Results for Point Group T



Characters of representations for molecular motions
Motion E 4C3 4(C3)2 3C2
Cartesian 3N 156 0 0 0
Translation (x,y,z) 3 0 0 -1
Rotation (Rx,Ry,Rz) 3 0 0 -1
Vibration 150 0 0 2


Decomposition to irreducible representations
Motion A E* T Total
Cartesian 3N 13 13 39 65
Translation (x,y,z) 0 0 1 1
Rotation (Rx,Ry,Rz) 0 0 1 1
Vibration 13 13 37 63



Molecular parameter
Number of Atoms (N) 52
Number of internal coordinates 150
Number of independant internal coordinates 13
Number of vibrational modes 63


Force field analysis


Allowed / forbidden vibronational transitions
Operator A E* T Total
Linear (IR) 13 13 37 37 / 26
Quadratic (Raman) 13 13 37 63 / 0
IR + Raman - - - - - - - - 37 37 / 0


Characters of force fields
(Symmetric powers of vibration representation)
Force field E 4C3 4(C3)2 3C2
linear 150 0 0 2
quadratic 11.325 0 0 77
cubic 573.800 50 50 152
quartic 21.947.850 0 0 3.002
quintic 675.993.780 0 0 5.852
sextic 17.463.172.650 1.275 1.275 79.002


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A E* T
linear 13 13 37
quadratic 963 963 2.812
cubic 47.888 47.838 143.412
quartic 1.829.738 1.829.738 5.486.212
quintic 56.334.278 56.334.278 168.996.982
sextic 1.455.284.988 1.455.283.713 4.365.773.412


Further Reading



Contributions to nonvanishing force field constants


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

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(A) ≤ i ≤ pos(T)
..91. AA...169. EE...703. TT.
Subtotal: 963 / 3 / 3
Irrep combinations (i,j) with indices: pos(A) ≤ i ≤ j ≤ pos(T)
Subtotal: 0 / 0 / 3
Total: 963 / 3 / 6


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A) ≤ i ≤ pos(T)
..455. AAA...910. EEE...16.909. TTT.
Subtotal: 18.274 / 3 / 3
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A) ≤ i ≤ j ≤ pos(T)
..2.197. AEE...9.139. ATT...18.278. ETT.
Subtotal: 29.614 / 3 / 6
Irrep combinations (i,j,k) with indices: pos(A) ≤ i ≤ j ≤ k ≤ pos(T)
Subtotal: 0 / 0 / 1
Total: 47.888 / 6 / 10


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A) ≤ i ≤ pos(T)
..1.820. AAAA...8.281. EEEE...585.599. TTTT.
Subtotal: 595.700 / 3 / 3
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A) ≤ i ≤ j ≤ pos(T)
..11.830. AEEE...219.817. ATTT...438.672. ETTT.
Subtotal: 670.319 / 3 / 6
Irrep combinations (i,i,j,j) with indices: pos(A) ≤ i ≤ j ≤ pos(T)
..15.379. AAEE...63.973. AATT...246.753. EETT.
Subtotal: 326.105 / 3 / 3
Irrep combinations (i,i,j,k) (i,j,j,k) (i,j,k,k) with indices: pos(A) ≤ i ≤ j ≤ k ≤ pos(T)
..237.614. AETT.
Subtotal: 237.614 / 1 / 3
Irrep combinations (i,j,k,l) with indices: pos(A) ≤ i ≤ j ≤ k ≤ l ≤ pos(T)
Subtotal: 0 / 0 / 0
Total: 1.829.738 / 10 / 15


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A E T
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Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement