Results for Point Group C3v



Characters of representations for molecular motions
Motion E 2C3 v
Cartesian 3N 99 0 3
Translation (x,y,z) 3 0 1
Rotation (Rx,Ry,Rz) 3 0 -1
Vibration 93 0 3


Decomposition to irreducible representations
Motion A1 A2 E Total
Cartesian 3N 18 15 33 66
Translation (x,y,z) 1 0 1 2
Rotation (Rx,Ry,Rz) 0 1 1 2
Vibration 17 14 31 62



Molecular parameter
Number of Atoms (N) 33
Number of internal coordinates 93
Number of independant internal coordinates 17
Number of vibrational modes 62


Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 E Total
Linear (IR) 17 14 31 48 / 14
Quadratic (Raman) 17 14 31 48 / 14
IR + Raman 17 14 31 48 / 14


Characters of force fields
(Symmetric powers of vibration representation)
Force field E 2C3 v
linear 93 0 3
quadratic 4.371 0 51
cubic 138.415 31 145
quartic 3.321.960 0 1.320
quintic 64.446.024 0 3.576
sextic 1.052.618.392 496 23.128


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A1 A2 E
linear 17 14 31
quadratic 754 703 1.457
cubic 23.152 23.007 46.128
quartic 554.320 553.000 1.107.320
quintic 10.742.792 10.739.216 21.482.008
sextic 175.448.128 175.425.000 350.872.632


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)
..153. A1A1...105. A2A2...496. EE.
Subtotal: 754 / 3 / 3
Irrep combinations (i,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
Subtotal: 0 / 0 / 3
Total: 754 / 3 / 6


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A1) ≤ i ≤ pos(E)
..969. A1A1A1...5.456. EEE.
Subtotal: 6.425 / 2 / 3
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
..1.785. A1A2A2...8.432. A1EE...6.510. A2EE.
Subtotal: 16.727 / 3 / 6
Irrep combinations (i,j,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(E)
Subtotal: 0 / 0 / 1
Total: 23.152 / 5 / 10


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A1) ≤ i ≤ pos(E)
..4.845. A1A1A1A1...2.380. A2A2A2A2...123.256. EEEE.
Subtotal: 130.481 / 3 / 3
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
..92.752. A1EEE...76.384. A2EEE.
Subtotal: 169.136 / 2 / 6
Irrep combinations (i,i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
..16.065. A1A1A2A2...75.888. A1A1EE...52.080. A2A2EE.
Subtotal: 144.033 / 3 / 3
Irrep combinations (i,i,j,k) (i,j,j,k) (i,j,k,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(E)
..110.670. A1A2EE.
Subtotal: 110.670 / 1 / 3
Irrep combinations (i,j,k,l) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ l ≤ pos(E)
Subtotal: 0 / 0 / 0
Total: 554.320 / 9 / 15


Calculate contributions to

A1 A2 E
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