Results for Point Group C3v



Characters of representations for molecular motions
Motion E 2C3 v
Cartesian 3N 15 0 3
Translation (x,y,z) 3 0 1
Rotation (Rx,Ry,Rz) 3 0 -1
Vibration 9 0 3


Decomposition to irreducible representations
Motion A1 A2 E Total
Cartesian 3N 4 1 5 10
Translation (x,y,z) 1 0 1 2
Rotation (Rx,Ry,Rz) 0 1 1 2
Vibration 3 0 3 6



Molecular parameter
Number of Atoms (N) 5
Number of internal coordinates 9
Number of independant internal coordinates 3
Number of vibrational modes 6


Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 E Total
Linear (IR) 3 0 3 6 / 0
Quadratic (Raman) 3 0 3 6 / 0
IR + Raman 3 0 3 6 / 0


Characters of force fields
(Symmetric powers of vibration representation)
Force field E 2C3 v
linear 9 0 3
quadratic 45 0 9
cubic 165 3 19
quartic 495 0 39
quintic 1.287 0 69
sextic 3.003 6 119


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A1 A2 E
linear 3 0 3
quadratic 12 3 15
cubic 38 19 54
quartic 102 63 165
quintic 249 180 429
sextic 562 443 999


Further Reading



Contributions to nonvanishing force field constants


pos(X) : Position of irreducible representation (irrep) X in character table of C3v

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(A1) ≤ i ≤ pos(E)
..6. A1A1...6. EE.
Subtotal: 12 / 2 / 3
Irrep combinations (i,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
Subtotal: 0 / 0 / 3
Total: 12 / 2 / 6


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A1) ≤ i ≤ pos(E)
..10. A1A1A1...10. EEE.
Subtotal: 20 / 2 / 3
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
..18. A1EE.
Subtotal: 18 / 1 / 6
Irrep combinations (i,j,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(E)
Subtotal: 0 / 0 / 1
Total: 38 / 3 / 10


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A1) ≤ i ≤ pos(E)
..15. A1A1A1A1...21. EEEE.
Subtotal: 36 / 2 / 3
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
..30. A1EEE.
Subtotal: 30 / 1 / 6
Irrep combinations (i,i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
..36. A1A1EE.
Subtotal: 36 / 1 / 3
Irrep combinations (i,i,j,k) (i,j,j,k) (i,j,k,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(E)
Subtotal: 0 / 0 / 3
Irrep combinations (i,j,k,l) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ l ≤ pos(E)
Subtotal: 0 / 0 / 0
Total: 102 / 4 / 15


Calculate contributions to

A1 A2 E
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