Results for Point Group T



Characters of representations for molecular motions
Motion E 4C3 4(C3)2 3C2
Cartesian 3N 36 0 0 -4
Translation (x,y,z) 3 0 0 -1
Rotation (Rx,Ry,Rz) 3 0 0 -1
Vibration 30 0 0 -2


Decomposition to irreducible representations
Motion A E* T Total
Cartesian 3N 2 2 10 14
Translation (x,y,z) 0 0 1 1
Rotation (Rx,Ry,Rz) 0 0 1 1
Vibration 2 2 8 12



Molecular parameter
Number of Atoms (N) 12
Number of internal coordinates 30
Number of independant internal coordinates 2
Number of vibrational modes 12


Force field analysis


Allowed / forbidden vibronational transitions
Operator A E* T Total
Linear (IR) 2 2 8 8 / 4
Quadratic (Raman) 2 2 8 12 / 0
IR + Raman - - - - - - - - 8 8 / 0


Characters of force fields
(Symmetric powers of vibration representation)
Force field E 4C3 4(C3)2 3C2
linear 30 0 0 -2
quadratic 465 0 0 17
cubic 4.960 10 10 -32
quartic 40.920 0 0 152
quintic 278.256 0 0 -272
sextic 1.623.160 55 55 952


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A E* T
linear 2 2 8
quadratic 43 43 112
cubic 412 402 1.248
quartic 3.448 3.448 10.192
quintic 23.120 23.120 69.632
sextic 135.538 135.483 405.552


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)
..3. AA...4. EE...36. TT.
Subtotal: 43 / 3 / 3
Irrep combinations (i,j) with indices: pos(A) ≤ i ≤ j ≤ pos(T)
Subtotal: 0 / 0 / 3
Total: 43 / 3 / 6


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A) ≤ i ≤ pos(T)
..4. AAA...8. EEE...176. TTT.
Subtotal: 188 / 3 / 3
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A) ≤ i ≤ j ≤ pos(T)
..8. AEE...72. ATT...144. ETT.
Subtotal: 224 / 3 / 6
Irrep combinations (i,j,k) with indices: pos(A) ≤ i ≤ j ≤ k ≤ pos(T)
Subtotal: 0 / 0 / 1
Total: 412 / 6 / 10


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A) ≤ i ≤ pos(T)
..5. AAAA...9. EEEE...1.626. TTTT.
Subtotal: 1.640 / 3 / 3
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A) ≤ i ≤ j ≤ pos(T)
..16. AEEE...352. ATTT...672. ETTT.
Subtotal: 1.040 / 3 / 6
Irrep combinations (i,i,j,j) with indices: pos(A) ≤ i ≤ j ≤ pos(T)
..12. AAEE...108. AATT...360. EETT.
Subtotal: 480 / 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)
..288. AETT.
Subtotal: 288 / 1 / 3
Irrep combinations (i,j,k,l) with indices: pos(A) ≤ i ≤ j ≤ k ≤ l ≤ pos(T)
Subtotal: 0 / 0 / 0
Total: 3.448 / 10 / 15


Calculate contributions to

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