Results for Point Group Td



Characters of representations for molecular motions
Motion E 8C3 3C2 6S4 6σd
Cartesian 3N 42 0 -2 0 6
Translation (x,y,z) 3 0 -1 -1 1
Rotation (Rx,Ry,Rz) 3 0 -1 1 -1
Vibration 36 0 0 0 6


Decomposition to irreducible representations
Motion A1 A2 E T1 T2 Total
Cartesian 3N 3 0 3 4 7 17
Translation (x,y,z) 0 0 0 0 1 1
Rotation (Rx,Ry,Rz) 0 0 0 1 0 1
Vibration 3 0 3 3 6 15



Molecular parameter
Number of Atoms (N) 14
Number of internal coordinates 36
Number of independant internal coordinates 3
Number of vibrational modes 15

Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 E T1 T2 Total
Linear (IR) 3 0 3 3 6 6 / 9
Quadratic (Raman) 3 0 3 3 6 12 / 3
IR + Raman - - - - 0 - - - - 3 6 6 / 3


Characters of force fields
(Symmetric powers of vibration representation)
Force field E 8C3 3C2 6S4 6σd
linear 36 0 0 0 6
quadratic 666 0 18 0 36
cubic 8.436 12 0 0 146
quartic 82.251 0 171 9 561
quintic 658.008 0 0 0 1.812
sextic 4.496.388 78 1.140 0 5.552


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A1 A2 E T1 T2
linear 3 0 3 3 6
quadratic 39 21 60 72 90
cubic 392 319 699 1.018 1.091
quartic 3.591 3.306 6.897 10.122 10.398
quintic 27.870 26.964 54.834 81.798 82.704
sextic 188.906 186.130 374.958 560.518 563.294


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)
..6. A1A1...6. EE...6. T1T1...21. T2T2.
Subtotal: 39 / 4 / 5
Irrep combinations (i,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(T2)
Subtotal: 0 / 0 / 10
Total: 39 / 4 / 15


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A1) ≤ i ≤ pos(T2)
..10. A1A1A1...10. EEE...1. T1T1T1...56. T2T2T2.
Subtotal: 77 / 4 / 5
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(T2)
..36. T1T1T2...18. A1EE...18. A1T1T1...63. A1T2T2...18. ET1T1...63. ET2T2...45. T1T2T2.
Subtotal: 261 / 7 / 20
Irrep combinations (i,j,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(T2)
..54. ET1T2.
Subtotal: 54 / 1 / 10
Total: 392 / 12 / 35


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A1) ≤ i ≤ pos(T2)
..15. A1A1A1A1...21. EEEE...36. T1T1T1T1...357. T2T2T2T2.
Subtotal: 429 / 4 / 5
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(T2)
..108. T1T1T1T2...30. A1EEE...3. A1T1T1T1...168. A1T2T2T2...24. ET1T1T1...210. ET2T2T2...378. T1T2T2T2.
Subtotal: 921 / 7 / 20
Irrep combinations (i,i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(T2)
..36. A1A1EE...36. A1A1T1T1...126. A1A1T2T2...72. EET1T1...252. EET2T2...423. T1T1T2T2.
Subtotal: 945 / 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)
..162. EET1T2...108. A1T1T1T2...162. ET1T1T2...54. A1ET1T1...189. A1ET2T2...135. A1T1T2T2...324. ET1T2T2.
Subtotal: 1.134 / 7 / 30
Irrep combinations (i,j,k,l) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ l ≤ pos(T2)
..162. A1ET1T2.
Subtotal: 162 / 1 / 5
Total: 3.591 / 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