Results for Point Group Td



Characters of representations for molecular motions
Motion E 8C3 3C2 6S4 d
Cartesian 3N 48 0 0 0 8
Translation (x,y,z) 3 0 -1 -1 1
Rotation (Rx,Ry,Rz) 3 0 -1 1 -1
Vibration 42 0 2 0 8


Decomposition to irreducible representations
Motion A1 A2 E T1 T2 Total
Cartesian 3N 4 0 4 4 8 20
Translation (x,y,z) 0 0 0 0 1 1
Rotation (Rx,Ry,Rz) 0 0 0 1 0 1
Vibration 4 0 4 3 7 18



Molecular parameter
Number of Atoms (N) 16
Number of internal coordinates 42
Number of independant internal coordinates 4
Number of vibrational modes 18


Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 E T1 T2 Total
Linear (IR) 4 0 4 3 7 7 / 11
Quadratic (Raman) 4 0 4 3 7 15 / 3
IR + Raman - - - - 0 - - - - 3 7 7 / 3


Characters of force fields
(Symmetric powers of vibration representation)
Force field E 8C3 3C2 6S4 d
linear 42 0 2 0 8
quadratic 903 0 23 1 53
cubic 13.244 14 44 0 256
quartic 148.995 0 275 11 1.095
quintic 1.370.754 0 506 0 4.056
sextic 10.737.573 105 2.277 11 13.803


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A1 A2 E T1 T2
linear 4 0 4 3 7
quadratic 54 27 81 97 123
cubic 626 498 1.110 1.586 1.714
quartic 6.519 5.966 12.485 18.319 18.861
quintic 58.192 56.164 114.356 170.267 172.295
sextic 451.172 444.265 895.332 1.338.464 1.345.360


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)
..10. A1A1...10. EE...6. T1T1...28. T2T2.
Subtotal: 54 / 4 / 5
Irrep combinations (i,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(T2)
Subtotal: 0 / 0 / 10
Total: 54 / 4 / 15


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A1) ≤ i ≤ pos(T2)
..20. A1A1A1...20. EEE...1. T1T1T1...84. T2T2T2.
Subtotal: 125 / 4 / 5
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(T2)
..42. T1T1T2...40. A1EE...24. A1T1T1...112. A1T2T2...24. ET1T1...112. ET2T2...63. T1T2T2.
Subtotal: 417 / 7 / 20
Irrep combinations (i,j,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(T2)
..84. ET1T2.
Subtotal: 84 / 1 / 10
Total: 626 / 12 / 35


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A1) ≤ i ≤ pos(T2)
..35. A1A1A1A1...55. EEEE...36. T1T1T1T1...616. T2T2T2T2.
Subtotal: 742 / 4 / 5
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(T2)
..126. T1T1T1T2...80. A1EEE...4. A1T1T1T1...336. A1T2T2T2...32. ET1T1T1...448. ET2T2T2...588. T1T2T2T2.
Subtotal: 1.614 / 7 / 20
Irrep combinations (i,i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(T2)
..100. A1A1EE...60. A1A1T1T1...280. A1A1T2T2...120. EET1T1...560. EET2T2...567. T1T1T2T2.
Subtotal: 1.687 / 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)
..336. EET1T2...168. A1T1T1T2...252. ET1T1T2...96. A1ET1T1...448. A1ET2T2...252. A1T1T2T2...588. ET1T2T2.
Subtotal: 2.140 / 7 / 30
Irrep combinations (i,j,k,l) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ l ≤ pos(T2)
..336. A1ET1T2.
Subtotal: 336 / 1 / 5
Total: 6.519 / 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