Results for Point Group C2h



Characters of representations for molecular motions
Motion E C2 i σh
Cartesian 3N 21 -3 -3 5
Translation (x,y,z) 3 -1 -3 1
Rotation (Rx,Ry,Rz) 3 -1 3 -1
Vibration 15 -1 -3 5


Decomposition to irreducible representations
Motion Ag Bg Au Bu Total
Cartesian 3N 5 4 4 8 21
Translation (x,y,z) 0 0 1 2 3
Rotation (Rx,Ry,Rz) 1 2 0 0 3
Vibration 4 2 3 6 15



Molecular parameter
Number of Atoms (N) 7
Number of internal coordinates 15
Number of independant internal coordinates 4
Number of vibrational modes 15


Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag Bg Au Bu Total
Linear (IR) 4 2 3 6 9 / 6
Quadratic (Raman) 4 2 3 6 6 / 9
IR + Raman - - - - - - - - - - - - - - - - 0* / 0
* Parity Mutual Exclusion Principle


Characters of force fields
(Symmetric powers of vibration representation)
Force field E C2 i σh
linear 15 -1 -3 5
quadratic 120 8 12 20
cubic 680 -8 -28 60
quartic 3.060 36 72 160
quintic 11.628 -36 -144 376
sextic 38.760 120 300 820


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field Ag Bg Au Bu
linear 4 2 3 6
quadratic 40 26 24 30
cubic 176 150 160 194
quartic 832 734 716 778
quintic 2.956 2.786 2.840 3.046
sextic 10.000 9.530 9.440 9.790


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)
..10. AgAg...3. BgBg...6. AuAu...21. BuBu.
Subtotal: 40 / 4 / 4
Irrep combinations (i,j) with indices: pos(Ag) ≤ i ≤ j ≤ pos(Bu)
Subtotal: 0 / 0 / 6
Total: 40 / 4 / 10


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(Ag) ≤ i ≤ pos(Bu)
..20. AgAgAg.
Subtotal: 20 / 1 / 4
Irrep combinations (i,i,j) (i,j,j) with indices: pos(Ag) ≤ i ≤ j ≤ pos(Bu)
..12. AgBgBg...24. AgAuAu...84. AgBuBu.
Subtotal: 120 / 3 / 12
Irrep combinations (i,j,k) with indices: pos(Ag) ≤ i ≤ j ≤ k ≤ pos(Bu)
..36. BgAuBu.
Subtotal: 36 / 1 / 4
Total: 176 / 5 / 20


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(Ag) ≤ i ≤ pos(Bu)
..35. AgAgAgAg...5. BgBgBgBg...15. AuAuAuAu...126. BuBuBuBu.
Subtotal: 181 / 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)
..30. AgAgBgBg...60. AgAgAuAu...210. AgAgBuBu...18. BgBgAuAu...63. BgBgBuBu...126. AuAuBuBu.
Subtotal: 507 / 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)
..144. AgBgAuBu.
Subtotal: 144 / 1 / 1
Total: 832 / 11 / 35


Calculate contributions to

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