Results for Point Group Td



Characters of representations for molecular motions
Motion E 8C3 3C2 6S4 d
Cartesian 3N 51 0 -1 -1 5
Translation (x,y,z) 3 0 -1 -1 1
Rotation (Rx,Ry,Rz) 3 0 -1 1 -1
Vibration 45 0 1 -1 5


Decomposition to irreducible representations
Motion A1 A2 E T1 T2 Total
Cartesian 3N 3 1 4 5 8 21
Translation (x,y,z) 0 0 0 0 1 1
Rotation (Rx,Ry,Rz) 0 0 0 1 0 1
Vibration 3 1 4 4 7 19



Molecular parameter
Number of Atoms (N) 17
Number of internal coordinates 45
Number of independant internal coordinates 3
Number of vibrational modes 19


Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 E T1 T2 Total
Linear (IR) 3 1 4 4 7 7 / 12
Quadratic (Raman) 3 1 4 4 7 14 / 5
IR + Raman - - - - 1 - - - - 4 7 7 / 5


Characters of force fields
(Symmetric powers of vibration representation)
Force field E 8C3 3C2 6S4 d
linear 45 0 1 -1 5
quadratic 1.035 0 23 1 35
cubic 16.215 15 23 -1 135
quartic 194.580 0 276 12 580
quintic 1.906.884 0 276 -12 1.876
sextic 15.890.700 120 2.300 12 6.300


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A1 A2 E T1 T2
linear 3 1 4 4 7
quadratic 55 37 92 118 135
cubic 717 650 1.352 1.990 2.058
quartic 8.290 7.994 16.284 24.146 24.430
quintic 79.954 79.022 158.976 237.854 238.798
sextic 664.018 660.862 1.324.760 1.984.478 1.987.622


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...1. A2A2...10. EE...10. T1T1...28. T2T2.
Subtotal: 55 / 5 / 5
Irrep combinations (i,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(T2)
Subtotal: 0 / 0 / 10
Total: 55 / 5 / 15


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A1) ≤ i ≤ pos(T2)
..10. A1A1A1...20. EEE...4. T1T1T1...84. T2T2T2.
Subtotal: 118 / 4 / 5
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(T2)
..70. T1T1T2...3. A1A2A2...30. A1EE...30. A1T1T1...84. A1T2T2...6. A2EE...40. ET1T1...112. ET2T2...84. T1T2T2.
Subtotal: 459 / 9 / 20
Irrep combinations (i,j,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(T2)
..28. A2T1T2...112. ET1T2.
Subtotal: 140 / 2 / 10
Total: 717 / 15 / 35


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A1) ≤ i ≤ pos(T2)
..15. A1A1A1A1...1. A2A2A2A2...55. EEEE...90. T1T1T1T1...616. T2T2T2T2.
Subtotal: 777 / 5 / 5
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(T2)
..280. T1T1T1T2...60. A1EEE...12. A1T1T1T1...252. A1T2T2T2...20. A2EEE...20. A2T1T1T1...35. A2T2T2T2...80. ET1T1T1...448. ET2T2T2...784. T1T2T2T2.
Subtotal: 1.991 / 10 / 20
Irrep combinations (i,i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(T2)
..6. A1A1A2A2...60. A1A1EE...60. A1A1T1T1...168. A1A1T2T2...10. A2A2EE...10. A2A2T1T1...28. A2A2T2T2...200. EET1T1...560. EET2T2...966. T1T1T2T2.
Subtotal: 2.068 / 10 / 10
Irrep combinations (i,i,j,k) (i,j,j,k) (i,j,k,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(T2)
..448. EET1T2...210. A1T1T1T2...42. A2T1T1T2...448. ET1T1T2...18. A1A2EE...120. A1ET1T1...336. A1ET2T2...252. A1T1T2T2...40. A2ET1T1...112. A2ET2T2.
..112. A2T1T2T2...784. ET1T2T2.
Subtotal: 2.922 / 12 / 30
Irrep combinations (i,j,k,l) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ l ≤ pos(T2)
..84. A1A2T1T2...336. A1ET1T2...112. A2ET1T2.
Subtotal: 532 / 3 / 5
Total: 8.290 / 40 / 70


Calculate contributions to

A1 A2 E T1 T2
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Last update January, 3rd 2020 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement