Results for Point Group D3



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


Decomposition to irreducible representations
Motion A1 A2 E Total
Cartesian 3N 25 27 52 104
Translation (x,y,z) 0 1 1 2
Rotation (Rx,Ry,Rz) 0 1 1 2
Vibration 25 25 50 100



Molecular parameter
Number of Atoms (N) 52
Number of internal coordinates 150
Number of independant internal coordinates 25
Number of vibrational modes 100


Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 E Total
Linear (IR) 25 25 50 75 / 25
Quadratic (Raman) 25 25 50 75 / 25
IR + Raman - - - - - - - - 50 50 / 0


Characters of force fields
(Symmetric powers of vibration representation)
Force field E 2C3 3C'2
linear 150 0 0
quadratic 11.325 0 75
cubic 573.800 50 0
quartic 21.947.850 0 2.850
quintic 675.993.780 0 0
sextic 17.463.172.650 1.275 73.150


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A1 A2 E
linear 25 25 50
quadratic 1.925 1.850 3.775
cubic 95.650 95.650 191.250
quartic 3.659.400 3.656.550 7.315.950
quintic 112.665.630 112.665.630 225.331.260
sextic 2.910.565.775 2.910.492.625 5.821.057.125


Further Reading



Contributions to nonvanishing force field constants


pos(X) : Position of irreducible representation (irrep) X in character table of D3

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(E)
..325. A1A1...325. A2A2...1.275. EE.
Subtotal: 1.925 / 3 / 3
Irrep combinations (i,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
Subtotal: 0 / 0 / 3
Total: 1.925 / 3 / 6


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A1) ≤ i ≤ pos(E)
..2.925. A1A1A1...22.100. EEE.
Subtotal: 25.025 / 2 / 3
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
..8.125. A1A2A2...31.875. A1EE...30.625. A2EE.
Subtotal: 70.625 / 3 / 6
Irrep combinations (i,j,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(E)
Subtotal: 0 / 0 / 1
Total: 95.650 / 5 / 10


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A1) ≤ i ≤ pos(E)
..20.475. A1A1A1A1...20.475. A2A2A2A2...813.450. EEEE.
Subtotal: 854.400 / 3 / 3
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
..552.500. A1EEE...552.500. A2EEE.
Subtotal: 1.105.000 / 2 / 6
Irrep combinations (i,i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
..105.625. A1A1A2A2...414.375. A1A1EE...414.375. A2A2EE.
Subtotal: 934.375 / 3 / 3
Irrep combinations (i,i,j,k) (i,j,j,k) (i,j,k,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(E)
..765.625. A1A2EE.
Subtotal: 765.625 / 1 / 3
Irrep combinations (i,j,k,l) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ l ≤ pos(E)
Subtotal: 0 / 0 / 0
Total: 3.659.400 / 9 / 15


Calculate contributions to

A1 A2 E
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Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement