Results for Point Group C2h



Characters of representations for molecular motions
Motion E C2 i σh
Cartesian 3N 90 0 0 30
Translation (x,y,z) 3 -1 -3 1
Rotation (Rx,Ry,Rz) 3 -1 3 -1
Vibration 84 2 0 30


Decomposition to irreducible representations
Motion Ag Bg Au Bu Total
Cartesian 3N 30 15 15 30 90
Translation (x,y,z) 0 0 1 2 3
Rotation (Rx,Ry,Rz) 1 2 0 0 3
Vibration 29 13 14 28 84



Molecular parameter
Number of Atoms (N) 30
Number of internal coordinates 84
Number of independant internal coordinates 29
Number of vibrational modes 84

Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag Bg Au Bu Total
Linear (IR) 29 13 14 28 42 / 42
Quadratic (Raman) 29 13 14 28 42 / 42
IR + Raman - - - - - - - - - - - - - - - - 0* / 0
* Parity Mutual Exclusion Principle


Characters of force fields
(Symmetric powers of vibration representation)
Force field E C2 i σh
linear 84 2 0 30
quadratic 3.570 44 42 492
cubic 102.340 86 0 5.770
quartic 2.225.895 989 903 53.853
quintic 39.175.752 1.892 0 423.516
sextic 581.106.988 15.136 13.244 2.907.424


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field Ag Bg Au Bu
linear 29 13 14 28
quadratic 1.037 769 770 994
cubic 27.049 24.121 24.164 27.006
quartic 570.410 542.989 543.032 569.464
quintic 9.900.290 9.687.586 9.688.532 9.899.344
sextic 146.010.698 144.549.418 144.550.364 145.996.508


Further Reading


Contributions to nonvanishing force field constants


pos(X) : Position of irreducible representation (irrep) X in character table of C2h

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(Ag) ≤ i ≤ pos(Bu)
..435. AgAg...91. BgBg...105. AuAu...406. BuBu.
Subtotal: 1.037 / 4 / 4
Irrep combinations (i,j) with indices: pos(Ag) ≤ i ≤ j ≤ pos(Bu)
Subtotal: 0 / 0 / 6
Total: 1.037 / 4 / 10


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(Ag) ≤ i ≤ pos(Bu)
..4.495. AgAgAg.
Subtotal: 4.495 / 1 / 4
Irrep combinations (i,i,j) (i,j,j) with indices: pos(Ag) ≤ i ≤ j ≤ pos(Bu)
..2.639. AgBgBg...3.045. AgAuAu...11.774. AgBuBu.
Subtotal: 17.458 / 3 / 12
Irrep combinations (i,j,k) with indices: pos(Ag) ≤ i ≤ j ≤ k ≤ pos(Bu)
..5.096. BgAuBu.
Subtotal: 5.096 / 1 / 4
Total: 27.049 / 5 / 20


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(Ag) ≤ i ≤ pos(Bu)
..35.960. AgAgAgAg...1.820. BgBgBgBg...2.380. AuAuAuAu...31.465. BuBuBuBu.
Subtotal: 71.625 / 4 / 4
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(Ag) ≤ i ≤ j ≤ pos(Bu)
Subtotal: 0 / 0 / 12
Irrep combinations (i,i,j,j) with indices: pos(Ag) ≤ i ≤ j ≤ pos(Bu)
..39.585. AgAgBgBg...45.675. AgAgAuAu...176.610. AgAgBuBu...9.555. BgBgAuAu...36.946. BgBgBuBu...42.630. AuAuBuBu.
Subtotal: 351.001 / 6 / 6
Irrep combinations (i,i,j,k) (i,j,j,k) (i,j,k,k) with indices: pos(Ag) ≤ i ≤ j ≤ k ≤ pos(Bu)
Subtotal: 0 / 0 / 12
Irrep combinations (i,j,k,l) with indices: pos(Ag) ≤ i ≤ j ≤ k ≤ l ≤ pos(Bu)
..147.784. AgBgAuBu.
Subtotal: 147.784 / 1 / 1
Total: 570.410 / 11 / 35


Calculate contributions to

Ag Bg Au Bu
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Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement