Results for Point Group C4



Characters of representations for molecular motions
Motion E C4 C2 (C4)3
Cartesian 3N 39 5 -5 5
Translation (x,y,z) 3 1 -1 1
Rotation (Rx,Ry,Rz) 3 1 -1 1
Vibration 33 3 -3 3


Decomposition to irreducible representations
Motion A B E* Total
Cartesian 3N 11 6 11 28
Translation (x,y,z) 1 0 1 2
Rotation (Rx,Ry,Rz) 1 0 1 2
Vibration 9 6 9 24



Molecular parameter
Number of Atoms (N) 13
Number of internal coordinates 33
Number of independant internal coordinates 9
Number of vibrational modes 24


Force field analysis


Allowed / forbidden vibronational transitions
Operator A B E* Total
Linear (IR) 9 6 9 18 / 6
Quadratic (Raman) 9 6 9 24 / 0
IR + Raman 9 - - - - 9 18 / 0


Characters of force fields
(Symmetric powers of vibration representation)
Force field E C4 C2 (C4)3
linear 33 3 -3 3
quadratic 561 3 21 3
cubic 6.545 1 -55 1
quartic 58.905 9 225 9
quintic 435.897 27 -531 27
sextic 2.760.681 27 1.653 27


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A B E*
linear 9 6 9
quadratic 147 144 135
cubic 1.623 1.622 1.650
quartic 14.787 14.778 14.670
quintic 108.855 108.828 109.107
sextic 690.597 690.570 689.757


Further Reading



Contributions to nonvanishing force field constants


pos(X) : Position of irreducible representation (irrep) X in character table of C4

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(A) ≤ i ≤ pos(E)
..45. AA...21. BB...81. EE.
Subtotal: 147 / 3 / 3
Irrep combinations (i,j) with indices: pos(A) ≤ i ≤ j ≤ pos(E)
Subtotal: 0 / 0 / 3
Total: 147 / 3 / 6


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A) ≤ i ≤ pos(E)
..165. AAA.
Subtotal: 165 / 1 / 3
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A) ≤ i ≤ j ≤ pos(E)
..189. ABB...729. AEE...540. BEE.
Subtotal: 1.458 / 3 / 6
Irrep combinations (i,j,k) with indices: pos(A) ≤ i ≤ j ≤ k ≤ pos(E)
Subtotal: 0 / 0 / 1
Total: 1.623 / 4 / 10


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A) ≤ i ≤ pos(E)
..495. AAAA...126. BBBB...3.015. EEEE.
Subtotal: 3.636 / 3 / 3
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A) ≤ i ≤ j ≤ pos(E)
Subtotal: 0 / 0 / 6
Irrep combinations (i,i,j,j) with indices: pos(A) ≤ i ≤ j ≤ pos(E)
..945. AABB...3.645. AAEE...1.701. BBEE.
Subtotal: 6.291 / 3 / 3
Irrep combinations (i,i,j,k) (i,j,j,k) (i,j,k,k) with indices: pos(A) ≤ i ≤ j ≤ k ≤ pos(E)
..4.860. ABEE.
Subtotal: 4.860 / 1 / 3
Irrep combinations (i,j,k,l) with indices: pos(A) ≤ i ≤ j ≤ k ≤ l ≤ pos(E)
Subtotal: 0 / 0 / 0
Total: 14.787 / 7 / 15


Calculate contributions to

A B E
Show only nonzero contributions Show all contributions
Up to quartic force fieldUp to quintic force fieldUp to sextic force field






Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement