Results for Point Group C28
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A |
B |
E1*
|
E2*
|
E3*
|
E4*
|
E5*
|
E6*
|
E7*
|
E8*
|
E9*
|
E10*
|
E11*
|
E12*
|
E13*
|
Total |
| Linear (IR) |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 / 0 |
| Quadratic (Raman) |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 / 0 |
| IR + Raman |
0 |
0 |
0 |
- - - - |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 / 0 |
Characters of force fields
(Symmetric powers of vibration representation)
| Force field |
E |
C28 |
C14 |
(C28)3 |
C7 |
(C28)5 |
(C14)3 |
C4 |
(C7)2 |
(C28)9 |
(C14)5 |
(C28)11 |
(C7)3 |
(C28)13 |
C2 |
(C28)15 |
(C7)4 |
(C28)17 |
(C14)9 |
(C28)19 |
(C7)5 |
(C4)3 |
(C14)11 |
(C28)23 |
(C7)6 |
(C28)25 |
(C14)13 |
(C28)27 |
| linear |
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 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
| quadratic |
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 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
| cubic |
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 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
| quartic |
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 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
| quintic |
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 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
| sextic |
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 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
| Force field |
A |
B |
E1*
|
E2*
|
E3*
|
E4*
|
E5*
|
E6*
|
E7*
|
E8*
|
E9*
|
E10*
|
E11*
|
E12*
|
E13*
|
| linear |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
| quadratic |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
| cubic |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
| quartic |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
| quintic |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
| sextic |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
Further Reading
- J.K.G. Watson, J. Mol. Spec. 41 229 (1972)
The Numbers of Structural Parameters and Potential Constants of Molecules
- X.F. Zhou, P. Pulay. J. Comp. Chem. 10 No. 7, 935-938 (1989)
Characters for Symmetric and Antisymmetric Higher Powers of Representations:
Application to the Number of Anharmonic Force Constants in Symmetrical Molecules
- F. Varga, L. Nemes, J.K.G. Watson. J. Phys. B: At. Mol. Opt. Phys. 10 No. 7, 5043-5048 (1996)
The number of anharmonic potential constants of the fullerenes C60 and C70
Contributions to nonvanishing force field constants
pos(X) : Position of irreducible representation (irrep) X in character table of C28
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(E13) |
|---|
| Subtotal: 0 / 0 / 15 |
| Irrep combinations (i,j) with indices: pos(A) ≤ i ≤ j ≤ pos(E13) |
|---|
| Subtotal: 0 / 0 / 105 |
| Total: 0 / 0 / 120 |
Contributions to nonvanishing cubic force field constants
| Irrep combinations (i,i,i) with indices: pos(A) ≤ i ≤ pos(E13) |
|---|
| Subtotal: 0 / 0 / 15 |
| Irrep combinations (i,i,j) (i,j,j) with indices: pos(A) ≤ i ≤ j ≤ pos(E13) |
|---|
| Subtotal: 0 / 0 / 210 |
| Irrep combinations (i,j,k) with indices: pos(A) ≤ i ≤ j ≤ k ≤ pos(E13) |
|---|
| Subtotal: 0 / 0 / 455 |
| Total: 0 / 0 / 680 |
Contributions to nonvanishing quartic force field constants
| Irrep combinations (i,i,i,i) with indices: pos(A) ≤ i ≤ pos(E13) |
|---|
| Subtotal: 0 / 0 / 15 |
| Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A) ≤ i ≤ j ≤ pos(E13) |
|---|
| Subtotal: 0 / 0 / 210 |
| Irrep combinations (i,i,j,j) with indices: pos(A) ≤ i ≤ j ≤ pos(E13) |
|---|
| Subtotal: 0 / 0 / 105 |
| Irrep combinations (i,i,j,k) (i,j,j,k) (i,j,k,k) with indices: pos(A) ≤ i ≤ j ≤ k ≤ pos(E13) |
|---|
| Subtotal: 0 / 0 / 1.365 |
| Irrep combinations (i,j,k,l) with indices: pos(A) ≤ i ≤ j ≤ k ≤ l ≤ pos(E13) |
|---|
| Subtotal: 0 / 0 / 1.365 |
| Total: 0 / 0 / 3.060 |
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Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement