Results for Point Group C3v



Characters of representations for molecular motions
Motion E 2C3 v
Cartesian 3N 36 0 4
Translation (x,y,z) 3 0 1
Rotation (Rx,Ry,Rz) 3 0 -1
Vibration 30 0 4


Decomposition to irreducible representations
Motion A1 A2 E Total
Cartesian 3N 8 4 12 24
Translation (x,y,z) 1 0 1 2
Rotation (Rx,Ry,Rz) 0 1 1 2
Vibration 7 3 10 20



Molecular parameter
Number of Atoms (N) 12
Number of internal coordinates 30
Number of independant internal coordinates 7
Number of vibrational modes 20


Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 E Total
Linear (IR) 7 3 10 17 / 3
Quadratic (Raman) 7 3 10 17 / 3
IR + Raman 7 3 10 17 / 3


Characters of force fields
(Symmetric powers of vibration representation)
Force field E 2C3 v
linear 30 0 4
quadratic 465 0 23
cubic 4.960 10 72
quartic 40.920 0 256
quintic 278.256 0 680
sextic 1.623.160 55 1.904


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A1 A2 E
linear 7 3 10
quadratic 89 66 155
cubic 866 794 1.650
quartic 6.948 6.692 13.640
quintic 46.716 46.036 92.752
sextic 271.497 269.593 541.035


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)
..28. A1A1...6. A2A2...55. EE.
Subtotal: 89 / 3 / 3
Irrep combinations (i,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
Subtotal: 0 / 0 / 3
Total: 89 / 3 / 6


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A1) ≤ i ≤ pos(E)
..84. A1A1A1...220. EEE.
Subtotal: 304 / 2 / 3
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
..42. A1A2A2...385. A1EE...135. A2EE.
Subtotal: 562 / 3 / 6
Irrep combinations (i,j,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(E)
Subtotal: 0 / 0 / 1
Total: 866 / 5 / 10


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A1) ≤ i ≤ pos(E)
..210. A1A1A1A1...15. A2A2A2A2...1.540. EEEE.
Subtotal: 1.765 / 3 / 3
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
..1.540. A1EEE...660. A2EEE.
Subtotal: 2.200 / 2 / 6
Irrep combinations (i,i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E)
..168. A1A1A2A2...1.540. A1A1EE...330. A2A2EE.
Subtotal: 2.038 / 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)
..945. A1A2EE.
Subtotal: 945 / 1 / 3
Irrep combinations (i,j,k,l) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ l ≤ pos(E)
Subtotal: 0 / 0 / 0
Total: 6.948 / 9 / 15


Calculate contributions to

A1 A2 E
Show only nonzero contributions Show all contributions
Up to quartic force fieldUp to quintic force fieldUp to sextic force field






Last update January, 3rd 2020 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement