Results for Point Group D5



Characters of representations for molecular motions
Motion E 2C5 2(C5)2 5C'2
Cartesian 3N 63 1.618 -0.618 -1
Translation (x,y,z) 3 1.618 -0.618 -1
Rotation (Rx,Ry,Rz) 3 1.618 -0.618 -1
Vibration 57 -1.618 0.618 1


Decomposition to irreducible representations
Motion A1 A2 E1 E2 Total
Cartesian 3N 6 7 13 12 38
Translation (x,y,z) 0 1 1 0 2
Rotation (Rx,Ry,Rz) 0 1 1 0 2
Vibration 6 5 11 12 34



Molecular parameter
Number of Atoms (N) 21
Number of internal coordinates 57
Number of independant internal coordinates 6
Number of vibrational modes 34

Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 E1 E2 Total
Linear (IR) 6 5 11 12 16 / 18
Quadratic (Raman) 6 5 11 12 29 / 5
IR + Raman - - - - - - - - 11 - - - - 11 / 0


Characters of force fields
(Symmetric powers of vibration representation)
Force field E 2C5 2(C5)2 5C'2
linear 57 -1.618 0.618 1
quadratic 1.653 1.618 -0.618 29
cubic 32.509 -1.000 -1.000 29
quartic 487.635 -0.000 0.000 435
quintic 5.949.147 12.000 12.000 435
sextic 61.474.519 -19.416 7.416 4.495


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A1 A2 E1 E2
linear 6 5 11 12
quadratic 180 151 331 330
cubic 3.265 3.236 6.502 6.502
quartic 48.981 48.546 97.527 97.527
quintic 595.137 594.702 1.189.827 1.189.827
sextic 6.149.697 6.145.202 12.294.899 12.294.911


Further Reading


Contributions to nonvanishing force field constants


pos(X) : Position of irreducible representation (irrep) X in character table of D5

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(E2)
..21. A1A1...15. A2A2...66. E1E1...78. E2E2.
Subtotal: 180 / 4 / 4
Irrep combinations (i,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E2)
Subtotal: 0 / 0 / 6
Total: 180 / 4 / 10


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A1) ≤ i ≤ pos(E2)
..56. A1A1A1.
Subtotal: 56 / 1 / 4
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E2)
..792. E1E1E2...90. A1A2A2...396. A1E1E1...468. A1E2E2...275. A2E1E1...330. A2E2E2...858. E1E2E2.
Subtotal: 3.209 / 7 / 12
Irrep combinations (i,j,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(E2)
Subtotal: 0 / 0 / 4
Total: 3.265 / 8 / 20


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A1) ≤ i ≤ pos(E2)
..126. A1A1A1A1...70. A2A2A2A2...2.211. E1E1E1E1...3.081. E2E2E2E2.
Subtotal: 5.488 / 4 / 4
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E2)
..3.432. E1E1E1E2...4.004. E1E2E2E2.
Subtotal: 7.436 / 2 / 12
Irrep combinations (i,i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E2)
..315. A1A1A2A2...1.386. A1A1E1E1...1.638. A1A1E2E2...990. A2A2E1E1...1.170. A2A2E2E2...8.778. E1E1E2E2.
Subtotal: 14.277 / 6 / 6
Irrep combinations (i,i,j,k) (i,j,j,k) (i,j,k,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(E2)
..4.752. A1E1E1E2...3.960. A2E1E1E2...1.650. A1A2E1E1...1.980. A1A2E2E2...5.148. A1E1E2E2...4.290. A2E1E2E2.
Subtotal: 21.780 / 6 / 12
Irrep combinations (i,j,k,l) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ l ≤ pos(E2)
Subtotal: 0 / 0 / 1
Total: 48.981 / 18 / 35


Calculate contributions to

A1 A2 E1 E2
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Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement