Results for Point Group C2h



Characters of representations for molecular motions
Motion E C2 i σh
Cartesian 3N 48 0 0 16
Translation (x,y,z) 3 -1 -3 1
Rotation (Rx,Ry,Rz) 3 -1 3 -1
Vibration 42 2 0 16


Decomposition to irreducible representations
Motion Ag Bg Au Bu Total
Cartesian 3N 16 8 8 16 48
Translation (x,y,z) 0 0 1 2 3
Rotation (Rx,Ry,Rz) 1 2 0 0 3
Vibration 15 6 7 14 42



Molecular parameter
Number of Atoms (N) 16
Number of internal coordinates 42
Number of independant internal coordinates 15
Number of vibrational modes 42


Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag Bg Au Bu Total
Linear (IR) 15 6 7 14 21 / 21
Quadratic (Raman) 15 6 7 14 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 16
quadratic 903 23 21 149
cubic 13.244 44 0 1.024
quartic 148.995 275 231 5.735
quintic 1.370.754 506 0 27.568
sextic 10.737.573 2.277 1.771 117.483


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field Ag Bg Au Bu
linear 15 6 7 14
quadratic 274 188 189 252
cubic 3.578 3.044 3.066 3.556
quartic 38.809 35.804 35.826 38.556
quintic 349.707 335.670 335.923 349.454
sextic 2.714.776 2.654.896 2.655.149 2.712.752


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)
..120. AgAg...21. BgBg...28. AuAu...105. BuBu.
Subtotal: 274 / 4 / 4
Irrep combinations (i,j) with indices: pos(Ag) ≤ i ≤ j ≤ pos(Bu)
Subtotal: 0 / 0 / 6
Total: 274 / 4 / 10


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(Ag) ≤ i ≤ pos(Bu)
..680. AgAgAg.
Subtotal: 680 / 1 / 4
Irrep combinations (i,i,j) (i,j,j) with indices: pos(Ag) ≤ i ≤ j ≤ pos(Bu)
..315. AgBgBg...420. AgAuAu...1.575. AgBuBu.
Subtotal: 2.310 / 3 / 12
Irrep combinations (i,j,k) with indices: pos(Ag) ≤ i ≤ j ≤ k ≤ pos(Bu)
..588. BgAuBu.
Subtotal: 588 / 1 / 4
Total: 3.578 / 5 / 20


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(Ag) ≤ i ≤ pos(Bu)
..3.060. AgAgAgAg...126. BgBgBgBg...210. AuAuAuAu...2.380. BuBuBuBu.
Subtotal: 5.776 / 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)
..2.520. AgAgBgBg...3.360. AgAgAuAu...12.600. AgAgBuBu...588. BgBgAuAu...2.205. BgBgBuBu...2.940. AuAuBuBu.
Subtotal: 24.213 / 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)
..8.820. AgBgAuBu.
Subtotal: 8.820 / 1 / 1
Total: 38.809 / 11 / 35


Calculate contributions to

Ag Bg Au Bu
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Last update January, 3rd 2020 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement