Results for Point Group Ci



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


Decomposition to irreducible representations
Motion Ag Au Total
Cartesian 3N 9 12 21
Translation (x,y,z) 0 3 3
Rotation (Rx,Ry,Rz) 3 0 3
Vibration 6 9 15



Molecular parameter
Number of Atoms (N) 7
Number of internal coordinates 15
Number of independant internal coordinates 6
Number of vibrational modes 15


Force field analysis


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


Characters of force fields
(Symmetric powers of vibration representation)
Force field E i
linear 15 -3
quadratic 120 12
cubic 680 -28
quartic 3.060 72
quintic 11.628 -144
sextic 38.760 300


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field Ag Au
linear 6 9
quadratic 66 54
cubic 326 354
quartic 1.566 1.494
quintic 5.742 5.886
sextic 19.530 19.230


Further Reading



Contributions to nonvanishing force field constants


pos(X) : Position of irreducible representation (irrep) X in character table of Ci

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(Au)
..21. AgAg...45. AuAu.
Subtotal: 66 / 2 / 2
Irrep combinations (i,j) with indices: pos(Ag) ≤ i ≤ j ≤ pos(Au)
Subtotal: 0 / 0 / 1
Total: 66 / 2 / 3


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(Ag) ≤ i ≤ pos(Au)
..56. AgAgAg.
Subtotal: 56 / 1 / 2
Irrep combinations (i,i,j) (i,j,j) with indices: pos(Ag) ≤ i ≤ j ≤ pos(Au)
..270. AgAuAu.
Subtotal: 270 / 1 / 2
Irrep combinations (i,j,k) with indices: pos(Ag) ≤ i ≤ j ≤ k ≤ pos(Au)
Subtotal: 0 / 0 / 0
Total: 326 / 2 / 4


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(Ag) ≤ i ≤ pos(Au)
..126. AgAgAgAg...495. AuAuAuAu.
Subtotal: 621 / 2 / 2
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(Ag) ≤ i ≤ j ≤ pos(Au)
Subtotal: 0 / 0 / 2
Irrep combinations (i,i,j,j) with indices: pos(Ag) ≤ i ≤ j ≤ pos(Au)
..945. AgAgAuAu.
Subtotal: 945 / 1 / 1
Irrep combinations (i,i,j,k) (i,j,j,k) (i,j,k,k) with indices: pos(Ag) ≤ i ≤ j ≤ k ≤ pos(Au)
Subtotal: 0 / 0 / 0
Irrep combinations (i,j,k,l) with indices: pos(Ag) ≤ i ≤ j ≤ k ≤ l ≤ pos(Au)
Subtotal: 0 / 0 / 0
Total: 1.566 / 3 / 5


Calculate contributions to

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