Results for Point Group C5v



Characters of representations for molecular motions
Motion E 2C5 2(C5)2 5σv
Cartesian 3N 90 0.000 -0.000 2
Translation (x,y,z) 3 1.618 -0.618 1
Rotation (Rx,Ry,Rz) 3 1.618 -0.618 -1
Vibration 84 -3.236 1.236 2


Decomposition to irreducible representations
Motion A1 A2 E1 E2 Total
Cartesian 3N 10 8 18 18 54
Translation (x,y,z) 1 0 1 0 2
Rotation (Rx,Ry,Rz) 0 1 1 0 2
Vibration 9 7 16 18 50



Molecular parameter
Number of Atoms (N) 30
Number of internal coordinates 84
Number of independant internal coordinates 9
Number of vibrational modes 50

Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 E1 E2 Total
Linear (IR) 9 7 16 18 25 / 25
Quadratic (Raman) 9 7 16 18 43 / 7
IR + Raman 9 7 16 - - - - 25 / 7


Characters of force fields
(Symmetric powers of vibration representation)
Force field E 2C5 2(C5)2 5σv
linear 84 -3.236 1.236 2
quadratic 3.570 5.854 -0.854 44
cubic 102.340 -7.236 -2.764 86
quartic 2.225.895 5.854 -0.854 989
quintic 39.175.752 14.764 19.236 1.892
sextic 581.106.988 -57.249 23.249 15.136


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A1 A2 E1 E2
linear 9 7 16 18
quadratic 380 336 715 712
cubic 10.275 10.189 20.468 20.470
quartic 223.085 222.096 445.180 445.177
quintic 3.918.528 3.916.636 7.835.146 7.835.148
sextic 58.118.260 58.103.124 116.221.383 116.221.419


Further Reading


Contributions to nonvanishing force field constants


pos(X) : Position of irreducible representation (irrep) X in character table of C5v

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)
..45. A1A1...28. A2A2...136. E1E1...171. E2E2.
Subtotal: 380 / 4 / 4
Irrep combinations (i,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E2)
Subtotal: 0 / 0 / 6
Total: 380 / 4 / 10


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A1) ≤ i ≤ pos(E2)
..165. A1A1A1.
Subtotal: 165 / 1 / 4
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E2)
..2.448. E1E1E2...252. A1A2A2...1.224. A1E1E1...1.539. A1E2E2...840. A2E1E1...1.071. A2E2E2...2.736. E1E2E2.
Subtotal: 10.110 / 7 / 12
Irrep combinations (i,j,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(E2)
Subtotal: 0 / 0 / 4
Total: 10.275 / 8 / 20


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A1) ≤ i ≤ pos(E2)
..495. A1A1A1A1...210. A2A2A2A2...9.316. E1E1E1E1...14.706. E2E2E2E2.
Subtotal: 24.727 / 4 / 4
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E2)
..14.688. E1E1E1E2...18.240. E1E2E2E2.
Subtotal: 32.928 / 2 / 12
Irrep combinations (i,i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E2)
..1.260. A1A1A2A2...6.120. A1A1E1E1...7.695. A1A1E2E2...3.808. A2A2E1E1...4.788. A2A2E2E2...41.616. E1E1E2E2.
Subtotal: 65.287 / 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)
..22.032. A1E1E1E2...17.136. A2E1E1E2...7.560. A1A2E1E1...9.639. A1A2E2E2...24.624. A1E1E2E2...19.152. A2E1E2E2.
Subtotal: 100.143 / 6 / 12
Irrep combinations (i,j,k,l) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ l ≤ pos(E2)
Subtotal: 0 / 0 / 1
Total: 223.085 / 18 / 35


Calculate contributions to

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