Results for Point Group D28



Characters of representations for molecular motions
Motion E 2C28 2C14 2(C28)3 2C7 2(C28)5 2(C14)3 2C4 2(C7)2 2(C28)9 2(C14)5 2(C28)11 2(C7)3 2(C28)13 C2 14C'2 14C''2
Cartesian 3N 0 0.000 0.000 0.000 0.000 0.000 0.000 0 0.000 0.000 0.000 0.000 0.000 0.000 0 0 0
Translation (x,y,z) 3 2.950 2.802 2.564 2.247 1.868 1.445 1 0.555 0.132 -0.247 -0.564 -0.802 -0.950 -1 -1 -1
Rotation (Rx,Ry,Rz) 3 2.950 2.802 2.564 2.247 1.868 1.445 1 0.555 0.132 -0.247 -0.564 -0.802 -0.950 -1 -1 -1
Vibration -6 -5.900 -5.604 -5.127 -4.494 -3.736 -2.890 -2 -1.110 -0.264 0.494 1.127 1.604 1.900 2 2 2


Decomposition to irreducible representations
Motion A1 A2 B1 B2 E1 E2 E3 E4 E5 E6 E7 E8 E9 E10 E11 E12 E13 Total
Cartesian 3N 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Translation (x,y,z) 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 2
Rotation (Rx,Ry,Rz) 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 2
Vibration 0 -2 0 0 -2 0 0 0 0 0 0 0 0 0 0 0 0 -4



Molecular parameter
Number of Atoms (N) 0
Number of internal coordinates -6
Number of independant internal coordinates 0
Number of vibrational modes -4


Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 E1 E2 E3 E4 E5 E6 E7 E8 E9 E10 E11 E12 E13 Total
Linear (IR) 0 -2 0 0 -2 0 0 0 0 0 0 0 0 0 0 0 0 -4 / 0
Quadratic (Raman) 0 -2 0 0 -2 0 0 0 0 0 0 0 0 0 0 0 0 -2 / -2
IR + Raman - - - - - - - - 0 0 -2 - - - - 0 0 0 0 0 0 0 0 0 0 0 -2 / 0


Characters of force fields
(Symmetric powers of vibration representation)
Force field E 2C28 2C14 2(C28)3 2C7 2(C28)5 2(C14)3 2C4 2(C7)2 2(C28)9 2(C14)5 2(C28)11 2(C7)3 2(C28)13 C2 14C'2 14C''2
linear -6 -5.900 -5.604 -5.127 -4.494 -3.736 -2.890 -2 -1.110 -0.264 0.494 1.127 1.604 1.900 2 2 2
quadratic 15 14.601 13.455 11.700 9.543 7.224 4.978 3 1.418 0.282 -0.433 -0.810 -0.961 -0.997 -1 -1 -1
cubic -20 -19.403 -17.702 -15.145 -12.098 -8.977 -6.176 -4 -2.616 -2.035 -2.122 -2.635 -3.286 -3.804 -4 -4 -4
quartic 15 14.601 13.455 11.700 9.543 7.224 4.978 3 1.418 0.282 -0.433 -0.810 -0.961 -0.997 -1 -1 -1
quintic -6 -5.900 -5.604 -5.127 -4.494 -3.736 -2.890 -2 -1.110 -0.264 0.494 1.127 1.604 1.900 2 2 2
sextic 1 1.000 1.000 1.000 1.000 1.000 1.000 1 1.000 1.000 1.000 1.000 1.000 1.000 1 1 1


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A1 A2 B1 B2 E1 E2 E3 E4 E5 E6 E7 E8 E9 E10 E11 E12 E13
linear 0 -2 0 0 -2 0 0 0 0 0 0 0 0 0 0 0 0
quadratic 2 3 0 0 4 1 0 0 0 0 0 0 0 0 0 0 0
cubic -6 -2 0 0 -4 -2 0 0 0 0 0 0 0 0 0 0 0
quartic 2 3 0 0 4 1 0 0 0 0 0 0 0 0 0 0 0
quintic 0 -2 0 0 -2 0 0 0 0 0 0 0 0 0 0 0 0
sextic 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0


Further Reading



Contributions to nonvanishing force field constants


pos(X) : Position of irreducible representation (irrep) X in character table of D28

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(E13)
..1. A2A2...1. E1E1.
Subtotal: 2 / 2 / 17
Irrep combinations (i,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E13)
Subtotal: 0 / 0 / 136
Total: 2 / 2 / 153


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A1) ≤ i ≤ pos(E13)
Subtotal: 0 / 0 / 17
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E13)
Subtotal: -6 / 0 / 272
Irrep combinations (i,j,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(E13)
Subtotal: 0 / 0 / 680
Total: -6 / 0 / 969


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A1) ≤ i ≤ pos(E13)
..1. E1E1E1E1.
Subtotal: 1 / 1 / 17
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E13)
Subtotal: 0 / 0 / 272
Irrep combinations (i,i,j,j) with indices: pos(A1) ≤ i ≤ j ≤ pos(E13)
..1. A2A2E1E1.
Subtotal: 1 / 1 / 136
Irrep combinations (i,i,j,k) (i,j,j,k) (i,j,k,k) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ pos(E13)
Subtotal: 0 / 0 / 2.040
Irrep combinations (i,j,k,l) with indices: pos(A1) ≤ i ≤ j ≤ k ≤ l ≤ pos(E13)
Subtotal: 0 / 0 / 2.380
Total: 2 / 2 / 4.845


Calculate contributions to

A1 A2 B1 B2 E1 E2 E3 E4 E5 E6 E7 E8 E9 E10 E11 E12 E13
Show only nonzero contributions Show all contributions






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