 16 / 1 / 10
Total: 126 / 11 / 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...11. T1T1T1T1...90. T2T2T2T2.
Subtotal: 112 / 4 / 5
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(T2)
..24. T1T1T1T2...8. A1EEE...40. A1T2T2T2...4. ET1T1T1...40. ET2T2T2...80. T1T2T2T2.
Subtotal: 196 / 6 / 20
Irrep combinations (i,i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(T2)
..9. A1A1EE...9. A1A1T1T1...30. A1A1T2T2...18. EET1T1...60. EET2T2...96. T1T1T2T2.
Subtotal: 222 / 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)
..32. EET1T2...24. A1T1T1T2...32. ET1T1T2...12. A1ET1T1...40. A1ET2T2...24. A1T1T2T2...64. ET1T2T2.
Subtotal: 228 / 7 / 30
Irrep combinations (i,j,k,l) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ l ≤ pos(T2)
..32. A1ET1T2.
Subtotal: 32 / 1 / 5
Total: 790 / 24 / 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