Results for Point Group D3h



Characters of representations for molecular motions
Motion E 2C3 3C'2 σh 2S3 v
Cartesian 3N 102 0 0 0 0 14
Translation (x,y,z) 3 0 -1 1 -2 1
Rotation (Rx,Ry,Rz) 3 0 -1 -1 2 -1
Vibration 96 0 2 0 0 14


Decomposition to irreducible representations
Motion A'1 A'2 E' A''1 A''2 E'' Total
Cartesian 3N 12 5 17 5 12 17 68
Translation (x,y,z) 0 0 1 0 1 0 2
Rotation (Rx,Ry,Rz) 0 1 0 0 0 1 2
Vibration 12 4 16 5 11 16 64



Molecular parameter
Number of Atoms (N) 34
Number of internal coordinates 96
Number of independant internal coordinates 12
Number of vibrational modes 64


Force field analysis


Allowed / forbidden vibronational transitions
Operator A'1 A'2 E' A''1 A''2 E'' Total
Linear (IR) 12 4 16 5 11 16 27 / 37
Quadratic (Raman) 12 4 16 5 11 16 44 / 20
IR + Raman - - - - 4 16 5 - - - - - - - - 16 / 9


Characters of force fields
(Symmetric powers of vibration representation)
Force field E 2C3 3C'2 σh 2S3 v
linear 96 0 2 0 0 14
quadratic 4.656 0 50 48 0 146
cubic 152.096 32 98 0 0 1.134
quartic 3.764.376 0 1.274 1.176 0 7.546
quintic 75.287.520 0 2.450 0 0 43.582
sextic 1.267.339.920 528 22.050 19.600 16 227.458


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A'1 A'2 E' A''1 A''2 E''
linear 12 4 16 5 11 16
quadratic 441 343 784 360 408 768
cubic 12.988 12.372 25.344 12.421 12.939 25.344
quartic 316.001 311.591 627.592 312.032 315.168 627.200
quintic 6.285.468 6.262.452 12.547.920 6.263.677 6.284.243 12.547.920
sextic 105.675.761 105.551.007 211.226.496 105.558.760 105.661.464 211.219.968


Further Reading



Contributions to nonvanishing force field constants


pos(X) : Position of irreducible representation (irrep) X in character table of D3h

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'1) ≤ i ≤ pos(E'')
..78. A'1A'1...10. A'2A'2...136. E'E'...15. A''1A''1...66. A''2A''2...136. E''E''.
Subtotal: 441 / 6 / 6
Irrep combinations (i,j) with indices: pos(A'1) ≤ i ≤ j ≤ pos(E'')
Subtotal: 0 / 0 / 15
Total: 441 / 6 / 21


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A'1) ≤ i ≤ pos(E'')
..364. A'1A'1A'1...816. E'E'E'.
Subtotal: 1.180 / 2 / 6
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A'1) ≤ i ≤ j ≤ pos(E'')
..120. A'1A'2A'2...1.632. A'1E'E'...180. A'1A''1A''1...792. A'1A''2A''2...1.632. A'1E''E''...480. A'2E'E'...480. A'2E''E''...2.176. E'E''E''.
Subtotal: 7.492 / 8 / 30
Irrep combinations (i,j,k) with indices: pos(A'1) ≤ i ≤ j ≤ k ≤ pos(E'')
..220. A'2A''1A''2...1.280. E'A''1E''...2.816. E'A''2E''.
Subtotal: 4.316 / 3 / 20
Total: 12.988 / 13 / 56


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A'1) ≤ i ≤ pos(E'')
..1.365. A'1A'1A'1A'1...35. A'2A'2A'2A'2...9.316. E'E'E'E'...70. A''1A''1A''1A''1...1.001. A''2A''2A''2A''2...9.316. E''E''E''E''.
Subtotal: 21.103 / 6 / 6
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A'1) ≤ i ≤ j ≤ pos(E'')
..9.792. A'1E'E'E'...3.264. A'2E'E'E'...4.080. A''1E''E''E''...8.976. A''2E''E''E''.
Subtotal: 26.112 / 4 / 30
Irrep combinations (i,i,j,j) with indices: pos(A'1) ≤ i ≤ j ≤ pos(E'')
..780. A'1A'1A'2A'2...10.608. A'1A'1E'E'...1.170. A'1A'1A''1A''1...5.148. A'1A'1A''2A''2...10.608. A'1A'1E''E''...1.360. A'2A'2E'E'...150. A'2A'2A''1A''1...660. A'2A'2A''2A''2...1.360. A'2A'2E''E''...2.040. E'E'A''1A''1.
..8.976. E'E'A''2A''2...51.392. E'E'E''E''...990. A''1A''1A''2A''2...2.040. A''1A''1E''E''...8.976. A''2A''2E''E''.
Subtotal: 106.258 / 15 / 15
Irrep combinations (i,i,j,k) (i,j,j,k) (i,j,k,k) with indices: pos(A'1) ≤ i ≤ j ≤ k ≤ pos(E'')
..6.600. E'E'A''1A''2...10.880. E'E'A''1E''...23.936. E'E'A''2E''...5.760. A'1A'2E'E'...5.760. A'1A'2E''E''...26.112. A'1E'E''E''...8.704. A'2E'E''E''...6.600. A''1A''2E''E''.
Subtotal: 94.352 / 8 / 60
Irrep combinations (i,j,k,l) with indices: pos(A'1) ≤ i ≤ j ≤ k ≤ l ≤ pos(E'')
..2.640. A'1A'2A''1A''2...15.360. A'1E'A''1E''...33.792. A'1E'A''2E''...5.120. A'2E'A''1E''...11.264. A'2E'A''2E''.
Subtotal: 68.176 / 5 / 15
Total: 316.001 / 38 / 126


Calculate contributions to

A'1 A'2 E' A''1 A''2 E''
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Last update January, 3rd 2020 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement