Results for Point Group C3v



Characters of representations for molecular motions
Motion E 2C3 v
Cartesian 3N 18 0 4
Translation (x,y,z) 3 0 1
Rotation (Rx,Ry,Rz) 3 0 -1
Vibration 12 0 4


Decomposition to irreducible representations
Motion A1 A2 E Total
Cartesian 3N 5 1 6 12
Translation (x,y,z) 1 0 1 2
Rotation (Rx,Ry,Rz) 0 1 1 2
Vibration 4 0 4 8



Molecular parameter
Number of Atoms (N) 6
Number of internal coordinates 12
Number of independant internal coordinates 4
Number of vibrational modes 8


Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 E Total
Linear (IR) 4 0 4 8 / 0
Quadratic (Raman) 4 0 4 8 / 0
IR + Raman 4 0 4 8 / 0


Characters of force fields
(Symmetric powers of vibration representation)
Force field E 2C3 v
linear 12 0 4
quadratic 78 0 14
cubic 364 4 36
quartic 1.365 0 85
quintic 4.368 0 176
sextic 12.376 10 344


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A1 A2 E
linear 4 0 4
quadratic 20 6 26
cubic 80 44 120
quartic 270 185 455
quintic 816 640 1.456
sextic 2.238 1.894 4.122


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)
..10. A1A1...10. EE.
Subtotal: 20 / 2 / 3
Irrep combinations (i,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
Subtotal: 0 / 0 / 3
Total: 20 / 2 / 6


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A1) ≤ i ≤ pos(E)
..20. A1A1A1...20. EEE.
Subtotal: 40 / 2 / 3
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
..40. A1EE.
Subtotal: 40 / 1 / 6
Irrep combinations (i,j,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(E)
Subtotal: 0 / 0 / 1
Total: 80 / 3 / 10


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A1) ≤ i ≤ pos(E)
..35. A1A1A1A1...55. EEEE.
Subtotal: 90 / 2 / 3
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
..80. A1EEE.
Subtotal: 80 / 1 / 6
Irrep combinations (i,i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
..100. A1A1EE.
Subtotal: 100 / 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: 270 / 4 / 15


Calculate contributions to

A1 A2 E
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