Results for Point Group D8h



Characters of representations for molecular motions
Motion E 2C8 2C4 2(C8)3 C2 4C'2 4C''2 i 2(S8)3 2S4 2S8 σh v d
Cartesian 3N 99 2.414 1 -0.414 -1 -1 -1 -3 -2.414 -1 0.414 1 9 1
Translation (x,y,z) 3 2.414 1 -0.414 -1 -1 -1 -3 -2.414 -1 0.414 1 1 1
Rotation (Rx,Ry,Rz) 3 2.414 1 -0.414 -1 -1 -1 3 2.414 1 -0.414 -1 -1 -1
Vibration 93 -2.414 -1 0.414 1 1 1 -3 -2.414 -1 0.414 1 9 1


Decomposition to irreducible representations
Motion A1g A2g B1g B2g E1g E2g E3g A1u A2u B1u B2u E1u E2u E3u Total
Cartesian 3N 4 2 4 2 6 6 6 2 5 2 4 7 6 6 62
Translation (x,y,z) 0 0 0 0 0 0 0 0 1 0 0 1 0 0 2
Rotation (Rx,Ry,Rz) 0 1 0 0 1 0 0 0 0 0 0 0 0 0 2
Vibration 4 1 4 2 5 6 6 2 4 2 4 6 6 6 58



Molecular parameter
Number of Atoms (N) 33
Number of internal coordinates 93
Number of independant internal coordinates 4
Number of vibrational modes 58


Force field analysis


Allowed / forbidden vibronational transitions
Operator A1g A2g B1g B2g E1g E2g E3g A1u A2u B1u B2u E1u E2u E3u Total
Linear (IR) 4 1 4 2 5 6 6 2 4 2 4 6 6 6 10 / 48
Quadratic (Raman) 4 1 4 2 5 6 6 2 4 2 4 6 6 6 15 / 43
IR + Raman - - - - 1 4 2 - - - - - - - - 6 2 - - - - 2 4 - - - - 6 6 0* / 33
* Parity Mutual Exclusion Principle


Characters of force fields
(Symmetric powers of vibration representation)
Force field E 2C8 2C4 2(C8)3 C2 4C'2 4C''2 i 2(S8)3 2S4 2S8 σh v d
linear 93 -2.414 -1 0.414 1 1 1 -3 -2.414 -1 0.414 1 9 1
quadratic 4.371 2.414 1 -0.414 47 47 47 51 2.414 1 -0.414 47 87 47
cubic 138.415 -1.000 -1 -1.000 47 47 47 -145 -1.000 -1 -1.000 47 543 47
quartic 3.321.960 -0.000 24 -0.000 1.128 1.128 1.128 1.320 0.000 24 0.000 1.128 3.288 1.128
quintic 64.446.024 0.000 -24 0.000 1.128 1.128 1.128 -3.576 -0.000 -24 0.000 1.128 16.344 1.128
sextic 1.052.618.392 -0.000 24 -0.000 18.424 18.424 18.424 23.128 0.000 24 0.000 18.424 77.672 18.424


Decomposition to irreducible representations
Column with number of nonvanshing force constants highlighted
Force field A1g A2g B1g B2g E1g E2g E3g A1u A2u B1u B2u E1u E2u E3u
linear 4 1 4 2 5 6 6 2 4 2 4 6 6 6
quadratic 170 113 146 136 271 282 270 130 140 130 140 270 270 270
cubic 4.409 4.238 4.386 4.262 8.636 8.648 8.636 4.268 4.392 4.268 4.392 8.660 8.660 8.660
quartic 104.760 103.092 104.196 103.656 207.564 207.840 207.564 103.500 104.040 103.500 104.040 207.540 207.540 207.540
quintic 2.016.360 2.011.428 2.015.796 2.011.992 4.027.512 4.027.800 4.027.512 2.012.148 2.015.952 2.012.148 2.015.952 4.028.100 4.028.100 4.028.100
sextic 32.912.820 32.879.584 32.903.608 32.888.796 65.787.792 65.792.392 65.787.792 32.886.196 32.901.008 32.886.196 32.901.008 65.787.204 65.787.204 65.787.204


