Results for Point Group C2h



Characters of representations for molecular motions
Motion E C2 i σh
Cartesian 3N 156 0 0 4
Translation (x,y,z) 3 -1 -3 1
Rotation (Rx,Ry,Rz) 3 -1 3 -1
Vibration 150 2 0 4


Decomposition to irreducible representations
Motion Ag Bg Au Bu Total
Cartesian 3N 40 38 38 40 156
Translation (x,y,z) 0 0 1 2 3
Rotation (Rx,Ry,Rz) 1 2 0 0 3
Vibration 39 36 37 38 150



Molecular parameter
Number of Atoms (N) 52
Number of internal coordinates 150
Number of independant internal coordinates 39
Number of vibrational modes 150

Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag Bg Au Bu Total
Linear (IR) 39 36 37 38 75 / 75
Quadratic (Raman) 39 36 37 38 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 2 0 4
quadratic 11.325 77 75 83
cubic 573.800 152 0 312
quartic 21.947.850 3.002 2.850 3.466
quintic 675.993.780 5.852 0 12.320
sextic 17.463.172.650 79.002 73.150 97.174


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field Ag Bg Au Bu
linear 39 36 37 38
quadratic 2.890 2.810 2.811 2.814
cubic 143.566 143.334 143.410 143.490
quartic 5.489.292 5.486.058 5.486.134 5.486.366
quintic 169.002.988 168.993.902 168.996.828 169.000.062
sextic 4.365.855.494 4.365.767.406 4.365.770.332 4.365.779.418


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)
..780. AgAg...666. BgBg...703. AuAu...741. BuBu.
Subtotal: 2.890 / 4 / 4
Irrep combinations (i,j) with indices: pos(Ag) ≤ i ≤ j ≤ pos(Bu)
Subtotal: 0 / 0 / 6
Total: 2.890 / 4 / 10


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(Ag) ≤ i ≤ pos(Bu)
..10.660. AgAgAg.
Subtotal: 10.660 / 1 / 4
Irrep combinations (i,i,j) (i,j,j) with indices: pos(Ag) ≤ i ≤ j ≤ pos(Bu)
..25.974. AgBgBg...27.417. AgAuAu...28.899. AgBuBu.
Subtotal: 82.290 / 3 / 12
Irrep combinations (i,j,k) with indices: pos(Ag) ≤ i ≤ j ≤ k ≤ pos(Bu)
..50.616. BgAuBu.
Subtotal: 50.616 / 1 / 4
Total: 143.566 / 5 / 20


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(Ag) ≤ i ≤ pos(Bu)
..111.930. AgAgAgAg...82.251. BgBgBgBg...91.390. AuAuAuAu...101.270. BuBuBuBu.
Subtotal: 386.841 / 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)
..519.480. AgAgBgBg...548.340. AgAgAuAu...577.980. AgAgBuBu...468.198. BgBgAuAu...493.506. BgBgBuBu...520.923. AuAuBuBu.
Subtotal: 3.128.427 / 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)
..1.974.024. AgBgAuBu.
Subtotal: 1.974.024 / 1 / 1
Total: 5.489.292 / 11 / 35


Calculate contributions to

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