Results for Point Group C2h



Characters of representations for molecular motions
Motion E C2 i σh
Cartesian 3N 156 -2 0 14
Translation (x,y,z) 3 -1 -3 1
Rotation (Rx,Ry,Rz) 3 -1 3 -1
Vibration 150 0 0 14


Decomposition to irreducible representations
Motion Ag Bg Au Bu Total
Cartesian 3N 42 36 35 43 156
Translation (x,y,z) 0 0 1 2 3
Rotation (Rx,Ry,Rz) 1 2 0 0 3
Vibration 41 34 34 41 150



Molecular parameter
Number of Atoms (N) 52
Number of internal coordinates 150
Number of independant internal coordinates 41
Number of vibrational modes 150

Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag Bg Au Bu Total
Linear (IR) 41 34 34 41 75 / 75
Quadratic (Raman) 41 34 34 41 75 / 75
IR + Raman - - - - - - - - - - - - - - - - 0* / 0
* Parity Mutual Exclusion Principle


Characters of force fields
(Symmetric powers of vibration representation)
Force field E C2 i σh
linear 150 0 0 14
quadratic 11.325 75 75 173
cubic 573.800 0 0 1.512
quartic 21.947.850 2.850 2.850 11.866
quintic 675.993.780 0 0 79.492
sextic 17.463.172.650 73.150 73.150 490.042


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field Ag Bg Au Bu
linear 41 34 34 41
quadratic 2.912 2.788 2.788 2.837
cubic 143.828 143.072 143.072 143.828
quartic 5.491.354 5.483.996 5.483.996 5.488.504
quintic 169.018.318 168.978.572 168.978.572 169.018.318
sextic 4.365.952.248 4.365.670.652 4.365.670.652 4.365.879.098


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)
..861. AgAg...595. BgBg...595. AuAu...861. BuBu.
Subtotal: 2.912 / 4 / 4
Irrep combinations (i,j) with indices: pos(Ag) ≤ i ≤ j ≤ pos(Bu)
Subtotal: 0 / 0 / 6
Total: 2.912 / 4 / 10


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(Ag) ≤ i ≤ pos(Bu)
..12.341. AgAgAg.
Subtotal: 12.341 / 1 / 4
Irrep combinations (i,i,j) (i,j,j) with indices: pos(Ag) ≤ i ≤ j ≤ pos(Bu)
..24.395. AgBgBg...24.395. AgAuAu...35.301. AgBuBu.
Subtotal: 84.091 / 3 / 12
Irrep combinations (i,j,k) with indices: pos(Ag) ≤ i ≤ j ≤ k ≤ pos(Bu)
..47.396. BgAuBu.
Subtotal: 47.396 / 1 / 4
Total: 143.828 / 5 / 20


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(Ag) ≤ i ≤ pos(Bu)
..135.751. AgAgAgAg...66.045. BgBgBgBg...66.045. AuAuAuAu...135.751. BuBuBuBu.
Subtotal: 403.592 / 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)
..512.295. AgAgBgBg...512.295. AgAgAuAu...741.321. AgAgBuBu...354.025. BgBgAuAu...512.295. BgBgBuBu...512.295. AuAuBuBu.
Subtotal: 3.144.526 / 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)
..1.943.236. AgBgAuBu.
Subtotal: 1.943.236 / 1 / 1
Total: 5.491.354 / 11 / 35


Calculate contributions to

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