Results for Point Group C3v



Characters of representations for molecular motions
Motion E 2C3 v
Cartesian 3N 12 0 2
Translation (x,y,z) 3 0 1
Rotation (Rx,Ry,Rz) 3 0 -1
Vibration 6 0 2


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



Molecular parameter
Number of Atoms (N) 4
Number of internal coordinates 6
Number of independant internal coordinates 2
Number of vibrational modes 4


Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 E Total
Linear (IR) 2 0 2 4 / 0
Quadratic (Raman) 2 0 2 4 / 0
IR + Raman 2 0 2 4 / 0


Characters of force fields
(Symmetric powers of vibration representation)
Force field E 2C3 v
linear 6 0 2
quadratic 21 0 5
cubic 56 2 8
quartic 126 0 14
quintic 252 0 20
sextic 462 3 30


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A1 A2 E
linear 2 0 2
quadratic 6 1 7
cubic 14 6 18
quartic 28 14 42
quintic 52 32 84
sextic 93 63 153


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


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A1) ≤ i ≤ pos(E)
..4. A1A1A1...4. EEE.
Subtotal: 8 / 2 / 3
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
..6. A1EE.
Subtotal: 6 / 1 / 6
Irrep combinations (i,j,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(E)
Subtotal: 0 / 0 / 1
Total: 14 / 3 / 10


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A1) ≤ i ≤ pos(E)
..5. A1A1A1A1...6. EEEE.
Subtotal: 11 / 2 / 3
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
..8. A1EEE.
Subtotal: 8 / 1 / 6
Irrep combinations (i,i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
..9. A1A1EE.
Subtotal: 9 / 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: 28 / 4 / 15


Calculate contributions to

A1 A2 E
Show only nonzero contributions Show all contributions
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