Results for Point Group C2h



Characters of representations for molecular motions
Motion E C2 i σh
Cartesian 3N 39 -5 -3 9
Translation (x,y,z) 3 -1 -3 1
Rotation (Rx,Ry,Rz) 3 -1 3 -1
Vibration 33 -3 -3 9


Decomposition to irreducible representations
Motion Ag Bg Au Bu Total
Cartesian 3N 10 8 7 14 39
Translation (x,y,z) 0 0 1 2 3
Rotation (Rx,Ry,Rz) 1 2 0 0 3
Vibration 9 6 6 12 33



Molecular parameter
Number of Atoms (N) 13
Number of internal coordinates 33
Number of independant internal coordinates 9
Number of vibrational modes 33


Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag Bg Au Bu Total
Linear (IR) 9 6 6 12 18 / 15
Quadratic (Raman) 9 6 6 12 15 / 18
IR + Raman - - - - - - - - - - - - - - - - 0* / 0
* Parity Mutual Exclusion Principle


Characters of force fields
(Symmetric powers of vibration representation)
Force field E C2 i σh
linear 33 -3 -3 9
quadratic 561 21 21 57
cubic 6.545 -55 -55 273
quartic 58.905 225 225 1.113
quintic 435.897 -531 -531 3.969
sextic 2.760.681 1.653 1.653 12.817


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field Ag Bg Au Bu
linear 9 6 6 12
quadratic 165 126 126 144
cubic 1.677 1.568 1.568 1.732
quartic 15.117 14.448 14.448 14.892
quintic 109.701 107.982 107.982 110.232
sextic 694.201 686.966 686.966 692.548


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)
..45. AgAg...21. BgBg...21. AuAu...78. BuBu.
Subtotal: 165 / 4 / 4
Irrep combinations (i,j) with indices: pos(Ag) ≤ i ≤ j ≤ pos(Bu)
Subtotal: 0 / 0 / 6
Total: 165 / 4 / 10


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(Ag) ≤ i ≤ pos(Bu)
..165. AgAgAg.
Subtotal: 165 / 1 / 4
Irrep combinations (i,i,j) (i,j,j) with indices: pos(Ag) ≤ i ≤ j ≤ pos(Bu)
..189. AgBgBg...189. AgAuAu...702. AgBuBu.
Subtotal: 1.080 / 3 / 12
Irrep combinations (i,j,k) with indices: pos(Ag) ≤ i ≤ j ≤ k ≤ pos(Bu)
..432. BgAuBu.
Subtotal: 432 / 1 / 4
Total: 1.677 / 5 / 20


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(Ag) ≤ i ≤ pos(Bu)
..495. AgAgAgAg...126. BgBgBgBg...126. AuAuAuAu...1.365. BuBuBuBu.
Subtotal: 2.112 / 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)
..945. AgAgBgBg...945. AgAgAuAu...3.510. AgAgBuBu...441. BgBgAuAu...1.638. BgBgBuBu...1.638. AuAuBuBu.
Subtotal: 9.117 / 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)
..3.888. AgBgAuBu.
Subtotal: 3.888 / 1 / 1
Total: 15.117 / 11 / 35


Calculate contributions to

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