Results for Point Group Td



Characters of representations for molecular motions
Motion E 8C3 3C2 6S4 6σd
Cartesian 3N 39 0 -5 -1 5
Translation (x,y,z) 3 0 -1 -1 1
Rotation (Rx,Ry,Rz) 3 0 -1 1 -1
Vibration 33 0 -3 -1 5


Decomposition to irreducible representations
Motion A1 A2 E T1 T2 Total
Cartesian 3N 2 0 2 4 7 15
Translation (x,y,z) 0 0 0 0 1 1
Rotation (Rx,Ry,Rz) 0 0 0 1 0 1
Vibration 2 0 2 3 6 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 3 6 6 / 7
Quadratic (Raman) 2 0 2 3 6 10 / 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 33 0 -3 -1 5
quadratic 561 0 21 -1 29
cubic 6.545 11 -55 1 105
quartic 58.905 0 225 9 385
quintic 435.897 0 -531 -9 1.141
sextic 2.760.681 66 1.653 -9 3.325


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A1 A2 E T1 T2
linear 2 0 2 3 6
quadratic 33 19 52 60 75
cubic 296 243 528 799 851
quartic 2.581 2.384 4.965 7.241 7.429
quintic 18.379 17.813 36.192 54.266 54.841
sextic 116.086 114.428 230.448 344.045 345.712


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...6. T1T1...21. T2T2.
Subtotal: 33 / 4 / 5
Irrep combinations (i,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(T2)
Subtotal: 0 / 0 / 10
Total: 33 / 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...1. T1T1T1...56. T2T2T2.
Subtotal: 65 / 4 / 5
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(T2)
..36. T1T1T2...6. A1EE...12. A1T1T1...42. A1T2T2...12. ET1T1...42. ET2T2...45. T1T2T2.
Subtotal: 195 / 7 / 20
Irrep combinations (i,j,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(T2)
..36. ET1T2.
Subtotal: 36 / 1 / 10
Total: 296 / 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...36. T1T1T1T1...357. T2T2T2T2.
Subtotal: 404 / 4 / 5
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(T2)
..108. T1T1T1T2...8. A1EEE...2. A1T1T1T1...112. A1T2T2T2...16. ET1T1T1...140. ET2T2T2...378. T1T2T2T2.
Subtotal: 764 / 7 / 20
Irrep combinations (i,i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(T2)
..9. A1A1EE...18. A1A1T1T1...63. A1A1T2T2...36. EET1T1...126. EET2T2...423. T1T1T2T2.
Subtotal: 675 / 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)
..72. EET1T2...72. A1T1T1T2...108. ET1T1T2...24. A1ET1T1...84. A1ET2T2...90. A1T1T2T2...216. ET1T2T2.
Subtotal: 666 / 7 / 30
Irrep combinations (i,j,k,l) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ l ≤ pos(T2)
..72. A1ET1T2.
Subtotal: 72 / 1 / 5
Total: 2.581 / 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