Further Reading



Contributions to nonvanishing force field constants


pos(X) : Position of irreducible representation (irrep) X in character table of D8h

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(A1g) ≤ i ≤ pos(E3u)
..10. A1gA1g...1. A2gA2g...10. B1gB1g...3. B2gB2g...15. E1gE1g...21. E2gE2g...21. E3gE3g...3. A1uA1u...10. A2uA2u...3. B1uB1u.
..10. B2uB2u...21. E1uE1u...21. E2uE2u...21. E3uE3u.
Subtotal: 170 / 14 / 14
Irrep combinations (i,j) with indices: pos(A1g) ≤ i ≤ j ≤ pos(E3u)
Subtotal: 0 / 0 / 91
Total: 170 / 14 / 105


Contributions to nonvanishing cubic force field constants
Irrep combinations (i,i,i) with indices: pos(A1g) ≤ i ≤ pos(E3u)
..20. A1gA1gA1g.
Subtotal: 20 / 1 / 14
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A1g) ≤ i ≤ j ≤ pos(E3u)
..90. E1gE1gE2g...4. A1gA2gA2g...40. A1gB1gB1g...12. A1gB2gB2g...60. A1gE1gE1g...84. A1gE2gE2g...84. A1gE3gE3g...12. A1gA1uA1u...40. A1gA2uA2u...12. A1gB1uB1u.
..40. A1gB2uB2u...84. A1gE1uE1u...84. A1gE2uE2u...84. A1gE3uE3u...10. A2gE1gE1g...15. A2gE2gE2g...15. A2gE3gE3g...15. A2gE1uE1u...15. A2gE2uE2u...15. A2gE3uE3u.
..84. B1gE2gE2g...84. B1gE2uE2u...42. B2gE2gE2g...42. B2gE2uE2u...126. E2gE3gE3g...126. E2gE1uE1u...126. E2gE3uE3u.
Subtotal: 1.445 / 27 / 182
Irrep combinations (i,j,k) with indices: pos(A1g) ≤ i ≤ j ≤ k ≤ pos(E3u)
..8. A2gB1gB2g...8. A2gA1uA2u...8. A2gB1uB2u...120. B1gE1gE3g...16. B1gA1uB1u...64. B1gA2uB2u...144. B1gE1uE3u...60. B2gE1gE3g...16. B2gA1uB2u...16. B2gA2uB1u.
..72. B2gE1uE3u...180. E1gE2gE3g...60. E1gA1uE1u...120. E1gA2uE1u...60. E1gB1uE3u...120. E1gB2uE3u...180. E1gE1uE2u...180. E1gE2uE3u...72. E2gA1uE2u...144. E2gA2uE2u.
..72. E2gB1uE2u...144. E2gB2uE2u...216. E2gE1uE3u...72. E3gA1uE3u...144. E3gA2uE3u...72. E3gB1uE1u...144. E3gB2uE1u...216. E3gE1uE2u...216. E3gE2uE3u.
Subtotal: 2.944 / 29 / 364
Total: 4.409 / 57 / 560


Contributions to nonvanishing quartic force field constants
Irrep combinations (i,i,i,i) with indices: pos(A1g) ≤ i ≤ pos(E3u)
..35. A1gA1gA1gA1g...1. A2gA2gA2gA2g...35. B1gB1gB1gB1g...5. B2gB2gB2gB2g...120. E1gE1gE1gE1g...357. E2gE2gE2gE2g...231. E3gE3gE3gE3g...5. A1uA1uA1uA1u...35. A2uA2uA2uA2u...5. B1uB1uB1uB1u.
..35. B2uB2uB2uB2u...231. E1uE1uE1uE1u...357. E2uE2uE2uE2u...231. E3uE3uE3uE3u.
Subtotal: 1.683 / 14 / 14
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A1g) ≤ i ≤ j ≤ pos(E3u)
..210. E1gE1gE1gE3g...336. E1uE1uE1uE3u...280. E1gE3gE3gE3g...336. E1uE3uE3uE3u.
Subtotal: 1.162 / 4 / 182
Irrep combinations (i,i,j,j) with indices: pos(A1g) ≤ i ≤ j ≤ pos(E3u)
..10. A1gA1gA2gA2g...100. A1gA1gB1gB1g...30. A1gA1gB2gB2g...150. A1gA1gE1gE1g...210. A1gA1gE2gE2g...210. A1gA1gE3gE3g...30. A1gA1gA1uA1u...100. A1gA1gA2uA2u...30. A1gA1gB1uB1u...100. A1gA1gB2uB2u.
..210. A1gA1gE1uE1u...210. A1gA1gE2uE2u...210. A1gA1gE3uE3u...10. A2gA2gB1gB1g...3. A2gA2gB2gB2g...15. A2gA2gE1gE1g...21. A2gA2gE2gE2g...21. A2gA2gE3gE3g...3. A2gA2gA1uA1u...10. A2gA2gA2uA2u.
..3. A2gA2gB1uB1u...10. A2gA2gB2uB2u...21. A2gA2gE1uE1u...21. A2gA2gE2uE2u...21. A2gA2gE3uE3u...30. B1gB1gB2gB2g...150. B1gB1gE1gE1g...210. B1gB1gE2gE2g...210. B1gB1gE3gE3g...30. B1gB1gA1uA1u.
..100. B1gB1gA2uA2u...30. B1gB1gB1uB1u...100. B1gB1gB2uB2u...210. B1gB1gE1uE1u...210. B1gB1gE2uE2u...210. B1gB1gE3uE3u...45. B2gB2gE1gE1g...63. B2gB2gE2gE2g...63. B2gB2gE3gE3g...9. B2gB2gA1uA1u.
..30. B2gB2gA2uA2u...9. B2gB2gB1uB1u...30. B2gB2gB2uB2u...63. B2gB2gE1uE1u...63. B2gB2gE2uE2u...63. B2gB2gE3uE3u...465. E1gE1gE2gE2g...780. E1gE1gE3gE3g...45. E1gE1gA1uA1u...150. E1gE1gA2uA2u.
..45. E1gE1gB1uB1u...150. E1gE1gB2uB2u...780. E1gE1gE1uE1u...465. E1gE1gE2uE2u...780. E1gE1gE3uE3u...666. E2gE2gE3gE3g...63. E2gE2gA1uA1u...210. E2gE2gA2uA2u...63. E2gE2gB1uB1u...210. E2gE2gB2uB2u.
..666. E2gE2gE1uE1u...1.548. E2gE2gE2uE2u...666. E2gE2gE3uE3u...63. E3gE3gA1uA1u...210. E3gE3gA2uA2u...63. E3gE3gB1uB1u...210. E3gE3gB2uB2u...1.107. E3gE3gE1uE1u...666. E3gE3gE2uE2u...1.107. E3gE3gE3uE3u.
..30. A1uA1uA2uA2u...9. A1uA1uB1uB1u...30. A1uA1uB2uB2u...63. A1uA1uE1uE1u...63. A1uA1uE2uE2u...63. A1uA1uE3uE3u...30. A2uA2uB1uB1u...100. A2uA2uB2uB2u...210. A2uA2uE1uE1u...210. A2uA2uE2uE2u.
..210. A2uA2uE3uE3u...30. B1uB1uB2uB2u...63. B1uB1uE1uE1u...63. B1uB1uE2uE2u...63. B1uB1uE3uE3u...210. B2uB2uE1uE1u...210. B2uB2uE2uE2u...210. B2uB2uE3uE3u...666. E1uE1uE2uE2u...1.107. E1uE1uE3uE3u.
