Results for Point Group C2h



Characters of representations for molecular motions
Motion E C2 i σh
Cartesian 3N 48 0 0 0
Translation (x,y,z) 3 -1 -3 1
Rotation (Rx,Ry,Rz) 3 -1 3 -1
Vibration 42 2 0 0


Decomposition to irreducible representations
Motion Ag Bg Au Bu Total
Cartesian 3N 12 12 12 12 48
Translation (x,y,z) 0 0 1 2 3
Rotation (Rx,Ry,Rz) 1 2 0 0 3
Vibration 11 10 11 10 42



Molecular parameter
Number of Atoms (N) 16
Number of internal coordinates 42
Number of independant internal coordinates 11
Number of vibrational modes 42


Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag Bg Au Bu Total
Linear (IR) 11 10 11 10 21 / 21
Quadratic (Raman) 11 10 11 10 21 / 21
IR + Raman - - - - - - - - - - - - - - - - 0* / 0
* Parity Mutual Exclusion Principle


Characters of force fields
(Symmetric powers of vibration representation)
Force field E C2 i σh
linear 42 2 0 0
quadratic 903 23 21 21
cubic 13.244 44 0 0
quartic 148.995 275 231 231
quintic 1.370.754 506 0 0
sextic 10.737.573 2.277 1.771 1.771


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field Ag Bg Au Bu
linear 11 10 11 10
quadratic 242 220 221 220
cubic 3.322 3.300 3.322 3.300
quartic 37.433 37.180 37.202 37.180
quintic 342.815 342.562 342.815 342.562
sextic 2.685.848 2.683.824 2.684.077 2.683.824


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)
..66. AgAg...55. BgBg...66. AuAu...55. BuBu.
Subtotal: 242 / 4 / 4
Irrep combinations (i,j) with indices: pos(Ag) ≤ i ≤ j ≤ pos(Bu)
Subtotal: 0 / 0 / 6
Total: 242 / 4 / 10


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(Ag) ≤ i ≤ pos(Bu)
..286. AgAgAg.
Subtotal: 286 / 1 / 4
Irrep combinations (i,i,j) (i,j,j) with indices: pos(Ag) ≤ i ≤ j ≤ pos(Bu)
..605. AgBgBg...726. AgAuAu...605. AgBuBu.
Subtotal: 1.936 / 3 / 12
Irrep combinations (i,j,k) with indices: pos(Ag) ≤ i ≤ j ≤ k ≤ pos(Bu)
..1.100. BgAuBu.
Subtotal: 1.100 / 1 / 4
Total: 3.322 / 5 / 20


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(Ag) ≤ i ≤ pos(Bu)
..1.001. AgAgAgAg...715. BgBgBgBg...1.001. AuAuAuAu...715. BuBuBuBu.
Subtotal: 3.432 / 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)
..3.630. AgAgBgBg...4.356. AgAgAuAu...3.630. AgAgBuBu...3.630. BgBgAuAu...3.025. BgBgBuBu...3.630. AuAuBuBu.
Subtotal: 21.901 / 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)
..12.100. AgBgAuBu.
Subtotal: 12.100 / 1 / 1
Total: 37.433 / 11 / 35


Calculate contributions to

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