Results for Point Group C3v



Characters of representations for molecular motions
Motion E 2C3 v
Cartesian 3N 63 0 5
Translation (x,y,z) 3 0 1
Rotation (Rx,Ry,Rz) 3 0 -1
Vibration 57 0 5


Decomposition to irreducible representations
Motion A1 A2 E Total
Cartesian 3N 13 8 21 42
Translation (x,y,z) 1 0 1 2
Rotation (Rx,Ry,Rz) 0 1 1 2
Vibration 12 7 19 38



Molecular parameter
Number of Atoms (N) 21
Number of internal coordinates 57
Number of independant internal coordinates 12
Number of vibrational modes 38


Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 E Total
Linear (IR) 12 7 19 31 / 7
Quadratic (Raman) 12 7 19 31 / 7
IR + Raman 12 7 19 31 / 7


Characters of force fields
(Symmetric powers of vibration representation)
Force field E 2C3 v
linear 57 0 5
quadratic 1.653 0 41
cubic 32.509 19 165
quartic 487.635 0 811
quintic 5.949.147 0 2.791
sextic 61.474.519 190 10.571


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A1 A2 E
linear 12 7 19
quadratic 296 255 551
cubic 5.507 5.342 10.830
quartic 81.678 80.867 162.545
quintic 992.920 990.129 1.983.049
sextic 10.251.102 10.240.531 20.491.443


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)
..78. A1A1...28. A2A2...190. EE.
Subtotal: 296 / 3 / 3
Irrep combinations (i,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
Subtotal: 0 / 0 / 3
Total: 296 / 3 / 6


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A1) ≤ i ≤ pos(E)
..364. A1A1A1...1.330. EEE.
Subtotal: 1.694 / 2 / 3
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
..336. A1A2A2...2.280. A1EE...1.197. A2EE.
Subtotal: 3.813 / 3 / 6
Irrep combinations (i,j,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(E)
Subtotal: 0 / 0 / 1
Total: 5.507 / 5 / 10


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A1) ≤ i ≤ pos(E)
..1.365. A1A1A1A1...210. A2A2A2A2...18.145. EEEE.
Subtotal: 19.720 / 3 / 3
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
..15.960. A1EEE...9.310. A2EEE.
Subtotal: 25.270 / 2 / 6
Irrep combinations (i,i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
..2.184. A1A1A2A2...14.820. A1A1EE...5.320. A2A2EE.
Subtotal: 22.324 / 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)
..14.364. A1A2EE.
Subtotal: 14.364 / 1 / 3
Irrep combinations (i,j,k,l) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ l ≤ pos(E)
Subtotal: 0 / 0 / 0
Total: 81.678 / 9 / 15


Calculate contributions to

A1 A2 E
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