..666. E2uE2uE3uE3u.
Subtotal: 19.171 / 91 / 91
Irrep combinations (i,i,j,k) (i,j,j,k) (i,j,k,k) with indices: pos(A1g) ≤ i ≤ j ≤ k ≤ pos(E3u)
..80. E1gE1gA1uA2u...180. E1gE1gA1uE2u...360. E1gE1gA2uE2u...80. E1gE1gB1uB2u...180. E1gE1gB1uE2u...360. E1gE1gB2uE2u...540. E1gE1gE1uE3u...120. E2gE2gA1uA2u...84. E2gE2gA1uB1u...168. E2gE2gA1uB2u.
..168. E2gE2gA2uB1u...336. E2gE2gA2uB2u...120. E2gE2gB1uB2u...1.512. E2gE2gE1uE3u...120. E3gE3gA1uA2u...252. E3gE3gA1uE2u...504. E3gE3gA2uE2u...120. E3gE3gB1uB2u...252. E3gE3gB1uE2u...504. E3gE3gB2uE2u.
..756. E3gE3gE1uE3u...360. A1gE1gE1gE2g...90. A2gE1gE1gE2g...360. B1gE1gE1gE2g...180. B2gE1gE1gE2g...1.260. E1gE2gE2gE3g...252. A1uE1uE1uE2u...504. A2uE1uE1uE2u...252. B1uE1uE1uE2u...504. B2uE1uE1uE2u.
..1.512. E1uE2uE2uE3u...40. A1gA2gE1gE1g...60. A1gA2gE2gE2g...60. A1gA2gE3gE3g...60. A1gA2gE1uE1u...60. A1gA2gE2uE2u...60. A1gA2gE3uE3u...336. A1gB1gE2gE2g...336. A1gB1gE2uE2u...168. A1gB2gE2gE2g.
..168. A1gB2gE2uE2u...504. A1gE2gE3gE3g...504. A1gE2gE1uE1u...504. A1gE2gE3uE3u...84. A2gB1gE2gE2g...84. A2gB1gE2uE2u...42. A2gB2gE2gE2g...42. A2gB2gE2uE2u...126. A2gE2gE3gE3g...126. A2gE2gE1uE1u.
..126. A2gE2gE3uE3u...80. B1gB2gE1gE1g...120. B1gB2gE2gE2g...120. B1gB2gE3gE3g...120. B1gB2gE1uE1u...120. B1gB2gE2uE2u...120. B1gB2gE3uE3u...504. B1gE2gE3gE3g...504. B1gE2gE1uE1u...504. B1gE2gE3uE3u.
..252. B2gE2gE3gE3g...252. B2gE2gE1uE1u...252. B2gE2gE3uE3u...630. E1gE3gE1uE1u...1.260. E1gE3gE2uE2u...630. E1gE3gE3uE3u...120. A1uA2uE1uE1u...120. A1uA2uE2uE2u...120. A1uA2uE3uE3u...84. A1uB1uE2uE2u.
..168. A1uB2uE2uE2u...252. A1uE2uE3uE3u...168. A2uB1uE2uE2u...336. A2uB2uE2uE2u...504. A2uE2uE3uE3u...120. B1uB2uE1uE1u...120. B1uB2uE2uE2u...120. B1uB2uE3uE3u...252. B1uE2uE3uE3u...504. B2uE2uE3uE3u.
Subtotal: 24.016 / 80 / 1.092
Irrep combinations (i,j,k,l) with indices: pos(A1g) ≤ i ≤ j ≤ k ≤ l ≤ pos(E3u)
..32. A1gA2gB1gB2g...32. A1gA2gA1uA2u...32. A1gA2gB1uB2u...480. A1gB1gE1gE3g...64. A1gB1gA1uB1u...256. A1gB1gA2uB2u...576. A1gB1gE1uE3u...240. A1gB2gE1gE3g...64. A1gB2gA1uB2u...64. A1gB2gA2uB1u.
..288. A1gB2gE1uE3u...720. A1gE1gE2gE3g...240. A1gE1gA1uE1u...480. A1gE1gA2uE1u...240. A1gE1gB1uE3u...480. A1gE1gB2uE3u...720. A1gE1gE1uE2u...720. A1gE1gE2uE3u...288. A1gE2gA1uE2u...576. A1gE2gA2uE2u.
..288. A1gE2gB1uE2u...576. A1gE2gB2uE2u...864. A1gE2gE1uE3u...288. A1gE3gA1uE3u...576. A1gE3gA2uE3u...288. A1gE3gB1uE1u...576. A1gE3gB2uE1u...864. A1gE3gE1uE2u...864. A1gE3gE2uE3u...120. A2gB1gE1gE3g.
..32. A2gB1gA1uB2u...32. A2gB1gA2uB1u...144. A2gB1gE1uE3u...60. A2gB2gE1gE3g...8. A2gB2gA1uB1u...32. A2gB2gA2uB2u...72. A2gB2gE1uE3u...180. A2gE1gE2gE3g...60. A2gE1gA1uE1u...120. A2gE1gA2uE1u.
..60. A2gE1gB1uE3u...120. A2gE1gB2uE3u...180. A2gE1gE1uE2u...180. A2gE1gE2uE3u...72. A2gE2gA1uE2u...144. A2gE2gA2uE2u...72. A2gE2gB1uE2u...144. A2gE2gB2uE2u...216. A2gE2gE1uE3u...72. A2gE3gA1uE3u.
..144. A2gE3gA2uE3u...72. A2gE3gB1uE1u...144. A2gE3gB2uE1u...216. A2gE3gE1uE2u...216. A2gE3gE2uE3u...64. B1gB2gA1uA2u...64. B1gB2gB1uB2u...720. B1gE1gE2gE3g...240. B1gE1gA1uE3u...480. B1gE1gA2uE3u.
..240. B1gE1gB1uE1u...480. B1gE1gB2uE1u...720. B1gE1gE1uE2u...720. B1gE1gE2uE3u...288. B1gE2gA1uE2u...576. B1gE2gA2uE2u...288. B1gE2gB1uE2u...576. B1gE2gB2uE2u...864. B1gE2gE1uE3u...288. B1gE3gA1uE1u.
..576. B1gE3gA2uE1u...288. B1gE3gB1uE3u...576. B1gE3gB2uE3u...864. B1gE3gE1uE2u...864. B1gE3gE2uE3u...360. B2gE1gE2gE3g...120. B2gE1gA1uE3u...240. B2gE1gA2uE3u...120. B2gE1gB1uE1u...240. B2gE1gB2uE1u.
..360. B2gE1gE1uE2u...360. B2gE1gE2uE3u...144. B2gE2gA1uE2u...288. B2gE2gA2uE2u...144. B2gE2gB1uE2u...288. B2gE2gB2uE2u...432. B2gE2gE1uE3u...144. B2gE3gA1uE1u...288. B2gE3gA2uE1u...144. B2gE3gB1uE3u.
..288. B2gE3gB2uE3u...432. B2gE3gE1uE2u...432. B2gE3gE2uE3u...360. E1gE2gA1uE1u...360. E1gE2gA1uE3u...720. E1gE2gA2uE1u...720. E1gE2gA2uE3u...360. E1gE2gB1uE1u...360. E1gE2gB1uE3u...720. E1gE2gB2uE1u.
..720. E1gE2gB2uE3u...2.160. E1gE2gE1uE2u...2.160. E1gE2gE2uE3u...120. E1gE3gA1uB1u...240. E1gE3gA1uB2u...360. E1gE3gA1uE2u...240. E1gE3gA2uB1u...480. E1gE3gA2uB2u...720. E1gE3gA2uE2u...360. E1gE3gB1uE2u.
..720. E1gE3gB2uE2u...3.240. E1gE3gE1uE3u...432. E2gE3gA1uE1u...432. E2gE3gA1uE3u...864. E2gE3gA2uE1u...864. E2gE3gA2uE3u...432. E2gE3gB1uE1u...432. E2gE3gB1uE3u...864. E2gE3gB2uE1u...864. E2gE3gB2uE3u.
..2.592. E2gE3gE1uE2u...2.592. E2gE3gE2uE3u...64. A1uA2uB1uB2u...144. A1uB1uE1uE3u...288. A1uB2uE1uE3u...432. A1uE1uE2uE3u...288. A2uB1uE1uE3u...576. A2uB2uE1uE3u...864. A2uE1uE2uE3u...432. B1uE1uE2uE3u.
..864. B2uE1uE2uE3u.
Subtotal: 58.728 / 131 / 1.001
Total: 104.760 / 320 / 2.380


Calculate contributions to

A1g A2g B1g B2g E1g E2g E3g A1u A2u B1u B2u E1u E2u E3u
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Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement