Results for Point Group D29d
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1g |
A2g |
E1g |
E2g |
E3g |
E4g |
E5g |
E6g |
E7g |
E8g |
E9g |
E10g |
E11g |
E12g |
E13g |
E14g |
A1u |
A2u |
E1u |
E2u |
E3u |
E4u |
E5u |
E6u |
E7u |
E8u |
E9u |
E10u |
E11u |
E12u |
E13u |
E14u |
Total |
| Linear (IR) |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
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 |
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 |
0 |
0 |
0 |
0 |
0 |
- - - - |
0 |
- - - - |
- - - - |
0 |
0 |
0* / 0 |
* Parity Mutual Exclusion Principle
Characters of force fields
(Symmetric powers of vibration representation)
| Force field |
E |
2C29 |
2(C29)2 |
2(C29)3 |
2(C29)4 |
2(C29)5 |
2(C29)6 |
2(C29)7 |
2(C29)8 |
2(C29)9 |
2(C29)10 |
2(C29)11 |
2(C29)12 |
2(C29)13 |
2(C29)14 |
29C'2 |
i |
2(S58)27 |
2(S58)25 |
2(S58)23 |
2(S58)21 |
2(S58)19 |
2(S58)17 |
2(S58)15 |
2(S58)13 |
2(S58)11 |
2(S58)9 |
2(S58)7 |
2(S58)5 |
2(S58)3 |
2S58 |
29σd |
| linear |
0 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0 |
0 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0 |
| quadratic |
0 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0 |
0 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0 |
| cubic |
0 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0 |
0 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0 |
| quartic |
0 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0 |
0 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0 |
| quintic |
0 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0 |
0 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0 |
| sextic |
0 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0 |
0 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0 |
Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
| Force field |
A1g |
A2g |
E1g |
E2g |
E3g |
E4g |
E5g |
E6g |
E7g |
E8g |
E9g |
E10g |
E11g |
E12g |
E13g |
E14g |
A1u |
A2u |
E1u |
E2u |
E3u |
E4u |
E5u |
E6u |
E7u |
E8u |
E9u |
E10u |
E11u |
E12u |
E13u |
E14u |
| linear |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
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 |
0 |
0 |
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 |
0 |
0 |
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 |
0 |
0 |
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 |
0 |
0 |
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 |
0 |
0 |
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 irrep
A1g
pos(X) : Position of irreducible representation (irrep) X in character table of D29d
Subtotal: <Contributions to irrep A1g in subsection>
/ <number of nonzero irrep combinations in subsection> / <number of irrep combinations in subsection>
Total: <Contributions to irrep A1g>
/ <number of nonzero irrep combinations in force field> / <number of irrep combinations in force field>
Contributions to irrep
A1g for symmetric power to 2
| Irrep combinations (i,i) with indices: pos(A1g) ≤ i ≤ pos(E14u) |
|---|
| Subtotal: 0 / 0 / 32 |
| Irrep combinations (i,j) with indices: pos(A1g) ≤ i ≤ j ≤ pos(E14u) |
|---|
| Subtotal: 0 / 0 / 496 |
| Total: 0 / 0 / 528 |
Contributions to irrep
A1g for symmetric power to 3
| Irrep combinations (i,i,i) with indices: pos(A1g) ≤ i ≤ pos(E14u) |
|---|
| Subtotal: 0 / 0 / 32 |
| Irrep combinations (i,i,j) (i,j,j) with indices: pos(A1g) ≤ i ≤ j ≤ pos(E14u) |
|---|
| Subtotal: 0 / 0 / 992 |
| Irrep combinations (i,j,k) with indices: pos(A1g) ≤ i ≤ j ≤ k ≤ pos(E14u) |
|---|
| Subtotal: 0 / 0 / 4.960 |
| Total: 0 / 0 / 5.984 |
Contributions to irrep
A1g for symmetric power to 4
| Irrep combinations (i,i,i,i) with indices: pos(A1g) ≤ i ≤ pos(E14u) |
|---|
| Subtotal: 0 / 0 / 32 |
| Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A1g) ≤ i ≤ j ≤ pos(E14u) |
|---|
| Subtotal: 0 / 0 / 992 |
| Irrep combinations (i,i,j,j) with indices: pos(A1g) ≤ i ≤ j ≤ pos(E14u) |
|---|
| Subtotal: 0 / 0 / 496 |
| Irrep combinations (i,i,j,k) (i,j,j,k) (i,j,k,k) with indices: pos(A1g) ≤ i ≤ j ≤ k ≤ pos(E14u) |
|---|
| Subtotal: 0 / 0 / 14.880 |
| Irrep combinations (i,j,k,l) with indices: pos(A1g) ≤ i ≤ j ≤ k ≤ l ≤ pos(E14u) |
|---|
| Subtotal: 0 / 0 / 35.960 |
| Total: 0 / 0 / 52.360 |
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Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement